Aspects of Astronomy

CONTENTS - 1. Essential Astronomy

Our Solar System
Asteroids
Comets
The Kuiper Belt and the Oort Cloud
What are the Stars?
Celestial Coordinate Systems
Galaxies
Telescopes
Choosing a Telescope
What time is it?

CONTENTS - 2. Specialized Topics

Cosmology
Dark Matter
Eclipses
The Equation of Time
Gamma-Ray Astronomy
The History of Astronomy
Meridian Astronomy
Meteors and Meteorites
Meteor Showers
Moon Phases
What's New on the Moon?
Aurora Borealis: The Northern Lights
Orbits and Gravitation
Photometry
Pulsars
Getting Started in Radio Astronomy
Relativity
The Sun
Sundials
Terrestrial Impact Craters
The Tides

Our Solar System

From our small world we have gazed upon the cosmic ocean for untold thousands of years. Ancient astronomers observed points of light that appeared to move among the stars. They called these objects planets, meaning wanderers, and named them after Roman deities Jupiter, king of the gods; Mars, the god of war; Mercury, messenger of the gods; Venus, the god of love and beauty, and Saturn, father of Jupiter and god of agriculture. The stargazers also observed comets with sparkling tails, and meteors or shooting stars apparently falling from the sky. Science flourished during the European Renaissance. Fundamental physical laws governing planetary motion were discovered, and the orbits of the planets round the Sun were calculated. In the 17th century, astronomers pointed a new device called the telescope at the heavens and made startling discoveries. But the years since 1959 have amounted to a golden age of solar system exploration. Advancements in rocketry after World War II enabled our machines to break the grip of Earth's gravity and travel to the Moon and to other planets.

The United States has sent automated spacecraft, then human-crewed expeditions, to explore the Moon. Our automated machines have orbited and landed on Venus and Mars; explored the Sun's environment; observed comets, and made close-range surveys while flying past Mercury, Jupiter, Saturn, Uranus and Neptune. These travellers brought a quantum leap in our knowledge and understanding of the solar system. Through the electronic sight and other senses of our automated spacecraft, colour and complexion have been given to worlds that for centuries appeared to Earth-bound eyes as fuzzy disks or indistinct points of light. And dozens of previously unknown objects have been discovered. Future historians will likely view these pioneering flights through the solar system as some of the most remarkable achievements of the 20th century.

Automated Spacecraft

The National Aeronautics and Space Administration's (NASA's) automated spacecraft for solar system exploration come in many shapes and sizes. While they are designed to fulfil separate and specific mission objectives, the craft share much in common.

Each spacecraft consists of various scientific instruments selected for a particular mission, supported by basic subsystems for electrical power, trajectory and orientation control, as well as for processing data and communicating with Earth. Electrical power is required to operate the spacecraft instruments and systems. NASA uses both solar energy from arrays of photo-voltaic cells and small nuclear generators to power its solar system missions. Rechargeable batteries are employed for backup and supplemental power. Imagine that a spacecraft has successfully journeyed millions of miles through space to fly but one time near a planet, only to have its cameras and other sensing instruments pointed the wrong way as it speeds past the target

To help prevent such a mishap, a subsystem of small thrusters is used to control spacecraft. The thrusters are linked with devices that maintain a constant gaze at selected stars. Just as Earth's early seafarers used the stars to navigate the oceans, spacecraft use stars to maintain their bearings in space. With the sub-system locked onto fixed points of reference, flight controllers can keep a spacecraft's scientific instruments pointed at the target body and the craft's communications antennas pointed toward Earth. The thrusters can also be used to fine-tune the flight path and speed of the spacecraft to ensure that a target body is encountered at the planned distance and on the proper trajectory.

Between 1959 and 1971, NASA spacecraft were dispatched to study the Moon and the solar environment; they also scanned the inner planets other than Earth -- Mercury, Venus and Mars. These three worlds, and our own, are known as the terrestrial planets because they share a solid-rock composition. For the early planetary reconnaissance missions, NASA employed a highly successful series of spacecraft called the Mariners. Their flights helped shape the planning of later missions. Between 1962 and 1975, seven Mariner missions conducted the first surveys of our planetary neighbours in space. All of the Mariners used solar panels as their primary power source. The first and the final versions of the spacecraft had two wings covered with photo-voltaic cells.

Other Mariners were equipped with four solar panels extending from their octagonal bodies. Although the Mariners ranged from the Mariner 2 Venus spacecraft, weighing in at 203 kilograms (447 pounds), to the Mariner 9 Mars Orbiter, weighing in at 974 kilograms (2,147 pounds), their basic design remained quite similar through-out the program. The Mariner 5 Venus spacecraft, for example, had originally been a backup for the Mariner 4 Mars flyby. The Mariner 10 spacecraft sent to Venus and Mercury used components left over from the Mariner 9 Mars Orbiter program.

In 1972, NASA launched Pioneer 10, a Jupiter spacecraft. Interest was shifting to four of the outer planets -- Jupiter, Saturn, Uranus and Neptune -- giant balls of dense gas quite different from the terrestrial worlds we had already surveyed. Four NASA spacecraft in all -- two Pioneers and two Voyagers -- were sent in the 1970s to tour the outer regions of our solar system. Because of the distances involved, these travellers took anywhere from 20 months to 12 years to reach their destinations. Barring faster spacecraft, they will eventually become the first human artefacts to journey to distant stars. Because the Sun's light becomes so faint in the outer solar system, these travellers do not use solar power but instead operate on electricity generated by heat from the decay of radioisotopes.

NASA also developed highly specialised spacecraft to revisit our neighbours Mars and Venus in the middle and late 1970s. Twin Viking Landers were equipped to serve as seismic and weather stations and as biology laboratories. Two advanced orbiters -- descendants of the Mariner craft -- carried the Viking Landers from Earth and then studied Martian features from above. Two drum-shaped Pioneer spacecraft visited Venus in 1978. The Pioneer Venus Orbiter was equipped with a radar instrument that allowed it to "see" through the planet's dense cloud cover to study surface features. The Pioneer Venus Multiprobe carried four probes that were dropped through the clouds. The probes and the main body -- all of which contained scientific instruments -- radioed information about the planet's atmosphere during their descent toward the surface. A new generation of automated spacecraft -- including Magellan, Galileo, Ulysses, and Cassini -- is being developed and sent out into the solar system to make detailed examinations that will increase our understanding of our neighbour-hood and our own planet.

THE SUN

A discussion of the objects in the solar system must start with the Sun. The Sun dwarfs the other bodies, representing approximately 99.86 percent of all the mass in the solar system; all of the planets, moons, asteroids, comets, dust and gas add up to only about 0.14 percent. This 0.14 percent represents the material left over from the Sun's formation. One hundred and nine Earth's would be required to fit across the Sun's disk, and its interior could hold over 1.3 million Earth's. As a star, the Sun generates energy through the process of fusion. The temperature at the Sun's core is 15 million degrees Celsius (27 million degrees Fahrenheit), and the pressure there is 340 billion times Earth's air pressure at sea level. The Sun's surface temperature of 5,500 degrees Celsius (10,000 degrees Fahrenheit) seems almost chilly compared to its core-temperature. At the solar core, hydrogen can fuse into helium, producing energy. The Sun also produces a strong magnetic field and streams of charged particles, both extending far beyond the planets. The Sun appears to have been active for 4.6 billion years and has enough fuel to go on for another five billion years or so.

At the end of its life, the Sun will start to fuse helium into heavier elements and begin to swell up, ultimately growing so large that it will swallow Earth. After a billion years as a "red giant," it will suddenly collapse into a "white dwarf"-- the final end product of a star like ours. It may take a trillion years to cool off completely.

Many spacecraft have explored the Sun's environment, but none have got any closer to its surface than approximately two thirds of the distance from Earth to the Sun. Pioneers 5-11, the Pioneer Venus Orbiter, Voyagers 1 and 2 and other spacecraft have all sampled the solar environment. The Ulysses spacecraft, launched on October 6, 1990, is a joint solar mission of NASA and the European Space Agency. On February 8, 1992, Ulysses flew close to Jupiter and used Jupiter's gravity to hurl it down below the plane of the planets. Although it will still be at great distance from the Sun, Ulysses will fly over the Sun's polar regions during 1994 and 1995 and will perform a wide range of studies using nine onboard scientific instruments. We are fortunate that the Sun is exactly the way it is. If it were different in almost any way, life would almost certainly never have developed on Earth.

MERCURY

Obtaining the first close-up views of Mercury was the primary objective of the Mariner 10 spacecraft, launched on November 3, 1973, from Kennedy Space Center in Florida. After a journey of nearly five months, which included a flyby of Venus, the spacecraft passed within 703 kilometres (437 miles) of the solar system's innermost planet on March 29, 1974. Until Mariner 10, little was known about Mercury. Even the best telescopic views from Earth showed Mercury as an indistinct object lacking any surface detail. The planet is so close to the Sun that it is usually lost in solar glare. When the planet is visible on Earth's horizon just after sunset or before dawn, it is obscured by the haze and dust in our atmosphere. Only radar telescopes gave any hint of Mercury's surface conditions prior to the voyage of Mariner 10. The photographs Mariner 10 radioed back to Earth revealed an ancient, heavily cratered surface, closely resembling our own Moon. The pictures also showed huge cliffs criss-crossing the planet. These apparently were created when Mercury's interior cooled and shrank, buckling the planet's crust. The cliffs are as high as 3 kilometres (2 miles) and as long as 500 kilometres (310 miles). Instruments on Mariner 10 discovered that Mercury has a weak magnetic field and a trace of atmosphere -- a trillionth the density of Earth's atmosphere and composed chiefly of argon, neon and helium. When the planet's orbit takes it closest to the Sun, surface temperatures range from 467 degrees Celsius (872 degrees Fahrenheit) on Mercury's sunlit side to -183 degrees Celsius (-298 degrees Fahrenheit) on the dark side. This range in surface temperature -- 650 degrees Celsius (1,170 degrees Fahrenheit) -- is the largest for a single body in the solar system. Mercury literally bakes and freezes at the same time.

Days and nights are long on Mercury. The combination of a slow rotation relative to the stars (59 Earth days) and a rapid revolution around the Sun (88 Earth days) means that one Mercury solar day takes 176 Earth days or two Mercury years -- the time it takes the inner-most planet to complete two orbits around the Sun Mercury appears to have a crust of light silicate rock like that of Earth. Scientists believe Mercury has a heavy iron-rich core making up slightly less than half of its volume. That would make Mercury's core larger, proportionally, than the Moon's core or those of any of the planets. After the initial Mercury encounter, Mariner 10 made two additional flybys -- on September 21, 1974, and March 16, 1975 -- before control gas used to orient the spacecraft was exhausted and the mission was concluded. Each flyby took place at the same local Mercury time when the identical half of the planet was illuminated; as a result, we still have not seen one-half of the planet's surface.

VENUS

Veiled by dense cloud cover, Venus -- our nearest planetary neighbour -- was the first planet to be explored. The Mariner 2 spacecraft, launched on August 27, 1962, was the first of more than a dozen successful American and Soviet missions to study the mysterious planet. As spacecraft flew by or orbited Venus, plunged into the atmosphere or gently landed on Venus' surface, romantic myths and speculations about our neighbour were laid to rest. On December 14, 1962, Mariner 2 passed within 34,839 kilometres (21,648 miles) of Venus and became the first spacecraft to scan another planet; onboard instruments measured Venus for 42 minutes. Mariner 5, launched in June 1967, flew much closer to the planet. Passing within 4,094 kilo-metres (2,544 miles) of Venus on the second American flyby, Mariner 5's instruments measured the planet's magnetic field, ionosphere, radiation belts and temperatures. On its way to Mercury, Mariner 10 flew by Venus and transmitted ultraviolet pictures to Earth showing cloud circulation patterns in the Venusian atmosphere.

In the spring and summer of 1978, two spacecraft were launched to further unravel the mysteries of Venus. On December 4 of the same year, the Pioneer Venus Orbiter became the first spacecraft placed in orbit around the planet. Five days later, the five separate components making up the second spacecraft -- the Pioneer Venus Multiprobe entered the Venusian atmosphere at different locations above the planet. The four small, independent probes and the main body radioed atmospheric data back to Earth during their descent toward the surface. Although designed to examine the atmosphere, one of the probes survived its impact with the surface and continued to transmit data for another hour. Venus resembles Earth in size, physical composition and density more closely than any other known planet. However, spacecraft have discovered significant differences as well. For example, Venus' rotation (west to east) is retrograde (backward) compared to the east-to-west spin of Earth and most of the other planets.

Approximately 96.5 percent of Venus' atmosphere (95 times as dense as Earth's) is carbon dioxide. The principal constituent of Earth's atmosphere is nitrogen. Venus' atmosphere acts like a greenhouse, permitting solar radiation to reach the surface but trapping the heat that would ordinarily be radiated back into space. As a result, the planet's average surface temperature is 482 degrees Celsius (900 degrees Fahrenheit), hot enough to melt lead. A radio altimeter on the Pioneer Venus Orbiter provided the first means of seeing through the planet's dense cloud cover and deter-mining surface features over almost the entire planet. NASA's Magellan spacecraft, launched on May 5, 1989, has been in orbit around Venus since August 10, 1990. The spacecraft used radar-mapping techniques to provide high-resolution images of 98 percent of the surface.

Magellan's radar revealed a landscape dominated by volcanic features, faults and impact craters. Huge areas of the surface show evidence of multiple periods of lava flooding with flows lying on top of previous ones. An elevated region named Ishtar Terra is a lava-filled basin as large as the United States. At one end of this plateau sits Maxwell Montes, a mountain the size of Mount Everest. Scarring the mountain's flank is a 100-kilometre (62-miles) wide, 2.5-kilometre (1.5-miles) deep impact crater named Cleopatra. (Almost all features on Venus are named for women; Maxwell Montes, Alpha Regio and Beta Regioare the exceptions.) Craters survive on Venus for perhaps 400 million years because there is no water and very little wind erosion.

Extensive fault-line networks cover the planet, probably the result of the same crustal flexing that produces plate tectonics on Earth. But on Venus the surface temperature is sufficient to weaken the rock, which cracks just about everywhere, preventing the formation of major plates and large earth quake faults like the San Andreas Fault in California. Venus' predominant weather pattern is a high-altitude, high-speed circulation of clouds that contain sulphuric acid. At speeds reaching as high as 360 kilometres (225 miles) per hour, the clouds circle the planet in only four Earth days. The circulation is in the same direction -- west to east -- as Venus' slow rotation of 243 Earth days, whereas Earth's winds blow in both directions -- west to east and east to west -- in six alternating bands. Venus' atmosphere serves as a simplified laboratory for the study of our weather.

EARTH

As viewed from space, our world's distinguishing characteristics are its blue waters, brown and green land masses and white clouds. We are enveloped by an ocean of air consisting of 78 percent nitrogen, 21 percent oxygen and 1 percent other constituents. The only planet in the solar system known to harbour life, Earth orbits the Sun at an average distance of 150 million kilometres (93 million miles). Earth is the third planet from the Sun and the fifth largest in the solar system, with a diameter just a few hundred kilometres larger than that of Venus. Our planet's rapid spin and molten nickel-iron core give rise to an extensive magnetic field, which, along with the atmosphere, shields us from nearly all of the harmful radiation coming from the Sun and other stars. Earth's atmosphere protects us from meteors as well, most of which burn up before they can strike the surface. Active geological processes have left no evidence of the pelting Earth almost certainly received soon after it formed - about 4.6 billion years ago. Along with the other newly formed planets, it was showered by space debris in the early days of the solar system.

From our journeys into space, we have learned much about our home planet. The first American satellite -- Explorer 1 -- was launched from Cape Canaveral in Florida on January 31, 1958, and discovered an intense radiation zone, now called the Van Allen radiation belts, surrounding Earth. Since then, other research satellites have revealed that our planet's magnetic field is distorted into a teardrop shape by the solar wind -- the stream if charged particles continuously ejected from the Sun. We've learned that the magnetic field does not fade off into space but has definite boundaries. And we now know that our wispy upper atmosphere, once believed calm and uneventful, seethes with activity -- swelling by day and contracting by night. Affected by changes in solar activity, the upper atmosphere contributes to weather and climate on Earth.

Besides affecting Earth's weather, solar activity gives rise to a dramatic visual phenomenon in our atmosphere. When charged particles from the solar wind become trapped in Earth's magnetic field, they collide with air molecules above our planet's magnetic poles. These air molecules then begin to glow and are known as the auroras or the northern and southern lights. Satellites about 35,789 kilometres (22,238 miles) out in space play a major role in daily local weather forecasting. These watchful electronic eyes warn us of dangerous storms. Continuous global monitoring provides a vast amount of useful data and contributes to a better understanding of Earth's complex weather systems. From their unique vantage points, satellites can survey Earth's oceans, land use and resources, and monitor the planet's health. These eyes in space have saved countless lives, provided tremendous conveniences and shown us that we may be altering our planet in dangerous ways.

THE MOON

The Moon is Earth's single natural satellite. The first human foot-steps on an alien world were made by American astronauts on the dusty surface of our airless, lifeless companion. In preparation for the human-crewed Apollo expeditions, NASA dispatched the automated Ranger, Surveyor and Lunar Orbiter spacecraft to study the Moon between 1964 and 1968. NASA's Apollo program left a large legacy of lunar materials and data. Six two-astronaut crews landed on and explored the lunar surface between 1969 and 1972, carrying back a collection of rocks and soil weighing a total of 382 kilograms (842 pounds) and consisting of more than 2,000 separate samples. From this material and other studies, scientists have constructed a history of the Moon that includes its infancy. Rocks collected from the lunar highlands date to about 4.0-4.3 billion years old. The first few million years of the Moon's existence were so violent that few traces of this period remain. As a molten outer layer gradually cooled and solidified into different kinds of rock, the Moon was bombarded by huge asteroids and smaller objects, and their collisions with the Moon created basins hundreds of kilometres across.

This catastrophic bombardment tapered off approximately four billion years ago, leaving the lunar highlands covered with huge, overlapping craters and a deep layer of shattered and broken rock. Heat produced by the decay of radioactive elements began to melt the interior of the Moon at depths of about 200 kilometres (125 miles) below the surface. Then, for the next 700 million years -- from about 3.8 to 3.1 billion years ago -- lava rose from inside the Moon. The lava gradually spread out over the surface, flooding the large impact basins to form the dark areas that Galileo Galilei, an astronomer of the Italian Renaissance, called maria, meaning seas. As far as we can tell, there has been no significant volcanic activity on the Moon for more than three billion years. Since then, the lunar surface has been altered only by micro-meteorites, by the atomic particles from the Sun and stars, by the rare impacts of large meteorites and by spacecraft and astronauts. If our astronauts had landed on the Moon a billion years ago, they would have seen a landscape very similar to the one today. Thousands of years from now, the footsteps left by the Apollo crews will remain sharp and clear.

The origin of the Moon is still a mystery. Four theories attempt an explanation: the Moon formed near Earth as a separate body; it was torn from Earth; it formed somewhere else and was captured by our planet's gravity, or it was the result of a collision between Earth and an asteroid about the size of Mars. The last theory has some good support but is far from certain.

MARS

Of all the planets, Mars has long been considered the solar system's prime candidate for harbouring extraterrestrial life. Astronomers studying the red planet through telescopes saw what appeared to be straight lines criss-crossing its surface. These observations -- later determined to be optical illusions -- led to the popular notion that intelligent beings had constructed a system of irrigation canals on the planet. In 1938, when Orson Welles broadcast a radio drama based on the science fiction classic War of the Worlds by H.G. Wells, enough people believed in the tale of invading Martians to cause a near panic. Another reason for scientists to expect life on Mars had to do with the apparent seasonal colour changes on the planet's surface. This phenomenon led to speculation that conditions might support a bloom of Martian vegetation during the warmer months and cause plant life to become dormant during colder periods. So far, six American missions to Mars have been carried out. Four Mariner spacecraft -- three flying by the planet and one placed into Martian orbit -- surveyed the planet extensively before the Viking Orbiters and Landers arrived.

Mariner 4, launched in late 1964, flew past Mars on July 14, 1965, coming within 9,846 kilometres (6,118 miles) of the surface. Transmitting to Earth 22 close-up pictures of the planet, the spacecraft found many craters and naturally occurring channels but no evidence of artificial canals or flowing water. Mariners 6 and 7 followed with their flybys during the summer of 1969 and returned 201 pictures. Mariners 4, 6 and 7 showed a diversity of surface conditions as well as a thin, cold, dry atmosphere of carbon dioxide. On May 30, 1971, the Mariner 9 Orbiter was launched on a mission to make a year-long study of the Martian surface. The spacecraft arrived five and a half months after lift-off, only to find Mars in the midst of a planet-wide dust storm that made surface photography impossible for several weeks. But after the storm cleared, Mariner 9 began returning the first of 7,329 pictures; these revealed previously unknown Martian features, including evidence that large amounts of water once flowed across the surface, etching river valleys and flood plains.

In August and September 1975, the Viking 1 and 2 spacecraft -- each consisting of an orbiter and a lander -- lifted off from Kennedy Space Center. The mission was designed to answer several questions about the red planet, including, Is there life there? Nobody expected the spacecraft to spot Martian cities, but it was hoped that the biology experiments on the Viking Landers would at least find evidence of primitive life -- past or present. Viking Lander 1 became the first spacecraft to successfully touch down on another planet when it landed on July 20, 1976, while the United States was celebrating its Bicentennial. Photos sent back from the Chryse Planitia ("Plains of Gold") showed a bleak, rusty-red landscape. Panoramic images returned by the lander revealed a rolling plain, littered with rocks and marked by rippled sand dunes. Fine red dust from the Martian soil gives the sky a salmon hue. When Viking Lander 2 touched down on Utopia Planitia on September 3, 1976, it viewed a more rolling landscape than the one seen by its predecessor -- one without visible dunes.

The results sent back by the laboratory on each Viking Lander were inconclusive. Small samples of the red Martian soil were tested in three different experiments designed to detect biological processes. While some of the test results seemed to indicate biological activity, later analysis confirmed that this activity was inorganic in nature and related to the planet's soil chemistry. Is there life on Mars? No one knows for sure, but the Viking mission found no evidence that organic molecules exist there. The Viking Landers became weather stations, recording wind velocity and direction as well as atmospheric temperature and pressure. Few weather changes were observed. The highest temperature recorded by either craft was - 14 degrees Celsius (7 degrees Fahrenheit) at the Viking Lander 1 site in midsummer. The lowest temperature, -120 degrees Celsius (-184 degrees Fahrenheit), was recorded at the more northerly Viking Lander 2 site during winter. Near-hurricane wind speeds were measured at the two Martian weather stations during global dust storms, but because the atmosphere is so thin, wind force is minimal. Viking Lander 2 photographed light patches of frost -- probably water-ice.

The Martian atmosphere, like that of Venus, is primarily carbon dioxide. Nitrogen and oxygen are present only in small percentages. Martian air contains only about 1/1,000 as much water as our air, but even this small amount can condense out, forming clouds that ride high in the atmosphere or swirl around the slopes of towering volcanoes. Local patches of early morning fog can form in valleys. There is evidence that in the past a denser Martian atmosphere may have allowed water to flow on the planet. Physical features closely resembling shorelines, gorges, river-beds and islands suggest that great rivers once marked the planet. Mars has two moons, Phobos and Deimos. They are small and irregularly shaped and possess ancient, cratered surfaces. It is possible the moons were originally asteroids that ventured too close to Mars and were captured by its gravity.

The Viking Orbiters and Landers exceeded by large margins their design lifetimes of 120 and 90 days, respectively. The first to fail was Viking Orbiter 2, which stopped operating on July 24, 1978, when a leak depleted its altitude-control gas. Viking Lander 2 operated until April 12, 1980, when it was shut down because of battery degeneration. Viking orbiter 1 quit on August 7, 1980, when the last of its attitude-control gas was used up. Viking Lander1 ceased functioning on November 13, 1983. Despite the inconclusive results of the Viking biology experiments, we know more about Mars than any other planet except Earth.

THE ASTEROIDS

The solar system has a large number of rocky and metallic objects that are in orbit around the Sun but are too small to be considered full-fledged planets. These objects are known as asteroids or minor planets. Most, but not all, are found in a band or belt between the orbits of Mars and Jupiter. Some have orbits that cross Earth's path, and there is evidence that Earth has been hit by asteroids in the past. One of the least eroded, best preserved examples is the Barringer Meteor Crater near Winslow, Arizona. Asteroids are material left over from the formation of the solar system. One theory suggests that they are the remains of a planet that was destroyed in a massive collision long ago. More likely, asteroids are material that never coalesced into a planet. In fact, if the estimated total mass of all asteroids was gathered into a single object, the object would be less than 1,500 kilometres (932 miles) across -- less than half the diameter of our Moon. Thousands of asteroids have been identified from Earth. It is estimated that 100,000 are bright enough to eventually be photographed through Earth-based telescopes.

Much of our understanding about asteroids comes from examining pieces of space debris that fall to the surface of Earth. Asteroids that are on a collision course with Earth are called meteoroids. When a meteoroid strikes our atmosphere at high velocity, friction causes this chunk of space matter to incinerate in a streak of light known as a meteor. If the meteoroid does not burn up completely, what's left strikes Earth's surface and is called a meteorite. One of the best places to look for meteorites is the ice cap of Antarctica. Of all the meteorites examined, 92.8 percent are composed of silicate (stone), and 5.7 percent are composed of iron and nickel; the rest are a mixture of the three materials. Stony meteorites are the hardest to identify since they look very much like terrestrial rocks. Since asteroids are material from the very early solar system, scientists are interested in their composition. Spacecraft that have flown through the asteroid belt have found that the belt is really quite empty and that asteroids are separated by very large distances. Current and future missions will fly by selected asteroids for closer examination. The Galileo spacecraft, launched by NASA in October 1989, investigated the main-belt asteroid Gaspra on October 29, 1991 and will encounter Ida on August 28, 1993 on its way to Jupiter. One day, space factories will mine the asteroids for raw materials.

JUPITER

Beyond Mars and the asteroid belt, in the outer regions of our solar system, lie the giant planets of Jupiter, Saturn, Uranus and Neptune. In 1972, NASA dispatched the first of four spacecraft slated to conduct the initial surveys of these colossal worlds of gas and their moons of ice and rock. Jupiter was the first port of call. Pioneer 10, which lifted off from Kennedy Space Center in March 1972, was the first spacecraft to penetrate the asteroid belt and travel to the outer regions of the solar system. In December 1973, it returned the first close-up images of Jupiter, flying within 132,252 kilometres (82,178 miles) of the planet's banded cloud tops. Pioneer 11 followed a year later. Voyagers 1 and 2 were launched in the summer of 1977 and returned spectacular photographs of Jupiter and its family of satellites during flybys in 1979. These travellers found Jupiter to be a whirling ball of liquid hydrogen and helium, topped with a colourful atmosphere composed mostly of gaseous hydrogen and helium. Ammonia ice crystals form white Jovian clouds. Sulphur compounds (and perhaps phosphorus) may produce the brown and orange hues that characterise Jupiter's atmosphere. It is likely that methane, ammonia, water and other gases react to form organic molecules in the regions between the planet's frigid cloud tops and the warmer hydrogen ocean lying below. because of Jupiter's atmospheric dynamics, however, these organic compounds -- if they exist -- are probably short-lived.

The Great Red Spot has been observed for centuries through telescopes on Earth. This hurricane-like storm in Jupiter's atmosphere is more than twice the size of our planet. As a high- pressure region, the Great Red Spot spins in a direction opposite to that of low-pressure storms on Jupiter; it is surrounded by swirling currents that rotate around the spot and are sometimes consumed by it. The Great Red Spot might be a million years old. Our spacecraft detected lightning in Jupiter's upper atmosphere and observed auroral emissions similar to Earth's northern lights at the Jovian polar regions. Voyager 1 returned the first images of a faint, narrow ring encircling Jupiter. Largest of the solar system's planets, Jupiter rotates at a dizzying pace -- once every 9 hours 55 minutes 30 seconds. The massive planet takes almost 12 Earth years to complete a journey around the Sun. With 16 known moons, Jupiter is something of a miniature solar system. A new mission to Jupiter -- the Galileo Project -- is under way. On December 7, 1995, after a six year cruise that takes the Galileo Orbiter once past Venus, twice past Earth and the Moon and once past two asteroids, the spacecraft will drop an atmospheric probe into Jupiter's cloud layers and relay data back to Earth. The Galileo Orbiter will spend two years circling the planet and flying close to Jupiter's large moons, exploring in detail what the two Pioneers and two Voyagers revealed.

Galilean Satellites

In 1610, Galileo Galilei aimed his telescope at Jupiter and spotted four points of light orbiting the planet. For the first time, humans had seen the moons of another world. In honour of their discoverer, these four bodies would become known as the Galilean satellites or moons. But Galileo might have happily traded this honour for one look at the dazzling photographs returned by the Voyager spacecraft as they flew past these planet sized satellites.

One of the most remarkable findings of the Voyager mission was the presence of active volcanoes on the Galilean moon Io. Volcanic eruptions had never before been observed on a world other than Earth. The Voyager cameras identified at least nine active volcanoes on Io, with plumes of ejected material extending as far as 280 kilometres (175 miles) above the moon's surface. Io's pizza-coloured terrain, marked by orange and yellow hues, is probably the result of sulphur-rich materials brought to the surface by volcanic activity. Volcanic activity on this satellite is the result of tidal flexing caused by the gravitational tug-of-war between Io, Jupiter and the other three Galilean moons.

Europa, approximately the same size as our Moon, is the brightest Galilean satellite. The moon's surface displays a complex array of streaks, indicating the crust has been fractured. Caught in a gravitational tug-of-war like Io, Europa has been heated enough to cause its interior ice to melt -- apparently producing a liquid-water ocean. This ocean is covered by an ice crust that has formed where water is exposed to the cold of space. Europa's core is made of rock that sank to its centre. Like Europa, the other two Galilean moons -- Ganymede and Callisto --are worlds of ice and rock. Ganymede is the largest satellite in the solar system -- larger than the planets Mercury and Pluto. The satellite is composed of about 50 percent ice or slush and the rest rock. Ganymede's surface has areas of different brightness, indicating that, in the past, material oozed out of the moon's interior and was deposited at various locations on the surface

Callisto, only slightly smaller than Ganymede, has the lowest density of any Galilean satellite, suggesting that large amounts of water are part of its composition. Callisto is the most heavily cratered object in the solar system; no activity during its history has erased old craters except more impacts. Detailed studies of all the Galilean satellites will be performed by the Galileo Orbiter.

SATURN

No planet in the solar system is adorned like Saturn. Its exquisite ring system is unrivalled. Like Jupiter, Saturn is composed mostly of hydrogen. But in contrast to the vivid colours and wild turbulence found in Jovian clouds, Saturn's atmosphere has a more subtle, butter-scotch hue, and its markings are muted by high-altitude haze. Given Saturn's somewhat placid-looking appearance, scientists were surprised at the high-velocity equatorial jet stream that blows some 1,770 kilometres (1,100 miles) per hour. Three American space-craft have visited Saturn. Pioneer 11 sped by the planet and its moon Titan in September 1979, returning the first close-up images. Voyager 1 followed in November 1980, sending back breathtaking photographs that revealed for the first time the complexities of Saturn's ring system and moons. Voyager 2 flew by the planet and its moons in August 1981. The rings are composed of countless low-density particles orbiting individually around Saturn's equator at progressive distances from the cloud tops. Analysis of spacecraft radio waves passing through the rings showed that the particles vary widely in size, ranging from dust to house-sized boulders. The rings are bright because they are mostly ice and frosted rock. The rings might have resulted when a moon or a passing body ventured too close to Saturn. The unlucky object would have been torn apart by great tidal forces on its surface and in its interior. Or the object may not have been fully formed to begin with and disintegrated under the influence of Saturn's gravity. A third possibility is that the object was shattered by collisions with larger objects orbiting the planet.

Unable either to form into a moon or to drift away from each other, individual ring particles appear to be held in place by the gravitational pull of Saturn and its satellites. These complex gravitational interactions form the thousands of ringlets that make up the major rings. Radio emissions quite similar to the static heard on an AM car radio during an electrical storm were detected by the Voyager spacecraft. These emissions are typical of lightning but are believed to be coming from Saturn's ring system rather than its atmosphere, where no lightning was observed. As they had at Jupiter, the Voyagers saw a version of Earth's auroras near Saturn's poles. The Voyagers discovered new moons and found several satellites that share the same orbit. We learned that some moons shepherd ring particles, maintaining Saturn's rings and the gaps in the rings. Saturn's 18th moon was discovered in 1990 from images taken by Voyager 2 in 1981.

Voyager 1 determined that Titan has a nitrogen-based atmosphere with methane and argon -- one more like Earth's in composition than the carbon dioxide atmospheres of Mars and Venus. Titan's surface temperature of -179 degrees Celsius (-290 degrees Fahrenheit) implies that there might be water-ice islands rising above oceans of ethane-methane liquid or sludge. Unfortunately, Voyager's cameras could not penetrate the moon's dense clouds. Continuing photochemistry from solar radiation may be converting Titan's methane to ethane, acetylene and -- in combination with nitrogen -- hydrogen cyanide. The latter compound is a building block of amino acids. These conditions may be similar to the atmospheric conditions of primeval Earth between three and four billion years ago. However, Titan's atmospheric temperature is believed to be too low to permit progress beyond this stage of organic chemistry.

The exploration of Saturn will continue with the Cassini mission. Scheduled for launch in the latter part of the 1990s, the Cassini mission is a collaborative project of NASA, the European Space Agency and the federal space agencies of Italy and Germany, as well as the United States Air Force and the Department of Energy. Cassini will orbit the planet and will also deploy a probe called Huygens, which will be dropped into Titan's atmosphere and fall to the surface. Cassini will use radar to peer through Titan's clouds and will spend years examining the Saturnian system.

URANUS

In January 1986, four and a half years after visiting Saturn, Voyager 2 completed the first close-up survey of the Uranian system. The brief flyby revealed more information about Uranus and its retinue of icy moons than had been gleaned from ground observations since the planet's discovery over two centuries ago by the English astronomer William Herschel. Uranus, third largest of the planets, is an oddball of the solar system. Unlike the other planets (with the exception of Pluto), this giant lies tipped on its side with its north and south poles alternately facing the sun during an 84-year swing around the solar system. During Voyager 2's flyby, the south pole faced the Sun. Uranus might have been knocked over when an Earth sized object collided with it early in the life of the solar system. Voyager 2 found that Uranus' magnetic field does not follow the usual north-south axis found on the other planets. Instead, the field is tilted 60 degrees and offset from the planet's centre, a phenomenon that on Earth would be like having one magnetic pole in New York City and the other in the city of Djakarta, on the island of Java in Indonesia.

Uranus' atmosphere consists mainly of hydrogen, with some 12 percent helium and small amounts of ammonia, methane and water vapour. The planet's blue colour occurs because methane in its atmosphere absorbs all other colours. Wind speeds range up to 580 kilometres (360 miles) per hour, and temperatures near the cloud tops average -221 degrees Celsius (-366 degrees Fahrenheit). Uranus' sunlit south pole is shrouded in a kind of photochemical "smog" believed to be a combination of acetylene, ethane and other sunlight-generated chemicals. Surrounding the planet's atmosphere and extending thousands of kilometres into space is a mysterious ultraviolet sheen known as electroglow." Approximately 8,000 kilometres (5,000 miles) below Uranus' cloud tops, there is thought to be a scalding ocean of water and dissolved ammonia some 10,000 kilometres (6,200 miles) deep. Beneath this ocean is an Earth-sized core of heavier materials.

Voyager 2 discovered 10 new moons, 16-169 kilometres (10- 105 miles) in diameter, orbiting Uranus. The five previously known -- Miranda, Ariel, Umbriel, Titania and Oberon -- range in size from 520 to 1,610 kilometres (323 to 1,000 miles) across. Representing a geological showcase, these five moons are half-ice, half-rock spheres that are cold and dark and show evidence of past activity, including faulting and ice flows.

The most remarkable of Uranus' moons is Miranda. Its surface features high cliffs as well as canyons, crater-pocked plains and winding valleys. The sharp variations in terrain suggest that, after the moon formed, it was smashed apart by a collision with another body -- an event not unusual in our solar system, which contains many objects that have impact craters or are fragments from large impacts. What is extraordinary is that Miranda apparently reformed with some of the material that had been in its interior exposed on its surface. Uranus was thought to have nine dark rings; Voyager 2 imaged 11. In contrast to Saturn's rings, which are composed of bright particles, Uranus' rings are primarily made up of dark, boulder sized chunks.

NEPTUNE

Voyager 2 completed its 12-year tour of the solar system with an investigation of Neptune and the planet's moons. On August 25, 1989, the spacecraft swept to within 4,850 kilometres (3,010 miles) of Neptune and then flew on to the moon Triton. During the Neptune encounter it became clear that the planet's atmosphere was more active than Uranus'. Voyager 2 observed the Great Dark Spot, a circular storm the size of Earth, in Neptune's atmosphere. Resembling Jupiter's Great Red Spot, the storm spins counter clockwise and moves westward at almost 1,200 kilometres (745 miles) per hour. Voyager 2 also noted a smaller dark spot and a fast moving cloud dubbed the "Scooter," as well as high-altitude clouds over the main hydrogen and helium cloud deck. The highest wind speeds of any planet were ob-served, up to 2,400 kilometres (1,500 miles) per hour. Like the other giant planets, Neptune has a gaseous hydrogen and helium upper layer over a liquid interior. The planet's core contains a higher percentage of rock and metal than those of the other gas giants. Neptune's distinctive blue appearance, like Uranus' blue colour, is due to atmospheric methane. Neptune's magnetic field is tilted relative to the planet's spin axis and is not centred at the core. This phenomenon is similar to Uranus' magnetic field and suggests that the fields of the two giants are being generated in an area above the cores, where the pressure is so great that liquid hydrogen assumes the electrical properties of a metal. Earth's magnetic field, on the other hand, is produced by its spinning metallic core and is only slightly tilted and offset relative to its centre.

Voyager 2 also shed light on the mystery of Neptune's rings. Observations from Earth indicated that there were arcs of material in orbit around the giant planet. It was not clear how Neptune could have arcs and ho these could be kept from spreading out into even, un-clumped rings. Voyager 2 detected these arcs, but they were, in fact, part of thin, complete rings. A number of small moons could explain the arcs, but such bodies were not spotted. Astronomers had identified the Neptunian moons Triton in 1846 and Nereid in 1949. Voyager 2 found six more. One of the new moons -- Proteus is actually larger than Nereid, but since Proteus orbits close to Neptune, it was lost in the planet's glare for observers on Earth.

Triton circles Neptune in a retrograde orbit in under six days. Tidal forces on Triton are causing it to spiral slowly towards the planet. In 10 to 100 million years (a short time in astronomical terms), the moon will be so close that Neptunian gravity will tear it apart, forming a spectacular ring to accompany the planet's modest current rings. Triton's landscape is as strange and unexpected as those of Io and Miranda. The moon has more rock than its counterparts at Saturn and Uranus. Triton's mantle is probably composed of water ice, but the moon's crust is a thin veneer of nitrogen and methane. The moon shows two dramatically different types of terrain: the so-called "cantaloupe" terrain and a receding ice cap.

Dark streaks appear on the ice cap. These streaks are the fallout from geyser-like volcanic vents that shoot nitrogen gas and dark, fine-grained particles to heights of 2 to 8 kilometres (1 to 5 miles). Triton's thin atmosphere, only 1/70,000th as thick as Earth's, has winds that carry the dark particles and deposit them as streaks on the ice cap -- the coldest surface yet found in the solar system (-235 degrees Celsius, -391 degrees Fahrenheit). Triton might be more like Pluto than any other object spacecraft have so far visited.

PLUTO

Pluto is the most distant of the planets, yet the eccentricity of its orbit periodically carries it inside Neptune's orbit, where it has been since 1979 and where it will remain until March 1999. Pluto's orbit is also highly inclined -- tilted 17 degrees to the orbital plane of the other planets. Discovered in 1930, Pluto appears to be little more than a celestial snowball. The planet's diameter is calculated to be approxi-mately 2,300 kilometres (1,430 miles), only two-thirds the size of our Moon. Ground-based observations indicate that Pluto's surface is covered with methane ice and that there is a thin atmosphere that may freeze and fall to the surface as the planet moves away from the Sun. Observations also show that Pluto's spin axis is tipped by 122 degrees. The planet has one known satellite, Charon, discovered in 1978. Charon's surface composition is different from Pluto's: the moon appears to be covered with water-ice rather than methane ice. Its orbit is gravitationally locked with Pluto, so both bodies always keep the same hemisphere facing each other. Pluto's and Charon's rotational period and Charon's period of revolution are all 6.4 Earth days. Although no spacecraft have ever visited Pluto, NASA is currently exploring the possibility of such a mission.

COMETS

The outermost members of the solar system occasionally pay a visit to the inner planets. As asteroids are the rocky and metallic remnants of the formation of the solar system, comets are the icy debris from that dim beginning and can survive only far from the Sun. Most comet nuclei reside in the Oort Cloud, a loose swarm of objects in a halo beyond the planets and reaching perhaps halfway to the nearest star. Comet nuclei orbit in this frozen abyss until they are gravitationally perturbed into new orbits that carry them close to the Sun. As a nucleus falls inside the orbits of the outer planets, the volatile elements of which it is made gradually warm; by the time the nucleus enters the region of the inner planets, these volatile elements are boiling. The nucleus itself is irregular and only a few miles across, and is made principally of water-ice with carbon monoxide, carbon dioxide, methane and ammonia -- materials very similar to those composing the moons of the giant planets As these materials boil off of the nucleus, they form a coma or cloud-like "head" that can measure tens of thousands of kilometres across. The coma grows as the comet gets closer to the Sun. Solar charged particles push on gas molecules and the pressure of sunlight pushes on the cloud of dust particles, blowing them back like flags in the wind and giving rise to the comet's "tails." Gases and ions are blown directly back from the nucleus, but dust particles are pushed more slowly. As the nucleus continues in its orbit, the dust particles are left behind in a curved arc.

Both the gas and dust tails are blown away from the Sun; in effect, the comet chases its tails as it recedes from the Sun. The tails can reach 150 million kilometres (93 million miles) in length, but the total amount of material contained in this dramatic display would fit in an ordinary suitcase. Comets -- from the Latin cometa, meaning "long-haired" -- are essentially dramatic light shows. Some comets pass through the solar system only once, but others have their orbits gravitationally modified by a close encounter with one of the giant outer planets. These latter visitors can enter closed elliptical orbits and repeatedly return to the inner solar system.

Halley's Comet is the most famous example of a relatively short period comet, returning on an average of once every 76 years and orbiting from beyond Neptune to within Venus' orbit. Confirmed sightings of the comet go back to 240 B.C. This regular visitor to our solar system is named for Sir Edmond Halley, because he plotted the comet's orbit and predicted its return, based on earlier sightings and Newtonian laws of motion. His name became part of astronomical lore when, in 1759, the comet returned on schedule. Unfortunately, Sir Edmond did not live to see it. A comet can be very prominent in the sky if it passes comparatively close to Earth. Unfortunately, on its most recent appearance, Halley's Comet passed no closer than 62.4 million kilometres (38.8 million miles) from our world. The comet was visible to the naked eye, especially for viewers in the southern hemisphere, but it was not spectacular. Comets have been so bright, on rare occasions, that they were visible during day-time. Historically, comet sightings have been interpreted as bad omens and have been artistically rendered as daggers in the sky. Several spacecraft have flown by comets at high speed; the first was NASA's International Cometary Explorer in 1985. An armada of five spacecraft (two Japanese, two Soviet and the Giotto spacecraft from the European Space Agency) flew by Halley's Comet in 1986. Additional comet missions are being examined in the United States and abroad.

Conclusion

Despite their efforts to peer across the vast distances of space through an obscuring atmosphere, scientists of the past had only one body they could study closely -- Earth. But since 1959, space flight through the solar system has lifted the veil on our neighbours in space. We have learned more about our solar system and its members than anyone had in the previous thousands of years. Our automated spacecraft have travelled to the Moon and to all the planets beyond our world except Pluto; they have observed moons as large as small planets, flown by comets and sampled the solar environment. Astronomy books now include detailed pictures of bodies that were only smudges in the largest telescopes for generations. We are lucky to be alive now to see these strange and beautiful places and objects.

The knowledge gained from our journeys through the solar system has redefined traditional Earth sciences like geology and meteorology and spawned an entirely new discipline called comparative planetology. By studying the geology of planets, moons, asteroids and comets, and comparing differences and similarities, we are learning more about the origin and history of these bodies and the solar system as a whole. We are also gaining insight into Earth's complex weather systems. By seeing how weather is shaped on other worlds and by investigating the Sun's activity and its influence throughout the solar system, we can better understand climatic conditions and processes on Earth.

We will continue to learn and benefit as our automated spacecraft explore our neighbourhood in space. Missions to each type of body in the solar system are in flight or under development or study. We can also look forward to the time when humans will once again set foot on an alien world. Although astronauts have not been back to the Moon since December 1972, plans are being formulated for our return to the lunar landscape and for the human exploration of Mars and even the establishment of Martian outposts. One day, taking a holiday may mean spending a week at a lunar base or a Martian colony

THE ORIGIN OF THE SOLAR SYSTEM

The earliest accounts of how the Sun, the Earth and the rest of the Solar System were formed are to be found in early myths, legends and religious texts. None of these can be considered a serious scientific account. The earliest scientific attempts to explain the origin of the solar system invoked collisions or condensations from a gas cloud. The discovery of `island universes', which we now know to be galaxies, was thought to confirm this latter theory.

During this century Jeans proposed the idea that material had been dragged out of the Sun by a passing star and that this material had then condensed to form the planets. There are serious flaws to this explanation but recent developments have been made suggesting that a filament was drawn out of a passing protostar at a time when the Sun was a member of a loose cluster of stars but the most favoured theories still involve the gravitational collapse of a gas and dust cloud. The problems to be faced by any theory for the formation of the Solar System Any theory has to account for certain rather tricky facts about the Solar System. These are in addition to the obvious facts that the Sun is at the centre with the planets in orbit around it. There are 5 of these problem areas.

1. The Sun spins slowly and only has 1 percent of the angular momentum of the Solar System but 99.9 percent of its mass. The planets carry the rest of the angular momentum.

2. The formation of the terrestrial planets with solid cores.

3. The formation of the gaseous giant planets.

4. The formation of planetary satellites.

5. An explanation of Bode's law which states that the distances of the planets from the Sun follow a simple arithmetic progression.

(Bode's `law' takes the form of a series in which the first term is 0, the second is 3 and each term is then double the previous one, to each term add 4 and divide the result by 10. This yields the series of numbers, 0.4, 0.7, 1.0, 1.6, 2.8, 5.2, 10.0, 19.6, 38.8; which may be compared to the mean distances of the planets from the Sun in AU, 0.39, 0.72, 1.0, 1.52, 5.2, 9.52, 19.26, 30.1,
39.8. The agreement for all but Neptune and Pluto is remarkable. The lack of a planet at 2.8 led to the discovery of the asteroids.) There are 5 theories which are still considered to be `reasonable' in that they explain many (but not all) of the phenomena exhibited by the solar system.

The Accretion theory

This assumes that the Sun passed through a dense interstellar cloud and emerged surrounded by a dusty, gaseous envelope. It thus separates the formation of the Sun from that of the planets thus losing problem 1. The problem which remains is that of getting the cloud to form the planets. The terrestrial planets can form in a reasonable time but the gaseous planets take far too long to form. The theory does not explain satellites or Bode's law and must be considered the weakest of those described here.

The Protoplanet theory

This assumes that initially there is a dense interstellar cloud which will eventually produce a cluster of stars. Dense regions in the cloud form and coalesce; as the small blobs have random spins the resulting stars will have a low rotation rates. The planets are smaller blobs captured by the star. The small blobs would have higher rotation than is seen in the planets but the theory accounts for this by having the `planetary blobs' split to give a planet and satellites. Thus many of the problem areas are covered but it is not clear how the planets came to be confined to a plane or why their rotations are in the same sense.

The Capture theory

This theory is a version of Jeans's theory in which the Sun interacts with a nearby protostar dragging a filament of material from the protostar. The low rotation speed of the Sun is explained as being due to its formation before the planets, the terrestrial planets are explained by collisions between the protoplanets close to the Sun and the giant planets and their satellites are explained as condensations in the drawn out filament.

The Modern Laplacian theory

Laplace in 1796 first suggested that the Sun and the planets formed in a rotating nebula which cooled and collapsed. It condensed into rings which eventually formed the planets and a central mass which became the Sun. The slow spin of the Sun could not be explained. The modern version assumes that the central condensation contains solid dust grains which create drag in the gas as the centre condenses. Eventually, after the core has been slowed its temperature rises and the dust is evaporated. The slowly rotating core becomes the Sun. The planets form from the faster rotating cloud.

The Modern Nebula theory

Observations of very young stars indicate that they are surrounded by dense dusty disks. While there are still difficulties in explaining some of the problem areas outlined above, in particular ways to slow down the rotation of the Sun, it is believed that the planets originated in a dense disk which formed from material in the gas and dust cloud which collapsed to give the Sun. The density of this disk has to be sufficient to allow the formation of the planets and yet be thin enough for the residual matter to be blown away by the Sun as its energy output increased.

Conclusion

There have been many attempts to develop theories for the origin of the Solar System. None of them can be described as totally satisfactory and it is possible that there will further developments which may better explain the known facts. We do believe, however, that we understand the overall mechanism which is that the Sun and the planets formed from the contraction of part of a gas/dust cloud under its own gravitational pull and that the small net rotation of the cloud was responsible for the formation of a disk around the central condensation. The central condensation eventually formed the Sun while small condensations in the disk formed the planets and their satellites. The energy from the young Sun blew away the remaining gas and dust leaving the solar system as we see it today.

Getting started in amateur radio astronomy

ASTEROIDS

Asteroids are rocky and metallic objects that orbit the Sun but are too small to be considered planets. They are known as minor planets. Asteroids range in size from Ceres, which has a diameter of about 1000 km, down to the size of pebbles. Sixteen asteroids have a diameter of 240 km or greater. They have been found inside Earth's orbit to beyond Saturn's orbit. Most, however, are contained within a main belt that exists between the orbits of Mars and Jupiter. Some -- an unknown number -- have orbits that cross Earth's path and several have hit the Earth in times past, and are likely to do so again, with possibly cataclysmic results for the future of our species and civilization. One of the best preserved examples is the Barringer Meteor Crater near Winslow, Arizona.

The Gulf of Mexico itself is thought by some geologists to be the remnants of a huge impact crater from an object which collided with Earth, resulting in the extinction of more than 95 percent of species on the planet's surface including the dinosaurs. This catastrophe -- the so-called KT event -- took place during the Cretaceous-Tertiary period 65 million years ago. Such collisions are no longer thought to be isolated events, but part of an ongoing cycle, possibly connected with the Solar System's passing through denser areas of the Milky Way during its slow revolution through the galaxy's arm.

Asteroids are material left over from the formation of the solar system. One theory suggests that they are the remains of a planet that was destroyed in a massive collision long ago. More likely, asteroids are material that never coalesced into a planet, or material 'picked up' by the sun's gravitational pull as we pass through interstellar space. In fact, if the estimated total mass of all asteroids was gathered into a single object, the object would be less than 1,500 kilometres (932 miles) across -- less than half the diameter of our Moon.

Much of our understanding about asteroids comes from examining pieces of space debris that fall to the surface of Earth. Asteroids that are on a collision course with Earth are called meteoroids. When a meteoroid strikes our atmosphere at high velocity, friction causes this chunk of space matter to incinerate in a streak of light known as a meteor. If the meteoroid does not burn up completely, what's left strikes Earth's surface and is called a meteorite.

Of all the meteorites examined, 92.8 percent are composed of silicate (stone), and 5.7 percent are composed of iron and nickel; the rest are a mixture of the three materials. Stony meteorites are the hardest to identify since they look very much like terrestrial rocks. Since asteroids are material from the very early solar system, scientists are interested in their composition. Space-craft that have flown through the asteroid belt have found that the belt is really quite empty and that asteroids are separated by very large distances. Recently the Galileo spacecraft has made close encounters with asteroids Gaspra and Ida.

Celestial Coordinate Systems

As we look up into the night sky, the stars appear to be points on a large inverted bowl above us. This inverted bowl is called the celestial sphere. Since all objects on the celestial sphere appear to be the same arbitrarily large distance from the observer, it is usually not necessary to know the object's true distance. It is only necessary to know the object's angular position as projected onto the celestial sphere.

Since the celestial sphere appears as a two dimensional, curved surface, two angular measurements are required to specify one object's position relative to another.

Although any arbitrary coordinate system could be used, these measurements are usually made in two specific systems by amateur astronomers. Each is characterised by a specific plane of reference which determines a great circle when projected onto the celestial sphere by angular measure around the great circle from the reference point and by angular distance from the reference plane along another great circle perpendicular to that point.

Topocentric Coordinated

Also called "alt-azimuth" or horizon coordinates, this system uses the plane of the local horizon as the plane of reference. The reference point within the plane is the geographic north point. (It might just as easily have been the geographic south point except that early civilisations and, hence, directional conventions, first developed in the northern hemisphere. The northern boas continues to this day.) The azimuth, designated 0 (theta), is measured along the horizon, eastward from the north point. From the definition, azimuth ranges from 0 degrees to 360 degrees. The common directions of due north, east, south and west corresponds respectively to azimuths of 0 degrees, 90 degrees, 180 degrees and 270 degrees. Altitude, designated a, is measured perpendicular to the horizon. Altitude values range from -90 degrees to +90 degrees. If the altitude of an object is negative, it is below the horizon. If the altitude is greater than 90 degrees, it should be measured from a point on the horizon 180 degrees away in azimuth. This would bring the altitude back to less than 90 degrees. The point directly overhead, having +90 degrees altitude is called the zenith.

Equatorial Coordinates

As the name suggests, the plane of the Earth's equator is chosen as the plane of reference.
The projection of this plane intersects the celestial sphere in a great circle called the celestial equator. The reference point on the celestial equator is defines with the aid of another plane, the plane of the Earth's orbit, called the ecliptic. The sun appears to follow the ecliptic as it moves day-to-day against the stellar background. The path was named ecliptic because lunar and solar eclipses occur along this path. Since the equator is inclined about 23.5 degrees to the ecliptic, the two projected great circles intersect at two points. That intersection where the Sun appears to cross the celestial equator from south to north is chosen as the reference point and is known as the vernal equinox.

Right Ascension

Right Ascension, is designated a, is measured along the celestial equator eastward from the vernal equinox. For convenience, right ascension is normally measured in hours and ranges from 0h to 24h. Note that, in the northern hemisphere, right ascension increases clockwise when you are facing north.

Declination

Declination, designated sigma, is measured perpendicular to the celestial equator. Declination ranges from -90 degrees to +90 degrees. Negative declinations indicate objects south of the celestial equator. As with altitude, a declination of greater than 90 degrees should be measured from a right ascension 12h (=180 degrees) away so that the corrected value is always with the +/- 90 degrees range.

AURORA BOREALIS - the northern lights,
By Franck Pettersen

Introduction

The Northern lights are poetry, they are nature's light show, and they are quantum leaps in the oxygen atom. They are elementary particle physics, superstition, mythology and fairy tales. The northern lights have filled people with wonder and inspired artists; they have frightened people to think that the end is at hand. More exact explanations of the phenomenon could not be given until modern particle physics were developed, and knowledge about details in the earth's magnetosphere has been based on measurements from satellites. When the northern lights are seen over Tromsx, it happens in a set pattern, although this pattern varies considerably. The outbursts starts with a phosphorescent glow over the horizon in north west. The glow dies out and comes back, and then an arch is lit. It drifts up over in the sky. And new arches are lit and follow the first one. Small waves and curls move along the arches. Then within a few minutes a dramatic change is seen in the sky. A hailstorm of particles hit the upper atmosphere in what is called an auroral sub-storm. Rays of light shoot down from space, forming draperies which spread all over the sky. And they really remind us of draperies or curtains which are flickering in the wind. And you can see a violet and a red trimming at the lower and upper ends. Or the colours are mixed all together, woven into each other.

The curtains are disappearing and forming all over again by new rays of light shooting down from space. Above our head we cans see rays going out in all directions forming what is called an auroral corona. After 10 to 20 minutes the storm is over and the activity decreases. The bands are spread out, disintegrating in a diffuse light all over the sky. We can not see individual pockets of light, but the total effect is bright enough to enable us to make out details of the countryside around us. If we look very carefully, we can see the remains of the northern lights display as faint, pulsating flames. Clouds of light which is turned on and off regularly every 5 - 10 seconds as though by an electric light-switch. The natures own gigantic light-show is over.

The Northern Lights and Folklore

Since time immemorial, through different cultures and whenever they occur, there have been many beliefs about the northern lights. The Inuit around Hudson Bay had the following explanation of what they saw: the sky is a huge dome of hard material arched over the flat earth. On the outside there is light. In the dome there are a large number of small holes, and trough these holes you can see the light from the outside when it is dark. And trough these holes the spirits of the dead can pass into the heavenly regions. The way to heaven leads over a narrow bridge which spans an enormous abyss. The spirits that were already in heaven light torches to guide the feet of the new arrivals. These torches are called the northern lights In Middle-Age Europe, the northern lights were thought to be reflections of heavenly warriors. As a kind of posthumous reward, the soldiers that gave their lives for their king and country were allowed to battle on the skies forever.

In contrast, we find a sober and objective description of the northern lights in the Nordic book Kongespeilet (The King's Mirror) written approximately 1230. Here the author writes: Otherwise it is the same with the northern lights as with anything else we know nothing about, that wise men put forward ideas and simple guesswork, and believe that what is most common and probable. He then puts forwards several theories, some of which are based upon the fact that the northern lights were then common over Greenland, but rare over Norway. For example, Some people say that when the sun is under the horizon at night, some rays of light reach up to the skies over Greenland, a land mass so close to the edge of the earth that the earth's curvature is which hides the sun must be less there. Even today there are many different theories about the northern lights.

Some say that if you wave to them, they will increase in activity or even reach down and catch you. Or that if you look at them you will damage your eyes. One visitor to the Planetarium in Tromsx wondered how they came right down to the ground. He had seen it happen several times. Another wanted an explanation for the crackling noises he could hear when the northern lights were strong. One common notion is that the lights only appear when it is cold. They are, of course unaffected by the weather, but to see them, it should be dark and the sky cloudless. Under such conditions it is generally cold in North Norway.

What Causes the Northern Lights?

To answer this, we start with the sun whose energy production is far from even and fluctuates on an 11 year cycle. Maximum production coincides with high sunspot activity when processes on the sun's surface throw particles far out in space. These particles are called the solar wind and cause the northern lights. The sun's surface temperature is approximately 6,000 0C, much cooler than the interior which is several million degrees. In the Sun's atmosphere or corona, the temperature rises again to several million degrees. At such temperatures, collisions between gas particles can be so violent that atoms disintegrate into electrons and nuclei. What was once hydrogen becomes a gas of free electrons and protons called plasma. This plasma escapes from the sun's corona through a hole in the Sun's magnetic field. As they escape, they are thrown out by the rotation of the sun in an ever widening spiral - the so-called garden-hose effect. The name originates from the pattern of water droplets formed if we swing a garden hose around and around above out heads.

The Earth's Magnetic Field

After 2-5 days' travel trough space, the plasma reaches the earth's magnetic field compressing it on the daylight side of the earth, and stretches it into a tail on the nightside. A few of the particles penetrate down to the earth along the lines of magnetic field in the polar areas. Most, however, are forced around the earth by the magnetic field and enter the "tail" which stretches out into a long cylinder. Its diameter is equivalent to 30-60 times the earth's radius, and its length up to 1000 times the same radius. It is, in effect, as if the earth's magnetic field creates a tunnel in the plasma current from the solar wind. Inside one end is the earth, and around its surface the earth's magnetism and the solar wind interact. The magnetic tail is divided into two by a sheet of plasma. The magnetic field lines from the earth's north and south pole stretch out in their respective halves such that the fields are in opposition. The electrons and protons in each half of the plasma rotate in opposite direction forming a huge "dynamo" with the positive pole on the side of the plasma sheet facing dawn and the negative pole facing evening. The dynamo" is driven by the current of charged particles between the two poles.

Aurora Outbreak

When the northern lights break out the following happens. The solar wind strengthens and the magnetic tail becomes unstable. Charged particles dive inwards towards the centre of the tail and cause it to increase in length and to taper. The particles draw the magnetic field lines toward the centre where they meet causing a magnetic "short-circuit" approximately 15 times the earth's radius above the earth on the night side. This occurs especially at the "dynamo's" two poles where a large amount of energy becomes stored. The magnetic field lines from both sides of the plasma layer now act as conductors in the "dynamo's" outer circuit. The circuit closes when the particles reaches the ionosphere, the outer layer of the earth's atmosphere. Here the thin gasses are composed of ionised particles and consequently act as electrical conductors. It is here that the "dynamo's" energy is converted to light .

Quatum Leap

Most of the northern lights we see originate in the electrons accelerate into the ionosphere. The mechanism by which their kinetic energy is converted to visible light is called the quantum leap. To explain this mechanism, let us first imagine a hydrogen atom consisting of a single positive proton nucleus around which spins a single electron at a set distance. Normally the electron is in an orbit as close to the proton as possible. In such a state the hydrogen atom a minimum of energy. There are however other possible orbits further away from the nucleus in which the electron can spin. When a free electron collides with the hydrogen electron at high speed, it releases energy. This results in the spinning electron moving into another, higher energy orbit further out from the nucleus. It now contains more potential energy, but is unstable and unable to retain this energy. It returns to its original orbit, releasing the extra energy as a photon of light. Billions of such quantum leaps occurring simultaneously create the northern lights . Only a bare minimum of the aurora is a result of quantum leaps in the hydrogen atom. The green colour which dominates the northern lights over North Norway is a result of such leaps in oxygen while red is usually formed in nitrogen.

Three Norwgian Pioneers

Lars Vegard was the first scientist to map the colours of the aurora, and his work contributed to the building of the Auroral Observatory in Tromsx. He used a spectrograph to record the wave lengths, and hence colours of the lights and determined the main green colour to be 558 x 10E-9 m. Kristian Birkeland, born in Oslo in 1867, professor in 1898, put forward a theory explaining the northern lights in 1896. Most of his theory, which he tested in the laboratory, still holds today. He was able to reconstruct the northern lights in the laboratory by bombarding a metal ball containing an electromagnet (representing the earth) with electrons (solar wind). He also made a series of theoretical calculations, and the electrical currents in the upper atmosphere are still called Birkeland-currents. Carl Stxrmer was the third of the Norwegian pioneers in northern lights research, and he continued where Birkeland left off in his theoretical calculations. He calculated that there was an belt like area around the earth in which particles where reflected to and from between the poles. This area was verified experimentally with measurements from satellite years later by the American physicist James Van Allan, and is now known as the Van Allen belt. Stxrmer also calculated the height of the northern lights to be 80-130 km by comparing photographs of their position with those of stars. At this height there is a complete vacuum such that any sound which may be associated with an outburst must have another source than ordinary sound waves in the aurora itself. One possibility is the discharge of electrical fields on the surface of the earth which may occur during an aurora outburst.

The Northern Lights Oval

The particles which stream down from the magnetic tail reach the earth in a belt called the northern lights oval. This belt is wider on the night side of the earth than on the day side and is centred around the magnetic pole while the earth revolves around the geographic poles. This means that the belt covers Tromsx from early evening until early the next morning. The width of the belt on the night side is up to 600 km. A common misconception is that the frequency of the northern lights increases with latitude. This is not so. In fact, when Tromsx is directly under the belt, the chances of seeing the aurora from Svalbard is less. The magnetic poles are not stationary such that when the saga was written, the northern lights passed to the north of Norway. That is why they were only seen on Greenland. The northern lights outburst, the way it is described in the beginning of this article, has to do with both how Tromsx moves in and out under the northern lights oval, and with gusts in the solar wind.

Northern Lights and Climate

In the days of old, the weather forecast was sometimes based on the northern lights. They were however, often contradictory. In Labrador, coloured lights forecasted fine weather, whereas on Greenland they were a sign of southerly winds and storms. Even at the turn of last century, one could read in the Encyclopaedia Brittanica that the northern lights and thundery weather were the result of the same phenomenon, but with different forms of electrical discharge. In North Norway, the northern lights were often associated with cold weather. Between 1645 and 1715, there was little sunspot activity and therefore little northern lights activity. This period is called the Maunder minimum, after the leader of the Greenwich Observatory in England who was the first to document this low activity. Petter Dass, a famous Norwegian priest and author of the same period, has described much of the North Norwegian way of life, but never mentions the northern lights. The northern lights oval was then in such a position that the northern lights should have been visible, but the sun was less active and the northern lights failed to appear. During such periods, the climate on earth has generally been colder and the Maunder minimum coincides with what is now known with as the Scandinavian "little ice age". Since then, sunspot activity has increased and reached a maximum in 1991. This was the largest maximum in 300 years with more solar energy release, greater sunspot activity and more northern lights. How much today's global warming is a result of increased solar activity is difficult to say, but we do know that when sunspots and northern lights were lacking, the climate was colder in the north.

COMETS

Unlike the other small bodies in the solar system, comets have been known since antiquity. There are Chinese records of Comet Halley going back to at least 240 BC. The famous Bayeux Tapestry, which commemorates the Norman Conquest of England in 1066, depicts an apparition of Comet Halley. As of 1995, 878 comets have been catalogued and their orbits at least roughly calculated. Of these 184 are periodic comets (orbital periods less than 200 years); some of the remainder are no doubt periodic as well, but their orbits have not been determined with sufficient accuracy to tell for sure. Comets are sometimes called dirty snowballs or "icy mudballs". They are a mixture of ices (both water and frozen gases) and dust that for some reason didn't get incorporated into planets when the solar system was formed. This makes them very interesting as samples of the early history of the solar system. When they are near the Sun and active, comets have several distinct parts:

Nucleus: relatively solid and stable, mostly ice and gas with
a small amount of dust and other solids;

Coma: dense cloud of water, carbon dioxide and other neutral
gases sublimed off of the nucleus;

Hydrogen Cloud: huge (millions of km in diameter) but very
sparse envelope of neutral hydrogen;

Dust Tail: up to 10 million km long composed of smoke-sized
dust particles driven off the nucleus by escaping gases; this is the
most prominent part of a comet to the naked eye;

Ion Tail: up to 100 million km long composed of plasma and laced
with rays and streamers caused by interactions with the solar wind.

Comets are invisible except when they are near the Sun. Most comets have highly eccentric orbits which take them far beyond the orbit of Pluto; these are seen once and then disappear for millennia. Only the short- and intermediate-period comets (like Comet Halley), stay within the orbit of Pluto for a significant fraction of their orbits. Repeated passes near the Sun boils off most of a comet's ice and gas leaving a rocky object very much like an asteroid in appearance. A comet whose orbit takes it near the Sun is also likely to either impact one of the planets or to be ejected out of the solar system by a close encounter (esp. with Jupiter).

By far the most famous comet is Comet Halley but SL 9 was a "big hit" for a week in the summer of 1994. Meteor shower sometimes occur when the Earth passes through the orbit of a comet. Some occur with great regularity: the Perseid meteor shower occurs every year between August 9 and 13 when the Earth passes through the orbit of Comet Swift-Tuttle. Comet Halley is the source of the Orionid shower in October. Many comets are first discovered by amateur astronomers.

COMET MOTIONS

Comets necessarily obey the same physical laws as every other object. They move according to the basic laws of motion and of universal gravitation discovered by Newton in the 17th century (ignoring very small relativistic corrections). If one considers only two bodies -- either the Sun and a planet, or the Sun and a comet -- the smaller body appears to follow an elliptical path or orbit about the Sun, which is at one focus of the ellipse. The geometrical constants which fully define the shape of the ellipse are the semimajor axis a and the eccentricity e. The semiminor axis b is related to those two quantities by the equation b = a(1-e^2). The focus is located a distance from the centre of the ellipse. Three further constants are required if one wishes to describe the orientation of the ellipse in space relative to some coordinate system, and a fourth quantity is required if one wishes to define the location of a body in that elliptical orbit.

At any given time the motion of any solar system body is affected by the gravitational pulls of all of the others. The Sun's pull is the largest by far, unless one body approaches very closely to another, so orbit calculations usually are carried out as two-body calculations (the body in question and the Sun) with small perturbations (small added effects due to the pull of other bodies). In 1705 Halley noted in his original paper predicting the return of his comet that Jupiter undoubtedly had serious effects on the comet's motion, and he presumed Jupiter to be the cause of changes in the period (the time required for one complete revolution about the Sun) of the comet. (Comet Halley's period is usually stated to be 76 years, but in fact it has varied between 74.4 and 79.2 years during the past 2,000 years.) In that same paper Halley also became the first to note the very real possibility of the collision of comets with planets, but stated that he would leave the consequences of such a contact or shock to be discussed by the Studious of Physical Matters.

In the case of Shoemaker-Levy 9 we have the perfect example both of large perturbations and their possible consequences. The comet was fragmented and perturbed into an orbit where the pieces will hit Jupiter one period later. In general one must note that Jupiter's gravity (or that of other planets) is perfectly capable of changing the energy of a comet's orbit sufficiently to throw it clear out of the solar system (to give it escape velocity from the solar system) and has done so on numerous occasions. This is exactly the same physical effect that permits using planets to change the orbital energy of a spacecraft in so-called gravity-assist manoeuvres such as were used by the Voyager spacecraft to visit all the outer planets except Pluto.

One of Newton's laws of motion states that for every action there is an equal and opposite reaction. Comets expel dust and gas, usually from localised regions, on the sunward side of the nucleus. This action causes a reaction by the cometary nucleus, slightly speeding it up or slowing it down. Such effects are called "non-gravitational forces" and are simply rocket effects, as if someone had set up one or more rocket motors on the nucleus. In general both the size and shape of a comet's orbit are changed by the non-gravitational forces -- not by much but by enough to totally confound all of the celestial mechanics experts of the 19th and early 20th centuries. Comet Halley arrived at its point closest to the Sun (perihelion) in 1910 more than three days late, according to the best predictions. Only after F. L. Whipple published his icy conglomerate model of a degassing nucleus in 1950 did it all begin to make sense. The predictions for the time of perihelion passage of Comet Halley in 1986, which took into account a crude model for the reaction forces, were off by less than five hours.

Much of modern physics is expressed in terms of conservation laws, laws about quantities which do not change for a given system. Conservation of energy is one of these laws, and it says that energy may change form, but it cannot be created or destroyed. Thus the energy of motion (kinetic energy) of Shoemaker-Levy 9 will be changed largely to thermal energy when the comet is halted by Jupiter's atmosphere and destroyed in the process. When one body moves about another in the vacuum of space, the total energy (kinetic energy plus potential energy) is conserved.

Another quantity that is conserved is called angular momentum. In the first paragraph of this section, it was stated that the geometric constants of an ellipse are its semimajor axis and eccentricity. The dynamical constants of a body moving about another are energy and angular momentum. The total (binding) energy is inversely proportional to the semimajor axis. If the energy goes to zero, the semimajor axis becomes infinite and the body escapes. The angular momentum is proportional both to the eccentricity and the energy in a more complicated way, but, for a given energy, the larger the angular momentum the more elongated the orbit.

The laws of motion do not require that bodies move in circles (or even ellipses for that matter), but if they have some binding energy, they must move in ellipses (not counting perturbations by other bodies), and it is then the angular momentum which determines how elongated is the ellipse. Comets simply are bodies which in general have more angular momentum per unit mass than do planets and therefore move in more elongated orbits. Sometimes the orbits are so elongated that, because we can observe only a small part of them, they cannot be distinguished from a parabola, which is an orbit with an eccentricity of exactly one. In very general terms, one can say that the energy determines the size of the orbit and the angular momentum the shape.

COSMOLOGY

The Universe

From a study of the motions of the galaxies it can be deduced that they are all moving away from one another. It is simple to deduce from this that at some time in the past they must have been much closer together than they are now. Cosmology is the study of the origin and development of the Universe and the currently most popular theory is that of the Big Bang. This theorises that at about 20,000,000,000 years ago all the matter and space that make up the Universe were concentrated into a very small volume. The theory states that the Universe came into being as an extremely small volume full of energy which gave the Universe a very high temperature. As the Universe expanded so the fundamental atomic particles were formed as a mixture dominated by hydrogen with some helium and almost nothing else.

Some of the greatest current problems in astrophysics arise from consideration of how the galaxies formed, and what is the nature of the mass of the Universe (we can only identify 10 percent of what must be there). The study of the early Universe is possible due to the finite speed of light. As we look at galaxies many millions of light years away we see them as they were when the light left them -- many millions of years ago. These remote objects are, of course, faint and that is why astronomers are always wanting to use larger telescopes and more efficient detectors so that they can measure further back in time.

Evidence for the Big Bang

Until well into this century astronomers did not know that the Milky Way was a galaxy and that the `island universes' seen through large telescopes were galaxies, systems of many, many stars grouped together like the Milky Way. The fundamental discovery which demonstrated this was that made by Hubble. He showed, from spectra of the galaxies, that there was an increase in the velocity of recession with distance. The deduction from this is that space is expanding and it was soon appreciated that the Milky Way was one of a very great number of galaxies and that it, like the Sun, had no special place in the system of galaxies.

From the observation of galaxies using optical wavelengths it was not possible to find evolutionary effects and so the hypothesis that the Universe was in a steady state was a plausible one. With the advent of the large radio telescopes it was found that there were far more faint radio galaxies than one would expect in a steady-state universe. In fact it was shown that it was likely that all the galaxies originated in a very small volume -- the Big Bang. This theory received a boost when radiation at 3 degrees K, the micro-wave background radiation, was discovered coming from all directions in space. This radiation was predicted to be a remnant from the very early time in the age of the Universe, before matter had been formed when the Universe was still filled with hot radiation. The radiation was isotropic and it corresponded to a temperature which was consistent with red-shifted radiation from the Big Bang.

Predictions from the Big Bang

The theoretical analysis of the Big Bang has had various successes in predicting properties of the resulting universe. The biggest of these is the prediction of the relative abundance's of the elements and their isotopic ratios. When the oldest stars, whose material has been altered least by the accumulation of material processed in the centres of earlier generations of stars, are investigated it has been shown that their abundance ratios are in excellent agreement with those predicted.

There are problems, however, with the theory. One of these is that the very isotropic nature of the micro-wave background indicates that the early stages of the universe were completely uniform. When we look at the universe today we see non-uniformity's at every level. We ourselves are examples of aggregates of mass as are stars, galaxies and the groupings of galaxies into clusters and strings. The puzzle of how this non-isotropic nature could result from an isotropic early universe was, to some extent relieved by the discovery by the COBE satellite that there are small variations in the temperature of the micro-wave radiation indicating that in homogeneity, at a very early time in the age of the Universe.

The expansion of the Universe from the Big Bang is strongly dependant on the mass of the Universe. There is one critical value which would mean that the Universe will expand for a long time, gradually slowing down and then reach a steady state. A mass less than this value will mean that the Universe will go on expanding for ever while a greater value will mean that the Universe will expand to a maximum size and then will start to contract -- eventually returning to a very small volume. Astronomers think that the mass of the Universe is equal to this critical value but can only `see' one tenth of the matter necessary to reach this value. The same discrepancy is seen in the gravitational pull of individual galaxies and in clusters of galaxies. The mass appears to be there but we can not identify it. This is called the `missing mass problem'.

The `Shape' of the Universe

One of the hardest concepts to accept is that the Universe is everything that is. Not only the matter and energy but all the dimensions as well. There is no `outside' to the Universe and it has no `edge'. When we think of the Big Bang we instinctively think of the small Universe expanding like a sphere into an empty void. Unfortunately this is incorrect. The dimensions that we commonly use, three spatial and one time, are all mixed up when the early Universe is concerned and our normal concepts of space and time are not valid. The only way that it can be partly understood is to consider the two-dimensional analogue of the surface of a balloon which is being inflated. The surface is everywhere continuous, has no edge and yet is expanding. The three-dimensional analogue (whose understanding defeats the writer) will represent the Universe.

DARK MATTER

All visible celestial objects known today account for only 10% of the mass in the universe. The rest of this "missing mass," also known as "dark matter," is presumably invisible because it does not emit or reflect visible light or other forms of electromagnetic radiation. Or perhaps its light is so feeble that current astronomical instruments are unable to detect it. However, dark matter can be indirectly detected due to its gravitational influence on other nearby visible objects.

The presence of dark matter was first discovered in 1932 by astronomer Jan Oort, who measured the perpendicular motions of nearby stars relative to the disk of our Milky Way. He studied the gravitational influence of the galactic disk on these stars, and so, was able to measure the mass of the disk (just as the mass of Earth can be calculated from the acceleration of a falling object). To his surprise, this calculated mass was twice the amount of mass seen as stars and nebulae. A year later, Fritz Zwicky examined the dynamics of clusters of galaxies, and also came to the startling conclusion that the observed galaxies only accounted for 10% of the mass needed to gravitationally bind the galaxies in the cluster.

One widely-used method to deduce the amount of missing mass involves measuring the rotation speed of a spiral galaxy. Spectroscopic and radio observations have obtained the rotation velocities of hundreds of spiral galaxies. These experiments have revealed that, in most cases, a galaxy's mass continues to increase toward the edge of its visible disk of stars. This implies that spiral galaxies are surrounded in haloes of matter that cannot be seen. Observations of elliptical galaxies, groups, and clusters of galaxies also indicate the presence of dark matter interacting gravitationally with the visible objects.

The nature of dark matter, and its abundance, are among the most important questions in modern cosmology today. What is it made of? Some astronomers believe that dark matter is composed of protons and neutrons, called baryonic or simply "normal" matter. Baryonic dark matter candidates include extra-solar planets, remnants of stellar evolution such as comets, objects not massive enough to ignite hydrogen fusion called brown dwarfs, dying embers of stars such as cold white dwarfs and neutron stars, as well as interstellar and intergalactic gases.

Non-baryonic dark matter, on the other hand, could be elementary particles that do not interact strongly with normal matter. Except for the neutrino particle, many such elementary particles are still in the realm of theory and have not been detected. Since all visible matter is only a small fraction of the total mass in the universe, the amount of dark mass that is present will determine the evolutionary future of the universe. If there is not enough dark matter to gravitationally bind the universe together, it could continue expanding forever. If there is enough mass in the universe to gravitationally hold it together, the universe may slow down its expansion, come to a halt, and begin to contract and eventually collapse.

The temperature of dark matter in the early universe also may have determined the early evolution of the universe. Not long after the Big Bang and prior to the formation of galaxies, matter began to aggregate under the influence of gravity. Dark matter might have provided the "seeds," a lumpy background in which ordinary matter could congregate to form galaxies and stars. If this "cold dark matter" were present, where particles had a negligible random motion, galaxy formation would begin on small scales. Matter would gather in sizes comparable to current galaxies or smaller, and eventually build to become clusters and superclusters due to the gravitational attraction of the galaxies. If, however, "warm dark matter" was present, it would erase the small galaxy-sized "seeds" that initially formed. Instead, enormous gaseous pancake-like structures as large as superclusters and clusters, are created, subsequently condensing into individual galaxies.

ECLIPSES

We generally talk of eclipses of the Sun and Moon but other bodies inside and outside the Solar System exhibit eclipses and are very important in astronomy. Eclipses of the moons of Jupiter were used in one of the first measures of the speed of light and eclipsing binary stars give us fundamental data on the masses of stars. An eclipse occurs when a body cuts off the light from a light source so that we can no longer see it shining. An eclipse can be due either to a dark body coming between us and a light emitter, so that we can no longer see the source, or it can be a body coming between a light source and the body that the light is illuminating, so that we no longer see the illuminated body. Let us first consider eclipses of the Sun and Moon.

Eclipses of the Sun and Moon.

An eclipse of the Sun occurs when the Moon comes directly between the Sun and the Earth so that the Earth lies in the shadow of the Moon. An eclipse of the Moon occurs when the Earth lies directly between the Sun and the Moon and the Moon lies in the shadow of the Earth. If the orbit of the Moon about the Earth lay in the same plane as the orbit of the Earth about the Sun then there would be eclipses of the Sun and Moon at every New and Full Moon respectively. The orbits are inclined, however, and eclipses can only occur when the Moon is close to the nodes of its orbit (when it is near to the places where the orbital planes cross).

Lunar Eclipses.

The amount of the Moon's disk that is eclipsed depends on how close the Moon is to the node of its orbit at Full Moon. Like all shadows of light from an extended source the shadow produced by the Earth has an umbra, where all the light from the Sun is shadowed, and a penumbra, where only some of it is. Penumbral eclipses of the Moon occur when the Moon passes only through the Earth's penumbral shadow. Although these are catalogued they are inconspicuous events and are not noteworthy.

When the Moon passes through the Earth's umbral shadow we can either see a Partial Eclipse, when only part of the Moon is obscured, or a Total Eclipse. The Earth's shadow is much larger than the Moon and so eclipses can last up to 3 hrs 40 mins, with totality lasting up to 1 hr 40 mins. They can be seen from anywhere on the side of the Earth which faces the Moon. During a Total Eclipse, the Moon does not, as might be expected, disappear entirely but turns a deep, dark red. The brightness and colour depend on the state of the Earth's atmosphere for the Moon, during eclipse, is illuminated by light that has passed through the Earth's atmosphere and has been bent towards the Moon by refraction.

Solar Eclipses

These, like Lunar Eclipses, can only occur when the Moon is near the nodes of its orbit but in this case at New Moon. The shadow of the Moon can then pass over the surface of the Earth. Because the Moon is much smaller than the Earth its shadow only covers a small part of the Earth's surface and a solar eclipse can only be seen from a restricted area. Like the Earth's shadow, the Moon's has an umbra and a penumbra. Viewed from the Earth a person in the umbra sees the whole of the Sun eclipsed while someone in the penumbra sees only part of the Sun obscured. These are called a Total and a Partial Eclipse respectively.

Quite by chance the apparent sizes if the Sun and Moon are very nearly the same. The apparent angular size of the Sun does not change very much due to the Earth's non-circular orbit but the Moon's apparent size varies quite a lot. For most solar eclipses the Moon's apparent diameter is less than the Sun's and so the whole solar disk is nowhere totally obscured. It is only when the Moon is close to the Earth that, at some places, the whole disk is obscured and a Total Eclipse is seen. The track of the small area on the Earth's surface where a total eclipse can be seen is several thousand miles long but only up to 160 miles wide. Outside this track and outside the short time of totality, maximum about 7 minutes, a Partial Eclipse is seen.

When the Moon is not at its closest to the Earth its apparent diameter is less than that of the Sun and even where the Moon's disk obscures the Sun centrally the outer ring of the Sun's disk is still visible. This is called an Annular Eclipse. Total eclipses of the Sun are much more spectacular than Partial eclipses as virtually all the light from the Sun is blocked out by the Moon and it becomes as dark as night and stars can be seen. The solar chromosphere and corona can be seen. The former as a reddish rim around the eclipsing Moon and the latter as a whitish glow surrounding the eclipsed Sun. The length of totality depends on how close the Moon is to the Earth. The 1991 total eclipse was the longest for 140 years. The next total solar eclipse to be visible in Britain will be in August 1999. It will only be visible from parts of Cornwall and Devon.

WARNING Never look at the Sun with any kind of telescope or binoculars. You could easily blind yourself. It is even dangerous to look at the fully bright Sun with the naked-eye.

Other Eclipses.

The eclipse of an apparently small object by one which appears much larger is generally called an occultation. Thus the Moon occults many stars as it moves across the sky. Observations of occultation's by the Moon were used for a long time to get the most accurate positions for the Moon and have been used to determine the position and size of such strange objects as radio stars. Eclipses of the satellites of Jupiter by the planet, and also by one another, were used in one of the first determinations of the speed of light. And occultation's of stars by the planets have allowed analyses of the planetary atmospheres. Eclipsing binary stars, in which two stars are in orbit about each other and each passes in front of the other as seen from the Earth, have given us most of our knowledge of the masses of different kinds of stars.

GALAXIES

Introduction - Island Universes

Galaxies are the lighthouses that plumb the Universe - constituents of the largest-scale texture we know. They span a vast range of properties, from dwarf galaxies with a few million stars barely outshining the brightest individual star clusters in our own galaxy, to vast assemblages of a trillion stars in the centres of great clusters. Our own galaxy, a reasonably bright spiral system, can be traced at least fifty thousand light-years from its nucleus, and we know of many galaxies much larger yet. Some elliptical galaxies show no evidence of having formed stars since a brilliant epoch early in cosmic history, while spiral and irregular galaxies have been making stars briskly over their entire lifetimes. Some galaxies produce most of their energy deep in the infrared, and some are so diffuse and faint as to be barely detectable against the faint glow of the Earth's night sky.

Some History

Our appreciation of the universe beyond the Milky Way is entirely an achievement of the twentieth century. The objects which we now know to be galaxies had, to be sure, occasionally drawn the curiosity of visual observers from the days of Charles Messier forward, particularly William Parsons (the Earl of Rosse), whose 72-inch (1.8-meter) telescope with its speculum-metal mirror had revealed the intriguing spiral forms of certain dim, cloudy objects (nebulae) seen, by and large, far from the encircling band of the Milky Way. However, further tools were to be needed to unravel the true nature of some of these objects. By the 1920s, photography had revealed that there must be tens of thousands of these objects, by then known as white nebulae to distinguish them from the clearly different gaseous nebulae such as the famous Orion Nebula, accessible to the telescopes of the time. They showed a variety of spiral, elongated, or oval forms. The most plausible theories to account for these nebulae made them either nearby objects - perhaps planetary systems in formation - or extremely distant, truly "island universes" of which our Milky Way, hitherto the entire known Universe, would be merely one among myriads.

The key observation in resolving this dispute came from Edwin Hubble, using the recently completed 100-inch (2.5-meter) telescope on Mount Wilson, California. Targeting the largest and brightest of the "white nebulae", as the ones most likely to be nearby in space, he repeatedly photographed selected portions of them as deeply as the available photographic plates would allow. Faint starlike points had been recognised in these nebulae, but could one show that these were in fact stars such as we know in the solar neighbourhood, and thus at the enormous distances required to make them appear so faint?

Hubble's breakthrough came in identifying stars with a particular kind of cyclic change in brightness, which them "standard candles" whose absolute brightness could be determined - Cepheid variable stars. Henrietta Leavitt at Harvard had shown that this class of pulsating stars has the useful property of a tight correlation between the period required to complete one pulsation in surface temperature and size (and thus brightness) and the amount of energy the star gives off (usually expressed as absolute magnitude, the stellar brightness which we would measure if a star were located at a reference distance of ten parsecs). Cepheid variables gave Hubble the first necessary yardstick in the ladder of extragalactic distances. (One of the major programs for the Hubble Space Telescope is the measurement of galaxy distances beyond the reach of ground-based instruments, by identifying Cepheid variables in more and more distant galaxies. One HST team has recently reported success in measuring Cepheids in galaxies of the Virgo Cluster, about twenty times as distant as the galaxies Hubble the astronomer was observing).

This discovery, in one stroke, opened a whole new vista of the Universe. Within a decade, many of the major strands of galaxy research had begun. Clusters and groups were recognised, classification schemes were proposed, and spectroscopic measurements were begun. Spectra of galaxies proved especially rewarding. Early measures by V.M. Slipher at Lowell Observatory, using very delicate multi-night exposures, had shown that some "spiral nebulae" exhibited unusually large Doppler shifts. It eventually developed that galaxies exhibit, on average, a relation between the redshift of features in their spectra and their estimated distances. This gave a way to estimate the distances of ever fainter and more remote galaxies, and provided the first glimpse of an expanding universe.

Kinds of Galaxies

Scientists and naturalists alike have the urge to sort, classify and organise new phenomena, in the hope of seeing underlying patterns that have physical meaning. Several classifications for galaxies were proposed early in their study; Hubble's classification system has proven remarkably robust, correlating well with physically interesting measurements such as stellar content, gas content, and environment despite being designed only to describe the appearance of the galaxy as seen on photographs with blue-sensitive emulsions. With later extensions by Gerard de Vaucouleurs and Sidney van den Bergh, this remains the most commonly used description of galaxy forms.

Elliptical galaxies were denoted by the letter E and a number describing the galaxy's apparent shape - 0 for a completely round form, 5 for one twice as long as wide, and 7 for the apparently flattest genuine ellipticals. We do not know, solely from an image, the true shape of such a galaxy; the same galaxy might have quite different degrees of flattening if viewed from different directions. Elliptical galaxies are, in general, characterised by old stellar populations and very little of the gas and dust needed to form new stars.

Spirals are divided into ordinary and barred spirals; in barred systems the spiral arms arise from a straight "bar" passing through the centre, while ordinary spirals have a more S-shaped inner configuration. Ordinary spiral are denoted S and barred systems SB. Both usually contain a central bulge, often sharing many properties with elliptical galaxies, surrounded by a thin rotating disk containing whatever spiral structure there may be. Spirals are subdivided into a sequence jointly defined by the winding and prominence of the spiral arms, and the relative importance of the central bulge. Sa galaxies have a bright bulge and tightly wound arms, while Sc galaxies have loosely wound arms and a relatively less important bulge. This sequence Sa-Sb-Sc-Sd has counterparts SBa-SBb-SBc-SBd in the barred spirals. As more detail was observed in some galaxies, intermediate subsets (Sab,Sbc,Scd,S0/a) could be added when necessary.

Some galaxies show no particular organisation, either because some recent event has left them in a disturbed state or because they simply lack the organising rotation and wave motions of a spiral. These are simply called irregulars; the ones that do not result from external disturbance form, in many respects, an extension beyond Sd of the spiral sequence. Hubble recognised that the connections among various types left an apparent hole which he called S0 - objects with a bulge and disk, but little or no star formation, dust, or gas. They would form a bridge between ellipticals and spirals. Later, many genuine S0 galaxies were in act recognised, and understanding their origin promises to tell us much about the history and development of galaxies in general.

Several refinements of the Hubble classification have proven widely useful. Gerard de Vaucouleurs introduced distinctions depending on whether the spiral structure proceeds from the nucleus in an S-shape (s) or from an inner ring (r), or some combination (rs) or (sr). He also recognised intermediate cases SAB between barred and non-barred galaxies. These new dimensions allowed a finer discrimination of galaxy structure and opened the way for more detailed study of the physical properties of spiral galaxies. Sidney van den Bergh noted that the most luminous spirals have long, well-developed spiral arms, and introduced a luminosity classification driven by the organisation and distinctness of the arms; Sc I galaxies are in the mean the brightest Sc galaxies, and Sc V the faintest. Note that the classification is based solely on a galaxy's appearance, with its absolute magnitude a correlating quantity.

Some galaxies are not well described by the Hubble system or its variants, even excluding "train wrecks" resulting from galaxy collisions. There exist, usually in rich clusters, enormous elliptical-like systems that may span millions of light-years with more extended outer regions than a similarly huge elliptical would show. These are given the designation cD, from a scheme developed at Yerkes Observatory by W.W. Morgan. Dwarf galaxies may be irregular, elliptical, or spheroidal, depending on their degree of symmetry and central concentration. Recent work has turned up galaxies of very low surface brightness, which must have had a rather different history from familiar spirals. While many of these look like the ghosts of ordinary spirals, it is not at all clear how they connect to the familiar Hubble types.

Content of Galaxies

We observe stars, gas, and dust in galaxies. Stars come in a wide range of age and mass, and are intricately linked to interstellar matter by processes of stellar birth and death. This means that galaxies have a history, which we can probe either by investigating the makeup of a galaxy in detail, or in a kind of fossil probe unique to astronomy, look at galaxies so distant that the light we observe left them when they were much younger than they are "today".

In tracing the makeup of galaxies, there are numerous clues as to the populations of stars present. Different kinds of stars (giant/dwarf, hot/cool, higher/lower abundance's of heavy elements) have different patterns and intensities of features in their spectra. In most galaxies, we can observe only their overall (integrated) spectrum, so that a mathematical solution can give constraints on the overall population, but the solution is not completely well-determined without additional assumptions (such a a smoothly varying star-formation rate, or fixed ratios of stars at various masses). To resolve these ambiguities, observations of very nearby galaxies are crucial, where individual (luminous) stars can be observed and counted.

Some components of a galaxy stand out in specific kinds of observations, so that interstellar matter and certain kinds of stars can be studied in isolation. The 21-cm radio emission of cold atomic hydrogen traces this component of a galaxy cleanly, giving one index of its gas content and tracing internal motions beautifully. The gas most immediately associated with the birth of new stars is colder and denser than neutral hydrogen, being mostly molecular hydrogen and best observed via the trace molecule CO, which emits spectral lines in the 1-3 mm range. The most massive young stars emit copious ultraviolet radiation, which may be absorbed by surrounding gas and re-emitted as spectral lines including H-alpha in the visible region, so that using special filters and image processing allows a view of these star-forming regions alone (so long as they are not hidden from view by intervening dust). The dust itself emits longer-wavelength infrared radiation, so we can trace the location of interstellar dust and locate the regions where it is warmed by starlight. Going to the ultraviolet, only the hottest stars give off enough radiation to see, so this region also allows us to trace regions of active star formation. Finally, looking at a galaxy in X-rays, we see only the highest-energy components -binary stars in which material falling onto a neutron star or black hole gives rise to extreme temperatures, emission from gas at millions of degrees, and sometimes emission from central quasar-like active nuclei which may not give an accurate indicator of temperature, since so-called non-thermal processes may be involved.

There is growing evidence that we may be completely ignorant of one of the most important constituents of galaxies - the dark matter. If gravity behaves over ranges of thousands of light years in the way that it does over smaller scales, the motions of stars and gas in galaxies, and of gas and galaxies in clusters, require that most of the mass in these systems is on some completely invisible forms. The main lines of evidence include:
 
 -- flat rotation curves in spiral galaxies. The orbital speed measured for material in the outer parts of spirals is nearly constant with distance, without the drop-off which would show that we are observing orbits outside the main mass concentration.
-- velocities of galaxies in clusters. Similarly, the measured motions of galaxies in clusters are too fast for them to be held together by the gravity of the visible stars comprising the galaxies. Hot gas between the galaxies, revealed by its X-ray emission, adds about
an equal amount of mass to the galaxies' stars, but a discrepancy often reaching a factor 10 remains between visible and gravitating masses.
 -- the extent of the hot gas in clusters of galaxies. At its observed temperatures, the amount of mass needed to hold it in place by gravity is comparable to that deduced to from galaxy motions. In fact, in many cases, the gas is regarded as a more reliable tracer, since a cluster contains only so many galaxies which can act as tracer particles, while the hot gas is a continuous medium which can be observed in as much detail as instrumentation permits.

The nature of this unseen matter remains elusive, and has provided a happy hunting ground for observer and theoretician alike. Proposals have included brown dwarf stars, Jupiter-like objects, quantum black holes produced in the early Universe, and a whole zoo of exotic particles which would also be remnants of the early Universe. Assorted astronomical and laboratory searches have yet to tell us what makes up most of the matter in the Universe. We are left with the sobering realisation that all of our vaunted technology and apparatus has been telling us about only 10% of the cosmos.
 

Clusters of galaxies

Early surveys of galaxies on the sky showed that certain regions have more than their share of galaxies; such concentrations as the Virgo cluster were known long before the nature of galaxies was understood. More complete statistics have shown that the distribution of galaxies in space is far from the uniform "sea" first envisaged, with many (perhaps most) galaxies arrayed in groups, clusters with thousands of members, superclusters, and even larger sheets and fingers stretching as far across the Universe as we can reliably map.

Clusters come in a variety of kinds, just as galaxies do. The richest and densest clusters are round assemblages, while sparser clusters have flattened or irregular shapes. The cluster environment is reflected in its galaxy content - dense environments like cluster cores are populated almost solely by elliptical and S0 galaxies, nearly devoid of gas and star formation. Less extreme environments can host, as well, spiral and irregular galaxies. This so-called morphology-density relation has engendered a classic heredity-environment question - were spiral galaxies never formed in those regions which would one day be rich clusters, or are they somehow destroyed or transformed in such clusters? The jury is still out, though there is strong evidence that in some clusters spirals were once numerous and have been transformed by external factors into elliptical or S0 systems. One such transforming mechanism is via galaxy mergers, which, while not common at the high speeds typical of cluster encounters today, might have been more common early on.

A second transforming mechanism could be provided if clusters contain some kind of external medium - intergalactic gas. Such a medium was indeed discovered by early X-ray astronomy satellites, and is known to be ubiquitous in clusters and even galaxy groups. Random motions in the cluster heat this gas to temperatures of 10,000,000 Kelvin, alas, SI usage is that there is no such thing as degrees K making it visible only by its own X-ray emission. This gas typically has as much mass as do stars in the visible galaxies, and as galaxies move through it, will provide an external wind. This would in principle be strong enough to sweep gas out of a spiral galaxy, and a gas-free spiral will cease star formation and quickly look like an S0. Detailed observations in local clusters such as Virgo in fact show that spirals nearest the centre seem to have lost the outermost parts of their gas distributions.

Detailed studies of the distance and redshifts of nearby galaxies have added another dynamic aspect to our understanding of clusters - they are still growing. At greater and greater distances, the gravity of a cluster takes longer to affect the motions of its surrounding galaxies, so that galaxies at larger distances will eventually turn around against the expansion of the Universe and fall into the cluster. Our own local group has a detectable motion toward the Virgo Cluster (more precisely, the core of the Local Supercluster), and such large-scale motions can be found near many nearby clusters. In this sense, the cosmic epoch of cluster formation is now.

Galaxies and cosmology

The very recognition of galaxies as objects at vast distances led to the first attempts to use them as tracers of the structure of the Universe as a whole - observational cosmology. Hubble's promulgation of the evidence for a relation between a galaxy's distance and its redshift led to a picture of an expanding Universe. As observational capabilities have increased, so has the volume of space where astronomers can search for signatures of the geometry of space-time.

The Hubble law for galaxy redshifts implied a uniform expansion - one in which every galaxy sees the same linear relation between distance and redshift when looking at other galaxies. The rate of this expansion is characterised by the Hubble constant - the ratio between redshift and distance for a fictitious average galaxy with no peculiar motion of its own with respect to the expansion. Not only does this value give us the size scale of the Universe, but it gives a measure of its age as well. If one runs the clock backwards on a uniform Hubble expansion, at a constant rate, the age of the expansion is the numerical inverse of the Hubble constant. Even if there has been deceleration of the expansion due to gravity, this age - the Hubble time - gives a scaling value for the age of the Universe.

The exact value of the Hubble constant has been contentious, with strong arguments presented for values from 50 to 100 km/sec per megaparsec. These correspond to Hubble times of, respectively, 20 and 10 billion years. Some of the disagreement between workers on the cosmic distance scale comes from different treatments of local galaxy motions superimposed on the smooth expansion, and some from regarding various measures of distance as primary or secondary. One of the major projects for the Hubble Space Telescope deals with direct measures of galaxies distant enough to expect a clean measurement of the Hubble constant.

The distribution of galaxies into groups, clusters, and superclusters carries information on masses and motions in the early Universe. In brief, if the initial distribution of pre-galactic material was as uniform as the COBE satellite data suggests, then in order to form clusters today surrounded by relatively empty areas, the cluster-galaxies-to-be must have been able to move fast enough to cross (at least) the size of these empty areas in a Hubble time. The necessary gravitational clumping to propel such motion early enough proves to be an important constraint on the early Universe.

Classical cosmology was once described as a search for two numbers -the Hubble constant H_0, and a second value, the deceleration parameter q_0. The deceleration parameter described how fast the Hubble constant changes with cosmic time as the overall gravity of all matter in the Universe slows the expansion. A value of 0 would indicate an empty Universe - mathematically simple and appealing, but not very interesting to us! There are there different cases - an open Universe, in which the expansion will never stop; a closed Universe, in which the expansion will someday stop and reverse; and the critical point between them, where the expansion will constantly slow and approach (but never quite reach) zero. These are separated by the critical value q_0=1/2. Many classical tests for the value of q_0 relied on using galaxies as standard candles, but have been defeated by the fact that galaxies evolve on the same timescales that must be probed to measure q_0. Current efforts in this direction use different probes, such as gravitational lensing or the mean mass density in the local Universe, in efforts to circumvent the unknowns of galaxy evolution. In any case, it is remarkable that q_0 is close to its critical value; otherwise the Universe might not have the right properties for us to exist and discover cosmology.

<Gross simplification alert - specialists will complain, but we don't have enough room for a textbook here>

Galaxy nomenclature and catalogues

Galaxies are generally denoted only by catalogue numbers; only a handful are well-known or unusual enough to rate distinctive names (such as the Whirlpool, Antennae, Pinwheel, and Cartwheel). A given galaxy may sport numbers from several catalogues. The most cited sources are: Messier number - from a list compiled visually by Charles Messier and several colleagues during the eighteenth century. Many of the brightest and most conspicuous galaxies (as well as gaseous nebulae and star clusters) appear in the Messier lists. NGC/IC (New General Catalogue and Index Catalogue) - compilations by J.L.E. Dreyer from the 1860s-1880s. These included results of the complete sky sweeps performed by William and John Herschel and discoveries by others, plus the first harvests of celestial photography. These catalogues include (besides the usual round of clusters and nebulae) about 10,000 of the most conspicuous galaxies. Until recently, almost all galaxies which could be studied in detail had NGC or IC numbers. Arp - Halton Arp produced an atlas of peculiar and interacting galaxies, which first drew the attention of many astronomers to the strange and spectacular forms that galaxies outside the normal Hubble classification can take. UGC (Uppsala General Catalogue) - galaxies only, covering the sky north of -2 degrees 30'. Peter Nilsson produced this catalogue of positions, sizes, orientations, and magnitudes from Palomar Sky Survey photographs.

Several other kinds of name comprise coordinate designations (first digits of the object right ascension and declination, either for epoch 1950 or 2000) and a survey name. Examples are the PKS (radio sources from the Parkes radio telescope in Australia) and IRAS (Infrared Astronomical Satellite) surveys. Thus we may have PKS 1413+003 or IRAS 09104+4109.

Many of the originally published versions of these catalogues are either rather obscure (university observatory transaction series, for example), or out of print (the NGC and IC being notable exceptions). Users of personal computers can get modern versions of these and many more on CD-ROMs (from the Astronomical Data Center at the NASA Goddard Space Flight Center, or the Almageste package from the ASP). Such a level of access, without need of a professional astronomical library, makes many kinds of advanced study and observing programs possible.

Note that wavelength/flux/surface brightness selection enters into what galaxies get selected for a particular catalogue or study. Malin 1, despite being large and luminous, was long missed for being too large. Several researchers have pointed out that galaxy catalogues are dominated by those kinds of galaxies which are easiest to see against the natural glow of the night sky, so we may still be ignorant of important parts of the extragalactic census.

Gamma-Ray Astronomy

Gamma-ray astronomy opens another window through which astronomers can observe the universe. Gamma rays are photons, or quanta, of extremely high-energy electromagnetic radiation, having much shorter wavelengths than X rays. They are produced by nuclear processes such as fission and fusion reactions and radioactive decay. Thus gamma-ray astronomy provides a means for studying the most energetic processes taking place in the universe, such as the creation and destruction of chemical elements within and between the stars. Conversely, however, because the rays are produced by nuclear fission, the presence of unshielded nuclear reactors in Earth orbit is proving a significant hindrance to such studies. Studies of gamma rays can also help explain the origin of the very high-energy particles called cosmic rays, the composition of material throughout the galaxies, and the way in which stars begin to form deep within interstellar clouds of dust and gas. By measuring the gravitational red shift in the gamma-ray region of celestial spectra, astronomers can learn more about the properties of neutron star surfaces, quasars, galactic cores, and the theoretically existing phenomena known as the black hole.

Development

The science of gamma-ray astronomy did not get started until well into the 20th century. Before 1960 unsuccessful attempts were made to detect celestial gamma rays with relatively simple instruments carried high into the atmosphere by balloons. Over the next ten years more sophisticated instruments were still unable to discriminate specific spectral lines of celestial gamma rays from the diffuse, uniform background radiation arising from other phenomena.In 1972 the first certain detection of celestial gamma rays was made with equipment aboard the U.S. OSO-3 satellite. In that same year another satellite, OSO-7, was used to detect gamma-ray emission lines in the Sun's spectrum. Thereafter, knowledge of the gamma-ray universe grew rapidly by means of such satellites as the U.S. SAS-2 (1972-73) and the European COS-B (1975-82). These and other devices have found gamma rays to be more intense in regions corresponding to the structure of our galaxy, probably arising from the interaction of cosmic rays with interstellar gas.

Three pulsars within our galaxy, two in or near the crab nebula and the other in the constellation Vela, are emitting gamma rays in fractional-second pulses. The largest discrete source of gamma rays (as well as other high-energy rays) yet discovered in our galaxy is the binary star system Cygnus X-3. Gamma rays originating from outside our galaxy have been detected emanating from Supernova 1987A. Other discrete sources thus far identified include radio and Seyfert galaxies and quasars. Unexplained bursts of low-energy gamma rays have also been observed, each lasting for roughly ten seconds, at intensities that fluctuate even at the shortest resolvable time intervals. No explanation has been found for the "bursters," although one theory posits that they originate in the universe's background radiation.

Instruments

Devices for detecting gamma rays include assemblies of scintillators of various types. More complicated techniques use large area detectors that, in effect, supply pictures of the tracks produced by the charged particles produced by high-energy photons. These spark-chamber telescopes make it possible to distinguish gamma-ray events and determine the arrival direction of each gamma ray individually. Higher energy gamma rays can produce detectable flashes of light in the atmosphere, through the Cherenkov effect of bombarded particles being caused to move at speeds faster than that at which light moves through the air. These flashes can be observed by suitably equipped ground-based telescopes and by high-altitude balloons. The Gamma Ray Observatory, the first major Earth satellite devoted solely to the study of rays, was successfully launched in April 1991 from a U.S. space shuttle.

MERIDIAN ASTRONOMY

What Is Meridian Astronomy?

We can all remember having Geography lessons and learning about latitude and longitude (even though most of us have forgotten which is which). If you look at a globe of the Earth, or at the maps in an atlas, you will see the familiar network of lines of latitude and longitude. But if you look down from an airliner you do not see black lines running all over the countryside and across the sea. The network is an imagined framework for stating geographical positions, and it is the job of surveyors to make accurate measurements so that the shape of continents and the positions of cities can be plotted out on this framework. Latitude is measured north and south, starting from the Equator and finishing at the poles.

Longitude is measured east and west, starting from a standard line which, by international agreement, has been chosen so as to run through the Royal Observatory at Greenwich. Notice that latitude and longitude do not tell us anything about height above the ground, or depth beneath it.

If you look at a celestial globe or at the maps of the sky in a star atlas, you will see a similar network of criss-crossing lines. But if you look up into the starry sky itself, you certainly do not see these lines running through the constellations. They are an imagined network for stating positions in the sky, and it is the job of Meridian Astronomy to make accurate measurements so that the positions of stars, planets and other objects in the sky can be plotted out on this framework.

In the sky, declination (like latitude on the Earth) is measured north and south, starting from 0 at the Celestial Equator which is overhead at the Earth's Equator. Declination increases to 90 at the Celestial Poles which are overhead at the Earth's poles. Corresponding to longitude, we have right ascension which is measured eastwards (never westwards) round the sky. The zero-point of right ascension, corresponding to Greenwich, is a point with the mysterious name of The First Point Of Aries. This is simply the point of the sky where the Sun appears to be as it crosses the Celestial Equator from south to north on about March 21 each year.

To sum up, Meridian Astronomy is that branch of astronomy concerned with making accurate measurements of positions (right ascension and declination) in the sky. Notice that these measurements do not include the distance of the object from the Earth; the measurement of distances is looked after by other branches of astronomy.

How Is Meridian Astronomy Done?

The Meridian astronomer uses a special telescope called a Transit Circle. The special thing about the telescope is the way in which it is mounted. Most telescopes are pivoted in two directions so that they can be aimed at any part of the sky and can follow a star as it appears to move across the sky. Such telescopes usually live in round houses with domes that can turn so as to give the telescope a view in any direction. The Transit Circle is pivoted in one direction only, with its cross axis supported by two fixed piers, east and west of the telescope. This means that it can look south, overhead, north, straight down, or at some slanting angle north or south. It lives in a rectangular house, with shutters that can open in the north and south walls, and more shutters in the roof that can open along the north--south centre--line. It does not follow the moving stars, but just watches them go by.

While a star is passing by, the observer has to measure two things. He observes accurately the time at which the star passes due north or south, that is, the time at which it crosses his meridian. He also measures accurately the angle to which he has to tilt his telescope to see the star, that is, the elevation or altitude of the star as it crosses his meridian. From the observed time he can work out the star's right ascension and from the observed altitude angle he can work out the star's declination. But, before he can do this, he needs to know the time at which the First Point of Aries crosses his meridian. Unfortunately these zero lines and points are not visible, and so he cannot make direct observations of them. His next problem then, is to find out where they are.

One way of locating the Celestial Equator would be to observe some object which moves above and below the Equator, so that on the average, its declination is zero. The Sun could be used for this purpose, because every year it moves among the stars along a track called the Ecliptic, which lies equally above and below the Equator. The Moon and the planets also follow tracks near the Ecliptic, so they too will have an average declination of zero if we observe them for a long enough time.

Another way of finding the invisible Equator is to use the fact that it is 90 from the Celestial Poles. These too are invisible, but can be located because they are the centres of the circles traced out by the stars each day and night. If we choose a star near the pole, it will trace out a fairly small circle. We can observe its altitude as it passes the meridian above the pole, and then, twelve hours later, observe its altitude as it re-crosses the meridian below the pole. The altitude of the pole, at the centre of the circle, is just mid--way between the two observed altitudes of the star.

In order to locate the First Point of Aries, all we have to do is to trace out the Ecliptic, the average path of the Sun, Moon and planets, and find the point where it crosses the Equator. There are actually two such points, diametrically opposite to one another in the sky: the First Point of Aries and the First Point of Libra. We select the First Point of Aries as our zero.

Why Not Use Photography?

Photographic telescopes are very good at showing the relative positions of many faint stars in a small region of the sky, but we cannot fit the photographs together like a jig--saw puzzle to cover the whole sky, and of course, the photographs do not show the invisible lines of right ascension and declination. In order to relate the faint--star positions to the invisible framework, we choose a limited number of reference stars spread over the sky and observe these stars with Transit Circles all over the world. The photographic telescopes can then relate the faint stars to the invisible framework via the reference stars.

The Carlsberg Automatic Meridian Circle

The Carlsberg Meridian Circle was made in 1952 to the same specification as the Cooke Reversible Transit Circle which was in operation at the RGO until 1982. It carried out observing programmes at Copenhagen University Observatory (CUO) from 1964 to 1976 when a major overhaul of the instrument was undertaken in order to automate the observing process. This removed the observer completely from the telescope thus eliminating such effects as heating of the instrument by the observer's proximity, mis-setting of the circle, mis-reading of the meteorological data and last, but not least, the inaccuracy of the observer's measurements.

In order to utilise the resultant increase in efficiency, it was decided to move the Carlsberg Automatic Meridian Circle (CAMC) to a better site. The telescope was taken out of operation in Denmark in March 1983 and refurbished before shipping to the Roque de Los Muchachos Observatory on La Palma in the Canary Islands in August 1983. It is operated through a tripartite collaboration between RGO, CUO and the Instituto y Observatorio de Marina, Spain.

The CAMC is now operating very efficiently on La Palma and the new site is providing exceptional observing conditions. In the first two years of operation, it measured the positions of over 20,000 stars, including 300 reference stars which enabled the European Space Agency to make sure that the spacecraft Giotto passed within the planned 500 km of the nucleus of Comet Halley.

Why Do It at All?

Three hundred years ago the Royal Observatory was founded at Greenwich, not to do fancy scientific research, but to solve a very practical problem that was of considerable importance to our life as a trading nation. That problem was the finding of the longitude of a ship at sea so that it could be navigated properly. This required using the stars as landmarks, or points of known position, and the observatory started making the necessary observations of star positions. A little later Sir Isaac Newton realised the scientific value of these observations, and encouraged the observatory to continue them in order to check his famous law of gravity as it applied to the Moon and planets. Later again, it became possible to combine the observations over a period of a century or so in order to show up the small individual motions of different stars. Nowadays it is possible to work out, from these motions, various theories of how old the stars are, and how the galaxy of stars evolved into its present state and shape. Finally, accurate star positions are needed to keep artificial satellites and spacecraft (such as Giotto) pointing the right way, and to help astronauts navigate. Meridian Astronomy may be a very old and classical part of astronomy, but it is still very much alive and is making an important contribution to our rapidly increasing knowledge of the universe.

Royal Greenwich Observatory.

METEORS AND METEORITES

All of us are familiar with the sight of a sudden flash of light passing across part of the night sky, possibly followed by a lasting streak of light. Although there are many aeroplanes and artificial satellites which can be seen none of these look the same as a `shooting star' or `falling-star'. Very occasionally the `shooting-star' is very bright, brighter than the stars, and sometimes appears to emit sparks or even break up into pieces. On rare occasions its passage can be heard as a roar or a series of remote explosions. These very bright objects are often called fire-balls. The trail left by a bright `shooting-star' may last for less than a second or for a fire-ball may last for minutes.

Meteors

What we are witnessing when we see a shooting-star is a small piece of interplanetary matter, called a meteor, entering the Earth's atmosphere and `burning up' at a height of about 100 km. These small particles are moving very fast relative to the Earth and when they enter the Earth's atmosphere they are rapidly slowed down. This means that they lose a lot of energy which appears as heat. Both the particle and the air that is forcing its way past are made very hot. The particle, unless it is large, is completely evaporated and the air in the path of the meteor is ionised. We see light from the emission of radiation from the ionised gas and from the white hot evaporating particle. The trail is the hot gas gradually cooling down. The astronauts when they re-enter the Earth's atmosphere have to take severe precautions to orientate their spacecraft correctly so that the shielding which is designed to absorb and dissipate the heat caused by the impact with the atmosphere can do its work. If, for some reason, the shields did not work the astronauts would suffer the same fate as a meteor

Meteorites

When large chunks of the interplanetary matter enter the atmosphere it is unlikely that all of the chunk will be evaporated. The outer layers will disappear but the centre is likely to survive and will hit the ground. The object which hits the ground is called a meteorite. The speed with which small meteorites hit the ground can be around 500 km/h. More than 2000 meteorites have been recovered. They are of different types, Stony meteorites, iron meteorites and the rare carbonaceous chondrites. The largest meteorite that has been found is the 60 tonne Hoba iron meteorite; the largest stony meteorite weighs about a tonne and the Allende carbonaceous chondrite was a series of chunks that totalled about 5 tonnes. Impact craters are known on the Earth that correspond to bodies far larger than these. One of the best known is the Arizona crater in the USA which is 1280 metres across and 180 metres deep. It was formed several thousand years ago by a 250,000 tonne meteorite with a diameter of 70 metres hitting the Earth at a speed nearly 60,000 km/h.

Meteor Streams

Many meteors originated in material stripped off from comets by radiation from the Sun. This material continues to follow the orbit of the originating comet but gets spread out along the orbit. If the path of the Earth passes through this stream of particles then we will see many meteors whose paths in the sky will appear to radiate from one point in the sky (the radiant) which is in the direction from which the stream is coming. Many such meteor showers are seen throughout the year. Some are associated with known comets while others are remnants of comets that are unknown. Most showers produce about 20, or so, meteors per hour but there are showers which can produce thousands of meteors over a period of less than an hour. Such shows are, unfortunately, very rare. Meteor showers are named after the constellation from which they appear to radiate.

Sporadic Meteors

Meteors may be seen on any night of the year when the Moon is not bright. If no prominent shower is active then most of the meteors that are seen will come from random directions in space and will thus show no tendency to radiate from any part of the sky. These meteors are called sporadic meteors and about 7 per hour is the normal rate for them to be seen. Most fire-balls and meteorites are sporadic meteors. The material in these meteors is associated with the material in the asteroids and it is likely that they represent material that has come from fragmented asteroids. Some rarer types of meteoric matter are believed to have originated on the Moon and on Mars, probably as a result of matter being exploded from the surface by the impact of a large meteorite.

METEOR SHOWERS

Meteors are flashes of light commonly referred to as shooting stars. They are small bits of ice, rock and or metal that hit our atmosphere at an altitude of 60 to 100 kilometres. Because of their velocities of tens of thousands of kilometres per hour, they are incinerated by friction with molecules of air high in the atmosphere. Most particles are the size of grains of sand. Some may be baseball sized. Meteors streak across the sky in an instant, sometimes being bright enough to cast shadows. Often a glowing path remains visible for a few seconds after the meteor vanishes. When a large chunk of material, perhaps the size of a basketball, hits our atmosphere and forms an exceptionally bright meteor, it is called a fireball. Fireballs often break up in flight causing bursts of light.

On any night of the year you can go out and see meteors. If the sky is bright because of the Moon or city lights you will have to patient and wait for one that is bright enough to shine through the background glow. In a dark sky you can expect to see about six per hour. But there are some times when there are many more meteors visible. These times are known as showers. Showers occur each year at about the same time.

Shower meteoroids, particles that are travelling in space towards Earth, are material left behind by comets. Comets are composed mostly of ice. Some orbit the Sun in elliptical orbits. Others come from deep space, pass near the Sun, and then fly off never to be seen again. The orbital path of the comet is often filled with grains of material that have separated from the comet's nucleus. It is possible for the path of a comet to intersect the orbit of Earth. In all probability Earth will be nowhere near the comet at that time, but as Earth orbits the Sun it will cross the path of the long gone comet and encounter some of the grains. When that occurs we have a shower.

Since Earth will reach the same point in space at the same time each year we can predict the dates of showers. Some showers are better than others and each shower varies from year to year. They last several days but peak during one night. Showers are named for the apparent point from which the meteors appear to originate. In other words, if you observe several meteors and plot their positions on a star chart, and then draw a line backwards, the lines will meet at one small region of the sky. For example, during the shower that peaks around October 20/21 of each year your map would show meteor streaks all over the sky. Extending each of those lines backwards, or in the opposite direction from which the meteor was heading, would find those lines meeting in the constellation of Orion. This shower is known as the Orionid meteor shower. This shower is from material lost by Halley's Comet.

The most famous and reliable meteor shower is the Perseid which occurs on the night of August 11/12 each year. Typically there are ten times the usual number of shooting stars, 60 or more per hour. The debris that creates the Perseids is from the comet P/Swift-Tuttle. Swift-Tuttle is a periodic comet-meaning that it is in orbit around the Sun. Its orbit carries it across Earth's orbit once each 130 years. The last passage was in December, 1992 so the Perseid shower could turn into a storm for the next several years. There might also be a large number of large chunks that could produce fireballs.

The best time to view meteors is typically after midnight. As Earth spins on its axis each day it also orbits the Sun. As viewed from above the north pole of the Sun or Earth, Earth spins counter clockwise and orbits the Sun counter-clockwise. This means that, at any given moment, half of Earth is facing forward into the direction that Earth orbits, and half facing in the direction that Earth has been. From midnight until noon we are on the leading side of Earth and from noon until midnight on the trailing side. In the evening the meteors have to catch up with Earth from behind. After midnight Earth is running into the particles and the number of meteors increases as does the speed at which they hit the atmosphere. This similar to the effect of driving in the rain. The front windshield is being hit with many raindrops while the back window may actually be dry.

Observing meteors is probably the easiest astronomical activity. All you need is a view of the sky and some patience. The darker sky the better, but you need no special equipment. In fact a telescope will do no good at all since telescopes have narrow fields of view and meteors cross a lot of sky. Binoculars can be used to try to see if there is any glow left in the meteors path but can not be used to spot the meteors themselves. Try to make yourself comfortable; a lawn chair or blanket will help and be sure to dress warmly enough. Snacks and drinks are a good idea, too.

If you want to make a record of your observations you should have a copy of a wide field of view star chart and a pencil. If you are in a group arrange the members so that each person is looking off in a different direction with a chart that covers the stars in their view. That way you can cover the whole sky.

You can photograph meteors but is difficult to get good photographs. You will need a camera, probably a 35mm, with a B setting or some other method for keeping the shutter open for a long period of time, and a tripod. A cable release can be attached to most 35mm cameras. The cable release can be secured so that the film remains exposed to the sky for as long as you leave it open. With a normal or wide angle lens and fast film, ISO 200 or higher, you are hoping that a bright meteor will shoot through the cameras field of view while the shutter is open. Plan to take several photographs of about ten minutes in length. If you think that a meteor has been captured on film, stop the exposure and go on to the next one.

MOON PHASES

Phases of the Moon is at the top of the list of things that students seriously misunderstand. Most teachers run into problems in trying to explain the Moon's phases to youngsters and evidence suggests that many have a very difficult time with the concepts. The problem starts immediately when the teacher uses a light piece of chalk on a dark board. Is he or she making the drawing as a positive or a negative? The supplies for this activity are rather modest. Each student will need a light coloured sphere of some sort. Ideally it can be placed on the end of a pencil. Try 5 cm. (2") or greater white Styrofoam balls. Get a larger sphere (15 cm. or so) for your use as leader. You need a light source to serve as the Sun. A lamp with a bright bulb (400 watts) and the shade removed works fine. A dark room is also required.

With the lamp in the centre of the room have each student place the ball at arm's length between the bulb and their eyes. They should hold the pencil in their left hand. The bulb is the Sun, the ball is the Moon and they are Earth. The view from their eyes is the same for both this exercise and for observations of the real sky.

At the start, the "Moon" is blocking the "Sun." (This is actually demonstrating a total solar eclipse which is very rare for any given location on Earth.) Usually the Moon passes above or below the Sun as viewed from Earth. Have the students move their moon up or down a bit so that they are looking into the Sun. As they look up (or down) at their moon they will see that all of the sunlight is shining on the far side, opposite the side that they are viewing. This phase is called "new moon" (like "no moon").

They should now move their hand towards the left, about 45 degrees (1/8) of the way around counter clockwise. Have them observe the sunlight on their Moon now. They should see the right hand edge illuminated as a crescent. The crescent will start out very thin and fatten up as the Moon moves farther away from the Sun. (Note: although the Moon is closer to the Sun during new and crescent phases, it is still 400 times closer to Earth; i.e., the Sun is VERY far away in reality.)

When their Moon is at 90 degrees to the left students will see the right half of the Moon illuminated. This phase is called "first quarter." Remember that fully one half of the sphere is illuminated at all times (except during lunar eclipses) but the illuminated portion that we observe changes as the Moon changes position. As they continue to move counter-clockwise past first quarter, the Moon goes into its "gibbous" phase (more than half but less than fully illuminated) which grows as the Moon moves towards 180 degrees.

When the Moon reaches the position directly opposite the Sun, as viewed from Earth, the half viewed from Earth is fully illuminated (unless the student's head is causing a lunar eclipse). Of course only half of the Moon is illuminated. It has taken the Moon about two weeks to move from new to full. This growth in illumination is known as "waxing." The Moon chases the Sun across the (day and night) sky.

Students should now switch the pencil to their right hand and face in the general direction of the Sun. Starting with the Moon at full, students should continue the Moon's counter clockwise motion. They will observe the reverse of the Moon's phases seen so far with the left portion of the Moon illuminated.

After the gibbous phase diminishes, the Moon will reach the 270 degrees position, straight out to the right. This is "third" or "last quarter." It is followed by a thinning crescent and a return to new moon. From full to new the Moon has been "waning" and leading the Sun. The phase cycle takes 29.53 days. Be sure to observe the real Moon. Most newspapers give the Moon phases along with the weather data, and of course Stella 2000 provides a real-time readout of the Moon's phase in Reports after clicking on the lunar disc in the sky window.

PHOTOMETRY

Measuring the Brightness of Stars

Photometry dates back more than 2,000 years to when the Greek astronomer Hipparchos divided the naked-eye stars into six brightness classes. The brightest visible stars he called stars of the first magnitude and the faintest visible he called stars of the sixth magnitude. Pogson in 1856 defined the magnitude scale so that a difference of 5 magnitudes was exactly a factor of 100 in brightness, which had earlier been shown by Herschel to be roughly the intensity ratio of first to sixth magnitude stars. Pogson defined his scale to be a logarithmic one where the difference in magnitude of two stars and is directly linked to the ratio of their intensities. The human eye can detect differences of brightness of about 20% or 0.2 magnitudes and with training and use of special techniques this can be reduced to 10%.

The apparent brightness of any object in the sky is due to its intrinsic brightness and to its distance. For instance, the brightest known object in the Universe is a very faint quasar as seen from the Earth but if it were as close as the nearest galaxy it would be easily visible to the naked-eye. After 1850, photography was used to determine the brightnesses of stars as the density and size of the image is directly related to brightness of the star. It was soon apparent, however, that the photographic magnitudes did not agree very well with those obtained visually. The reason for this is that early photographs responded mainly to blue light whereas the eye responds best to greenish-yellow. Stars have different ratios in the amount of light they emit in these different colours; some stars appear reddish, others bluish and this difference causes the determined brightnesses to be different. With modern photographic plates, which have been developed specially for astronomy, and filters to isolate different regions of the spectrum astronomers can use large field telescopes to obtain plates covering several square degrees of the sky. Such plates can contain a million images of stars and galaxies which can be measured by computer-controlled automatic measuring machines, such as the APM at Cambridge.

During this century photo-conductive cells and later, and more importantly, photoelectric devices were developed. These, used with sensitive amplifiers, now detect each individual photon received by the telescope and by counting these, astronomers can directly compare the light intensities received from individual stars. The modern successor to the photographic plate, the CCD (used in many TV cameras) is capable of measuring individual photons from stars and galaxies in fields of a few square arc minutes. For many applications it is supplanting the photoelectric photometer.

Identical distances, ages and compositions. The observation of all the members of a cluster gives us an instant picture of what a large number of stars are like at one particular age. By combining pictures for different clusters of different ages we can deduce how a star's properties change with age. The classical diagram of this kind is shown in Fig. 1. It is known that even the very fastest phases of the evolution of the stars take thousands of years and it is likely that the Sun will remain essentially the same for more than 5 thousand million years.

Variable Stars

Our Sun is believed to be of constant brightness (although it may vary very slightly). Many other stars, however, change their brightness quite markedly. By studying the manner in which they change, astronomers can learn more about the details of stellar evolution and the internal structure of stars. Many stars are not single stars, like the Sun, but double. The two component stars circle one another and if the plane of their mutual orbit is near the line of sight, one star will pass in front of the other thus eclipsing it and giving a reduction in the observed total brightness. Due to the very large distances to stars, the two stars cannot be separated even in the biggest telescopes but by an analysis of the shape of the light variation the masses and sizes of the two individual stars may be found.

Some stars are intrinsically variable; that is, the variability is due to internal causes rather than external ones. The cepheid variables are members of a very important class of variables. These are stars that brighten and fade because of a cyclic expansion and contraction of the whole star. In 1908 Miss Leavitt noted that in one of the Magellanic clouds (which are satellite galaxies to the Milky Way), there was a strong relationship between the brightness of the cepheids and their period of pulsation. This period-luminosity relation, as it is called, has been studied in great detail and is now one of the most important methods used for determining the distances to other galaxies.

Orbits and Gravitation

The first to propose a system of planetary orbits which would set the scene for major advances was Copernicus, who in De Revolutionibus Orbium Coelestium (1543), argued that the planets and the Earth were in orbit round the Sun. Although a major breakthrough, Copernicus proposed circular orbits for the planets and accurate astronomical observations soon began to show that his proposal was not strictly accurate. In 1600, Kepler became assistant to Tycho Brahe who was making accurate observations of the planets. After Brahe died in 1601, Kepler continued the work, calculating planetary orbits to unprecedented accuracy. Kepler showed that a planet moves round the Sun in an elliptical orbit which has the Sun in one of its two foci. He also showed that a line joining the planet to the Sun sweeps out equal areas in equal times as the planet describes its orbit. Both these laws were first formulated for the planet Mars, and published in Astronomia Nova (1609). However scientists certainly did not accept Kepler's first two laws with enthusiasm. The first was given a cool reception and was certainly thought to require further work to confirm it. The second of Kepler's laws suffered an even worse fate in being essentially ignored by scientists for around 80 years. Kepler's third law, that the squares of the periods of planets are proportional to the cubes of the mean radii of their orbits, appeared in Harmonice Mundi (1619) and, perhaps surprisingly in view of the above comments, was widely accepted right from the time of its publication.

Hooke wrote a letter to Newton. In the letter he explained how he considered planetary motion to be the result of a central force continuously diverting the planet from its path in a straight line. Newton did not answer this directly but explained his own idea that the rotation of the Earth could be proved from the fact that an object dropped from the top of a tower should have a greater tangential velocity than one dropped near the foot of the tower. Newton provided a sketch of the path that the particle would follow, quite incorrectly showing it spiral towards the centre of the Earth. Hooke replied that his theory of planetary motion would lead to the path of the particle being an ellipse so that the particle, were it not for the fact that the Earth was in the way, would return to its original position after traversing the ellipse.

Newton, not one to like being corrected, had to admit that his original sketch was incorrect but he "corrected" Hooke's sketch on the assumption that gravity was constant. Hooke replied to Newton that his own theory involved an inverse square law for gravitational attraction. Many years later Hooke was to claim priority for proposing the inverse square law of gravitation and used this letter to support his claim.

It is worth emphasising that there is a major step to be made from an inverse square law of force to explain planetary motion and a universal law of gravitation. Certainly the motion of the Moon round the Earth was not seen to necessarily be part of the same laws which govern the motion of the planets round the Sun. Fifty years after these events, Newton was to record his own recollections of these events which, although interesting, do not really agree with the known historical facts [I preserve Newton's old English.]

"In the same year I began to think of gravity extending to ye orb of the Moon & (having found out how to estimate the force with wch globe revolving within a sphere presses the surface of a sphere) from Kepler's rule of the periodical times of the Planets being in sesquialternate proportion to their distances from the centres of their Orbs, I deduced that the forces wch keep the Planets in their Orbs must reciprocally as the squares of their distances from the centres about w‚î they revolve: & thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the Earth, & found them answer pretty nearly. All this was in the two plague years of 1665-1666".

In 1684, Hooke and Halley discussed, at the Royal Society, whether the elliptical shape of planetary orbits was a consequence of an inverse square law of force depending on the distance from the Sun. Halley wrote that "Mr Hook said that he had it, but that he would conceale it for some time so that others, triing and failing might know how to value it, when he should make it publick".

Later in the same year in August, Halley visited Newton in Cambridge and asked him what orbit a body would follow under an inverse square law of force, Sr Isaac replied immediately that it would be an Ellipsis, the Doctor struck with joy & amazement asked him how he knew it, why, said he I have calculated it, whereupon Dr Halley asked him for his calculation without any farther delay, Sr Isaac looked among his papers but could not find it, but he promised him to renew it, & then to send it him.

Despite the claims by Newton in the above quote, he had in fact proved this result in 1680 as a direct result of the letters from Hooke, Newton indeed reworked his proof and sent a nine page paper (De motu corporum in gyrum ) On the motion of bodies in an orbit to Halley. It did not state the law of universal gravitation nor Newton's three laws of motion. All this was to develop over the next couple of years to become the basis for the Principia. Halley was largely responsible for ensuring that the Principia was published. He received Newton's complete manuscript by April of 1687 but there were many problems not the least being that Newton tried to prevent the publication of the Book III when Hooke claimed priority with the inverse square law of force.

In the Principia the problem of two attracting bodies with an inverse square law of force is completely solved (in Propositions 1-17, 57-60 in Book I). Newton argues that an inverse square law must give produce elliptical, parabolic or hyperbolic orbits. A bright comet had appeared on 14 November 1680. It remained visible until 5 December 1680 when it moved too close to the Sun to be observed. It reappeared two weeks later moving away from the Sun along almost the same path along which it had approached. Newton found good agreement between its orbit and a parabola. He uses the orbit of this comet, and comets in general, to support his inverse square law of gravitation in the Principia. In the Principia, Newton also deduced Kepler's third law. He looked briefly (in Propositions 65 and 66) at the problem of three bodies. However, Newton later said that an exact solution for three bodies exceeds, if I am not mistaken, the force of any human mind.

It is important at this stage to examine the problems which now arose. Newton had completely solved the theoretical problem of the motion of two point masses under an inverse square law of attraction. For more than two point masses only approximations to the motion of the bodies could be found and this line of research led to a large effort by mathematicians to develop methods to attack this three body problem. However the problem of the actual motion of the planets and moons in the solar system was highly complicated by other considerations.

Even if the Earth - Moon system were considered as a two body problem, theoretically solved in the Principia, the orbits would not be simple ellipses. Neither the Earth nor the Moon is a perfect sphere so does not behave as a point mass. This was to lead to the development of mechanics of rigid bodies, but even this would not give a completely accurate picture of the two body problem since tidal forces mean that neither the Earth nor Moon is rigid. The observational data used by Newton in the Principia was provided by the Royal Greenwich Observatory. However, modern scholars such as Richard Westfall claim that Newton sometimes adjusted his calculations to fit his theories. Certainly the observational evidence could not be used to prove the inverse square law of gravitation. Many problems relating observation to theory existed at the time of the Principia and more would arise.

Newton's method had found almost parabolic orbits for a number of comets. When he computed the orbits for three comets which had appeared in 1537, 1607 and one Halley observed himself in 1682, he found that the characteristics of the orbits were almost identical. Halley deduced they were the same comet and later was able to identify it with one which had appeared in 1456 and 1378. He computed an elliptical orbit for the comet and he noticed that Jupiter and Saturn were perturbing the orbit slightly between each return of the comet. Taking the perturbations into account, Halley predicted the comet would return and reach perihelion (the point nearest the Sun) on 13 April 1759. He gave an error of one month on either side of this date. The comet was actually first seen again in December 1758 reaching perihelion on 12 March 1759.

In 1713 a second edition of the Principia, edited by Roger Cotes, appeared. Cotes wrote a preface defending the theory of gravitation given in the Principia. Cotes was himself to provide the next mathematical steps by finding the derivatives of the trigonometric functions, results published after his death.

Euler developed methods of integrating linear differential equations in 1739 and made known Cotes' work on trigonometric functions. He drew up lunar tables in 1744, clearly already studying gravitational attraction in the Earth, Moon, Sun system. Clairaut. and D'Alembert were also studying perturbations of the Moon and, in 1747, Clairaut proposed adding a 1/r = "^4" term to the gravitational law to explain the observed motion of the perihelion, the point in the orbit of the Moon where it is closest to the Earth.

However by the end of 1748 Clairaut had discovered that a more accurate application of the inverse square law came close to explaining the orbit. He published his version in 1752 and, two years later, d'Alembert published his calculations going to more terms in his approximation than Clairaut. In fact this work was of importance in having Newton's inverse square law of force accepted in Continental Europe.

The Earth's axis of rotation precesses, that is the direction of the axis of rotation itself rotates in a circle with a period of about 26000 years. Precession is caused by the gravitational attraction of the Sun on the equatorial bulge of the Earth, the bulge being predicted by Newton. Cassini made a measurement of an arc of longitude in 1712 but obtained a result which wrongly suggested that the Earth was elongated at the poles. In 1736, Maupertuis obtained the correct result verifying Newton's predictions. However this illustrates the problems encountered by mathematicians at this time with basic data about bodies in the solar system, even the Earth, being highly inaccurate.

There is a small periodic effect called nutation superimposed on precession caused by the motion of the perihelion of the Moon. This superimposed effect has a period of 18.6 years and was first observed by Bradley in 1730 but not announced until 18 years later when he had observed the full cycle. D'Alembert quickly showed that Bradley's observed period was deducible from the inverse square law and Euler further clarified this with further work on the mechanics of rigid bodies during the 1750's.

The problem of the orbits of Jupiter and Saturn had troubled astronomers and mathematicians from Kepler's first theory of elliptical orbits. The Paris Academy offered Prizes for work on this topic in 1748, 1750 and 1752. In 1748. Euler's studies of the perturbation of Saturn's orbit won him the Prize. His work for the 1752 Prize, however, contains many mathematical errors and was not published until 17 years later. It did contain significant ideas, however, which were independently discovered since Euler's work was not known.

Lagrange won the Paris Academy Prize in 1764 for a work on the libration of the Moon. This is a periodic movement in the axis the Moon pointing towards the Earth which allows, over a period of time, more than 50% of the surface of the Moon to be seen. He also won the Paris Academy Prize of 1766 for work on the orbits of the moons of Jupiter where he gave a mathematical analysis to explain an observed inequality in the sequence of eclipses of the moons.

Euler, from 1760 onwards, seems to be the first to study the general problem of three bodies under mutual gravitation (rather than looking at bodies in the solar system) although at first he only considered the restricted three body problem when one of the bodies has negligible mass. When one body has negligible mass it is assumed that the motions of the other two can be solved as a two body problem, the body of negligible mass having no effect on the other two. Then the problem is to determine the motion of the third body attracted to the other two bodies which orbit each other. Even in this form the problem does not lead to exact solutions. Euler, however, found a particular solution with all three bodies in a straight line.

The first comet to have an elliptical orbit calculated which was far from a parabola was observed by Messier in 1769. The elliptical orbit was computed by Lexell who correctly realised that the small elliptical orbit had been produced by perturbations by Jupiter. The comet made no reappearance and again Lexell correctly deduced that Jupiter had changed the orbit so much that it was thrown far away from the Sun.

The Paris Academy Prize of 1772 for work on the orbit of the Moon was jointly won by Lagrange and Euler. Lagrange submitted (Essai sur le problme des trois corps) in which he showed that Euler's restricted three body solution held for the general three body problem. He also found another solution where the three bodies were at the vertices of an equilateral triangle. Lagrange considers his solutions do not apply to the solar system but we now know the both the Earth and Jupiter have small bodies sharing their orbits in the equilateral triangle solution configuration discovered by Lagrange. For Jupiter these bodies are called Trojan planets, the first to be discovered being Achilles in 1908. The Trojan planets move 60 degrees in front and 60 degrees behind Jupiter at what are now called the Lagrangian points.

However all this work on the orbits of bodies in the solar system failed to keep pace with observations which always seemed one step ahead giving further and yet further problems for the theorists to explain. Laplace, from 1774 onwards, became an important contributor to the attempt of the theoreticians to explain the observations of the observers.

Lagrange introduced the method of variation of the arbitrary constants in a paper in 1776 stating that the method was of interest in celestial mechanics and, in special cases, had been already been used by Euler, Laplace and himself. Lagrange published further major papers in 1783 and 1784 on the theory of perturbations of orbits using methods of variations of the arbitrary constants and, in 1785, applied his theory to the orbits of Jupiter and Saturn.

An important development occurred on 13 March 1781 when the astronomer William Herschel (father of John Herschel) observing in his private observatory in Bath, England found (a curious either nebulous star or perhaps a comet.) Almost immediately it was realised that it was a planet and within a year of its discovery it was shown to have an almost circular orbit. The name Uranus was eventually adopted although Herschel himself proposed Georgium Sidus (perhaps in the hope of more funds from King George ) while in France it was known as Herschel until the middle of the following century.

Laplace read a memoir to the Paris Academy on 23 November 1785 in which he gave a theoretical explanation of all the remaining major discrepancies between theory and observation of all the planets and their moons excluding Uranus. He also addressed the question of the stability of the solar system for the first time. This work was to culminate in the publication of (Micanique cileste) (1799) in which, among many other important results, he claimed to prove the stability of the solar system.

The remaining observations not explained by theory at the end of the 18 C concerned the motion of the Moon. Laplace's work of 1787, that of Adams of 1854 and later Delaunay's work described below eventually provided solutions. Observations of Uranus in the early years of the 19 C showed there were problems with its orbit and by 1830 Uranus had departed by 15" from the best fitting ellipse.

The next body to be discovered in the solar system was the minor planet Ceres, discovered in 1801. In 1766 J D Titus and in 1772 J E Bode had noted that (0+4)/10, (3+4)/10, (6+4)/10, (12+4)/10, (24+4)/10, (48+4)/10, (96+4)/10 gave the distances of the 6 known planets from the Sun (taking the Earth's distance to be 1) except there was no planet at distance 2.8. The discovery of Uranus at distance 19.2 was close to the next term of the sequence 19.6.

A search was made for a planet at distance 2.8 and on 1 January 1801 G Piazzi discovered such a body. On 11 February Piazzi fell ill and ended his observations. The new planet, unobserved by other astronomers, passed behind the Sun and was lost. However Gauss, in a brilliant piece of work was able to compute an orbit from the small number of observations. In fact Gauss' method requires only 3 observations and is still essentially that used today in calculating orbits. Ceres, so named by Piazzi, was found to be where Gauss predicted by Olbers. Its distance from the Sun fitted exactly the 2.8 prediction of the Titus-Bode law.

Johann Encke, a student of Gauss, computed (using Gauss's method) an elliptical orbit for the comet of 1818. It had the shortest known period of 3.3 years. The period showed a periodic decrease which Encke could not explain by perturbations by other planets. Work on the general three body problem during the 19 C had begun to take two distinct lines. One was the developing of highly complicated methods of approximating the motions of the bodies. The other line was to produce a sophisticated theory to transform and integrate the equations of motion. The first of these lines was celestial mechanics while the second was rational or analytic mechanics. Both the theory of perturbations and the theory of variations of the arbitrary constants were of major mathematical significance as well as contributing greatly to the understanding of planetary orbits.

Papers published by Hamilton in 1834 and 1835 made major contributions to the mechanics of orbiting bodies. as did the significant paper published by Jacobi in 1843 where he reduced the problem of two actual planets orbiting a sun to the motion of two theoretical point masses. As a first approximation the theoretical point masses orbited the centre of gravity of the original system in ellipses. He then used a method, first discovered by Lagrange, to compute the perturbations. Bertrand extended Jacobi's work in 1852.

In 1836, Liouville studied planetary theory, the three body problem and the motion of the minor planets Ceres and Vesta. Many mathematicians around this period devoted much of their time to these problems. Liouville made a number of very important mathematical discoveries while working on the theory of perturbations including the discovery of Liouville's theorem "when a bounded domain in phase space evolves according to Hamilton's equations its volume is conserved".

By around 1840 irregularities in the orbit of Uranus prompted many scientists to seek reasons them. Alexis Bouvard (a collector of planetary data) proposed that a planet might explain the irregularities and he wrote to the English Astronomer Royal Airy proposing this idea. Bessel also proposed this solution to the problem but died before completing his calculations. Delaunay, famed for his work on the orbit of the Moon, investigated the perturbations in a paper of 1842. Arago urged Le Verrier to work on the problem and on 1 June 1846. Le Verrier showed that the irregularities could be explained by an unknown planet and he determined the coordinates at which the planet would be found. The astronomer Galle in Berlin found the new planet on 26 September remarkably close to the position predicted by Le_Verrier".The observations were confirmed on 29 September 1846 at the Paris observatory.

This was a remarkable achievement for Newton's theory of gravitation and of celestial mechanics. Le Verrier's personal triumph however was somewhat diminished when, on 15 October, a letter was published from the English astronomer Challis claiming that John Couch Adams.of Cambridge University had made similar calculations to those of Le Verrier which he had completed in September 1845. His predicted position for the new planet had been almost as accurate as Le Verrier's but the English astronomers had been much less industrious in their search. John Herschel and Airy also supported Adams claim. In fact Challis had, after a long delay, begun to search for the new planet on 29 July 1846. He observed it on 4 August but did not compare his observations with those of the previous night so only realised he had observed the planet after its discovery in Berlin about 7 weeks later was unimpressed by Adams priority claims.

Mr Adams does not have the right to appear in the history of the discovery of the planet. Le Verrier either with a detailed citation or even with the faintest allusion. In the eyes of all impartial men, this discovery will remain one of the most magnificent triumphs of theoretical astronomy, one of the glories of the Acadi mie and one of the most beautiful distinctions of our country.

The success of the mathematical analysis of both Le Verrier and Adams was somewhat fortunate. The orbits which they predicted were different and both not particularly good except around the 1840's. An argument over the naming of the new planet was, however, unfortunate. Arago was given the task of selecting a name by Le Verrier and Le Verrier made his wishes known in an unsubtle way by writing a paper on Herschel's planet, insisting that Uranus should be named after its discoverer. Encke, Gues's' student referred to above, suggested Neptune as a name. However, Arago said, ( commit myself never to call the new planet by any other name than Le Verrier. In this way, I think I will give an impeachable token of my love for science and follow the inspiration of a legitimate national sentiment).

The argument over a name led to Le Verrier resigning from the Bureau des Longitudes and eventually, Arago lost his battle over the name which became accepted as Neptune.
Delaunay, mentioned above for his work on the perturbations of Uranus, worked for 20 years on lunar theory. He treated it as a restricted three body problem and used transformations to produce infinite series solutions for the longitude, latitude and parallax for the Moon. The beginnings of his theory was published in 1847 and he had refined the theory until it was published in 2 volumes in 1860 and 1867 and was extremely accurate, its only drawback being the slow convergence of the infinite series. Delaunay detected discrepancies between the observed motion of the Moon and his predictions. Le Verrier claimed that Delaunay's methods were in error but Delaunay claimed that the discrepancies were due to unknown factors. In 1865 Delaunay suggested that the discrepancies arose from a slowing of the Earth's rotation due to tidal friction, an explanation which is today believed to be correct.

Le Verrier had published an account of his theory of Mercury in 1859. He pointed out that there was a discrepancy of 38" per century between the predicted motion of the perihelion (the point of closest approach of the planet to the Sun) which was 527" per century and the observed value of 565" per century. In fact the actual discrepancy was 43" per century and this was pointed out by later by Simon Newcomb. Le Verrier was convinced that a planet or ring of material lay inside the orbit of Mercury but being close to the Sun had not been observed.

Le Verrier's search proved in vain and by 1896 Tisserand had concluded that no such perturbing body existed. Newcomb explained the discrepancy in the motion of the perihelion by assuming a minute departure from an inverse square law of gravitation. This was the first time that Newton's theory had been questioned for a long time. In fact this discrepancy in the motion of the perihelion of Mercury was to provide the proof that Newtonian theory had to give way to Einstein's theory of relativity.

G W Hill published an account of his lunar theory in 1878. Earlier approaches started with an elliptic orbit of the Moon round the Earth, assuming the Sun had no effect, then perturbing the orbit to take account of the gravitation of the Sun. Hill, on the other hand, started with circular orbits for the Sun and Moon about the Earth and went on to examine the perturbations caused by assuming elliptic orbits.

The final major step forward in the study of the three body problem which we shall consider was that Poincari Bruns proved in 1887 that apart from the 10 classical integrals, 6 for the centre of gravity, 3 for angular momentum and one for energy, no others could exist. In 1889 Poincari proved that for the restricted three body problem no integrals exit apart from the Jacobian. In 1890 Poincari proved his famous recurrence theorem, namely that in any small region of phase space trajectories exist which pass through the region infinitely often. Poincare published 3 volumes of Les mithods nouvelle de la michanique celeste between 1892 and 1899. He discussed convergence and uniform convergence of the series solutions discussed by earlier mathematicians and proved them not to be uniformly convergent. The stability proofs of Lagrange and Laplace became inconclusive after this result.

Poincari introduced further topological methods in 1912 for the theory of stability of orbits in the three body problem. It fact Poincari essentially invented topology in his attempt to answer stability questions in the three body problem. He conjectured that there are infinitely many periodic solutions of the restricted problem, the conjecture being later proved by Birkhoff. The stability of the orbits in the three body problem was also investigated by Levi-Civita and others.

The History of Astronomy
by Steven J. Dick

The history of astronomy comprises three broadly defined areas that have characterised the science of the heavens since its beginnings. With varying degrees of emphasis among particular civilisations and during particular historical periods, astronomers have sought to understand the motions of celestial bodies, to determine their physical characteristics, and to study the size and structure of the universe. The latter study is known as cosmology. From the dawn of civilisation until the time of Copernicus, astronomy was dominated by the study of the motions of celestial bodies. Such work was essential for astrology, for the determination of the calendar, and for the prediction of eclipses, and it was also fuelled by the desire to reduce irregularity to order and to predict positions of celestial bodies with ever-increasing accuracy. The connection between the calendar and the motions of the celestial bodies is especially important, because it meant that astronomy was essential to determining the times for the most basic functions of early societies, including the planting and harvesting of crops and the celebration of religious feasts.

The celestial phenomena observed by the ancients were the same as those of today. The Sun progressed steadily westward in the course of a day, and the stars and the five visible planets did the same at night. The Sun could be observed at sunset to have moved eastward about one degree a day against the background of the stars, until in the course of a year it had completely traversed the 360 degree path of constellations that came to be known as the zodiac. The planets generally also moved eastward along the zodiac, with 8 degrees of the Sun's apparent annual path (the ecliptic), but at times they made puzzling reversals in the sky before resuming their normal eastward motion. By comparison, the Moon moved across the ecliptic in about 27 1/3 days and went through several phases. The earliest civilisations did not realise that these phenomena were in part a product of the motion of the Earth itself; they merely wanted to predict the apparent motions of the celestial bodies.

Although the Egyptians must have been familiar with these general phenomena, their systematic study of celestial motions was limited to the connection of the flooding of the Nile with the first visible rising of the star Sirius. An early attempt to develop a calendar based on the Moon's phases was abandoned at too complex, and as a result astronomy played a lesser role in Egyptian civilisation than it otherwise might have. Similarly, the Chinese did not systematically attempt to determine celestial motions. Surprising evidence of a more substantial interest in astronomy is found the presence of ancient stone alignments and stone circles found throughout Europe and Great Britain, the most notable of which is Stonehenge in England. As early as 3000 BC, the collection of massive stones at Stonehenge functioned as an ancient observatory, where priests followed the annual motion of the Sun each morning along the horizon in order to determine the beginning of the seasons. By about 2500 BC, Stonehenge may have been used to predict eclipses of the Moon. Not until 1000 AD were similar activities undertaken by New World cultures.

 Babylonian Tables

Astronomy reached its first great heights among the Babylonians. In the period from about 1800 to 400 BC, the Babylonians developed a calendar based on the motion of the Sun and the phases of the Moon. During the 400 years that followed, they focused their attention on the prediction of the precise time the new crescent Moon first became visible and defined the beginning of the month according to this event. Cuneiform tablets deciphered only within the last century demonstrate that the Babylonians solved the problem within an accuracy of a few minutes of time; this was achieved by compiling precise observational tables that revealed smaller variations in the velocity of the Sun and of the Moon than ever before measured. These variations--and others such as changes in the Moon's latitude--were analysed numerically by noting how the variations fluctuated with time in a regular way. They used the same numerical method, utilising the same variations, to predict lunar and solar eclipses.

Greek Spheres and Circles

The Greeks used a geometrical rather than a numerical approach to understand the same celestial motions. Influenced by Plato's metaphysical concept of the perfection of circular motion, the Greeks sought to represent the motion of the divine celestial bodies by using spheres and circles. This explanatory method was not upset until Kepler replaced the circle with the ellipse in 1609.

Plato's student Eudoxus of Cnidus, c.408-c.355 BC, was the first to offer a solution along these lines. He assumed that each planet is attached to one of a group of connected concentric spheres centred on the Earth, and that each planet rotates on differently oriented axes to produce the observed motion. With this scheme of crystalline spheres he failed to account for the variation in brightness of the planets; the scheme was incorporated, however, into Aristotle's cosmology during the 4th century BC. Thus the Hellenic civilisation that culminated with Aristotle attempted to describe a physical cosmology. In contrast, the Hellenistic civilisation that followed the conquests of Alexander the Great developed over the next four centuries soon predominant mathematical mechanisms to explain celestial phenomena. The basis for this approach was a variety of circles known as eccentrics, deferents, and epicycles. The Hellenistic mathematician Apollonius of Perga, c.262-c.190 BC, noted that the annual motion of the Sun can be approximated by a circle with the Earth slightly off-centre, or eccentric, thus accounting for the observed variation in speed over a year. Similarly, the Moon traces an eccentric circle in a period of 27 1/3 days. The periodic reverse, or retrograde, motion of the planets across the sky required a new theoretical device. Each planet was assumed to move with uniform velocity around a small circle (the epicycle) that moved around a larger circle (the deferent), with a uniform velocity appropriate for each particular planet. Hipparchus, c.190-120 BC, the most outstanding astronomer of ancient times, made refinements to the theory of the Sun and Moon based on observations from Nicaea and the island of Rhodes, and he gave solar theory essentially its final form. It was left for Ptolemy, c.100-c.165, to compile all the knowledge of Greek astronomy in the Almagest and to develop the final lunar and planetary theories.

With Ptolemy the immense power and versatility of these combinations of circles as explanatory mechanisms reached new heights. In the case of the Moon, Ptolemy not only accounted for the chief irregularity, called the equation of the centre, which allowed for the prediction of eclipses. He also discovered and corrected another irregularity, evection, at other points of the Moon's orbit by using an epicycle on a movable eccentric deferent, whose centre revolved around the Earth. When Ptolemy made a further refinement known as prosneusis, he was able to predict the place of the Moon within 10', or 1/6 deg, of arc in the sky; these predictions were in good agreement with the accuracy of observations made with the instruments used at that time. Similarly, Ptolemy described the motion of each planet in the Almagest, which passed, with a few notable elaboration's, through Islamic civilisation and on to the Renaissance European civilisation that nurtured Copernicus.

The revolution associated with the name of Copernicus was not a revolution in the technical astronomy of explaining motions, but rather belongs to the realm of cosmology. Prodded especially by an intense dislike of one of Ptolemy's explanatory devices, known as the equant, which compromised the principle of uniform circular motions, Copernicus placed not the Earth but the Sun at the centre of the universe; this view was put forth in his De revolutionibus orbium caelestium (On the Revolutions of the Heavenly Spheres, 1543). In that work, however, he merely adapted the Greek system of epicycles and eccentrics to the new arrangement. The result was an initial simplification and harmony as the diurnal and annual motions of the Earth assumed their true meaning, but no overall simplification in the numbers of epicycles needed to achieve the same accuracy of prediction as had Ptolemy. It was therefore not at all clear that this new cosmological system held the key to the true mathematical system that could accurately explain planetary motions.

 Keplerian Ellipses and Newtonian Gravitation

The German astronomer Johannes Kepler provided a daring solution to the problem of planetary motions and demonstrated the validity of the heliocentric theory of Copernicus, directly associating the Sun with the physical cause of planetary motions. At issue for Kepler was a mere 8' discrepancy between theory and observation for the position of the planet Mars. This degree of accuracy would have delighted Ptolemy or Copernicus, but it was unacceptable in light of the observations of the Danish astronomer Tycho Brahe, made from Uraniborg Observatory with a variety of newly constructed sextants and quadrants and accurate to within 1' to 4'. This new scale of accuracy revolutionised astronomy, for in his Astronomia nova (New Astronomy, 1609), Kepler announced that Mars and the other planets must move in elliptical orbits, readily predictable by the laws of planetary motion that he proceeded to expound in this work and in the Harmonices mundi (Harmonies of the World, 1619). Only by abandoning the circle could the heavens be reduced to an order comparable to the most accurate observations.

Kepler's laws and the Copernican theory reached their ultimate verification with Newton's enunciation of the laws of universal gravitation in the Principia (1687). In these laws, the Sun was assigned as the physical cause of planetary motion. The laws also served as the theoretical basis for deriving Kepler's laws. During the 18th century, the implications of gravitational astronomy were recognised and analysed by able mathematicians, notably Jean d'alembert, Alexis Clairraut, Leonhard Euler, Joseph Lagrange, and Pierre Laplace. The science of celestial mechanics was born and the goal of accurate prediction was finally realised.

During all of this discussion the stars had been regarded as fixed. While working on his catalogue of 850 stars, however, Hipparchus had already recognised the phenomenon known as the Precession Of The Equinoxes, an apparent slight change in the positions of stars over a period of hundreds of years caused by a wobble in the Earth's motion. In the 18th century, Edmond Halley, determined that the stars had their own motion, known as Proper Motion, that was detectable even over a period of a few years. The observations of stellar positions, made with transit instruments through the monumental labours of such scientists as John Flamsteed, laid the groundwork for solving a cosmological problem of another era: the distribution of the stars and the structure of the universe.

Physical Characteristics of Celestial Bodies

The study of the motions of the celestial bodies required only that they be regarded as mere points of light. But already in the 4th century BC, Aristotle proposed in his De caelo (On the Heavens) a theory of the physical nature of these bodies, which conferred on them the properties of perfection and unchangeability thought appropriate to the divine celestial regions, in contrast to the ever-changing Earth. In the next century, Aristarchus of Samos, again exhibiting the mathematical penchant of the Hellenistic era, offered an observationally based estimate, although about ten times too low, of the sizes of the Sun and Moon. These size estimates were universally admired, and Aristotle's physical hypothesis only sporadically challenged, by medieval commentators.

Moon and Planets

The physical similarity of the Earth and planets became a matter of significant inquiry only after Copernicus showed that the Earth and all of the planets are in motion around the central Sun. The question might have remained forever unresolved had not Galileo Galilei constructed a telescope, although not the first in Europe, which he turned toward the heavens in 1609. The results, announced in the Sidereus nuncius (Sidereal Messenger, 1610), were shattering to the Aristotelian view. The Moon was found to be a mountainous body "not unlike the face of the Earth." Galileo's further discovery of the moons of Jupiter and the phases of Venus was more evidence that the planets had Earthlike characteristics.

Such discoveries--extremely important as verification for the physical reality of the Copernican theory--slowly accumulated throughout the 17th and 18th centuries. The nature of the Moon was discussed in increasing detail in Kepler's Somnium (1634), Johannes Hevelius's Selenographia (1647), and G. B. Riccioli's Almagestum novum (1651). Christiaan Huygens, the greatest observational astronomer of the 17th century, first correctly interpreted the rings of Saturn in his Systema Saturnium (1659), observed dark markings on Mars, and belts of clouds on Jupiter, and speculated that Venus was shrouded in clouds. With more refined telescopes, such as those built by Sir William Herschel in England, the details of the solar system became better known. Herschel himself made the spectacular discovery of the planet Uranus in 1781. In 1846, the presence of yet another planet (Neptune), predicted by J. C. Adams and U. J. J. Leverrier, was confirmed observationally--a triumph for both theory and observation.

With the invention of spectroscopy in the 1860s, and with the work of Sir William Huggins and Norman Joseph Lockyer in England, P. A. Secchi in Rome, Cesar Janssen in Paris, Lewis Rutherfurd (1816-92) in the United States, and Hermann Vogel (1842-1907) in Germany, the science of astrophysics was born. By spreading the light of the celestial bodies into the constituent colours of the spectrum, each interspersed with lines characteristic of the elements present, a powerful new tool was given to the astronomer. The ability to determine the chemical composition of planetary atmospheres and even of the stars, a task which the positivist philosopher Auguste Comte had offered less than 30 years before as the paradigm of what science could never achieve, now became possible.

Sun and Stars

Astrophysics yielded its most substantial results in the study of the Sun and stars, where the myriads of observed spectral lines were gradually interpreted as a precise set of chemical fingerprints. With spectroscopy and the almost simultaneous invention of photography, astronomers compiled great catalogues mapping the solar spectrum. Knowledge of the Sun, which had not advanced substantially since Galileo's discovery of sunspots, now outstripped planetary astronomy. The means were at hand to determine the temperature, composition, age, and structure of the Sun and to compare this data with that of the other stars, which were now for the first time proved to be other suns. In conjunction with advances in nuclear physics the investigations of the latter half of the 19th century led to the building of a firm foundation for a discussion in the first quarter of the 20th century of the internal constitution and evolution of stars. This program was pioneered by A. S. Eddington and Karl Schwarzchild. By providing a wealth of data previously unavailable, astrophysics fuelled the controversy over the possible existence of extraterrestrial life not only in our solar system, but throughout a universe of other possible solar systems.

Cosmology: The Structure if the Universe

The study of the motions and physical characteristics of celestial bodies could be undertaken on a case-by-case basis. Cosmology, on the other hand, by definition had to mold from the whole body of observations a coherent theory of the structure of the universe. From the time of Aristotle until the Copernican revolution this structure had been conceived firmly as Earth-centred, in spite of Aristarchus's heliocentric views. Between the inner Earth and the outer sphere of fixed stars each planet was considered imbedded in a crystalline sphere that was in uniform circular motion. Within this neat compact structure the whole history of humankind and the universe unfolded. The work of Kepler and Newton on planetary motion and of Galileo and others on the physical nature of the planets resulted in the gradual acceptance during the 17th century of the Copernican heliocentric hypothesis as a physically valid system. This acceptance had profound implications for cosmology. Not only did Kepler's theory of ellipses make obsolete the theory of crystalline spheres of Aristotle, the absence of any detectable stellar parallax--apparent change in the direction of a star--even when measured from opposite sides of the Earth's orbit, demonstrated the necessity of acknowledging the enormous size of the universe. The subsequent shift from the closed tightly structured world to an infinite homogenous universe was one of the landmarks in the history of astronomy. Giordano Bruno and Thomas Digges were among its earliest exponents, and Descartes and Newton incorporated it as a standard part of the new view of the universe.

The Galaxy

The downfall of the concept of the sphere of fixed stars opened the way for investigations into the distribution of the stars. The phenomenon of the Milky Way, shown by Galileo to consist of myriads of stars, hinted that some previously unsuspected structure might exist among the stars. In 1750 the English theologian and astronomer Thomas Wright sought to explain the brilliantly luminous band of the Milky Way as a collection of stars that extended further in the direction of the band than in other directions. In 1780, William Herschel initiated an observational program of star counts, or gauges, of selected regions of the sky. By assuming that the brightness of a star is a measure of its distance from the Earth, this program resulted in a picture of a flattened disc-shaped system with the Sun near the centre. In spite of his incorrect assumptions, Herschel's research marked the beginnings of an understanding of the structure of the stellar system and earned him the title of founder of stellar astronomy.

Because of the lack of a direct method for determining stellar distances, progress in cosmology lagged for more than a century after Herschel's star gauges. Only with improved instrumentation did Friedrich Bessel, Wilhelm Struve, and Thomas Henderson (1798-1844) in 1838 succeed in measuring the first stellar distances. An annual parallactic shift of .31" in the position of the star 61 Cygni implied a distance equivalent to 590,000 times that of the Earth from the Sun. But difficulties innate to the method resulted in fewer than 300 known stellar distances by the end of the century--far too few to solve the problem of the structure of the stellar system.

Along with continuous attempts at parallax measurements, a major task of 19th-century astronomers was the compilation of astronomical catalogues and atlases containing the precise magnitudes, positions, and motions of stars. The work of Friedrich Argelander, David GILL, and J. C. Kapteyn is especially notable in this regard, with the latter two astronomers utilising new photographic techniques. Such surveys yielded the two-dimensional distribution of stars over the celestial sphere. Heroic efforts were made, especially by Hugo von Seeliger, to extrapolate from this data to an understanding of three-dimensional structure.

Real progress was finally made only through an analysis of the extremely small motions of stars, known as proper motion. Building on the astronomical catalogues of James Bradley, G. F. Arthur von Auwers (1838-1915), and Lewis Boss (1846-1912), and on his own observations, J. C. Kapteyn, exploiting the new field of statistical astronomy, applied statistical methods of distance determination to find an ellipsoidal shape for the system of stars. In 1904 he found that the stars streamed in two directions. Only in 1927 did J. H. Oort, working on the basis of Bertil Linblad's studies, determine that Kapteyn's observational data could be accounted for if the galaxy were assumed to be rotating. In a cosmological shock comparable to the Copernican revolution four centuries before, the Galaxy was found to be 100,000 light years in diameter, with the Earth's solar system some 30,000 light years from the centre.

Other Galaxies

The question of whether or not the Galaxy constituted the entirety of the universe came to a head in the 1920s with the debate between H. D. Curtus and Harlow Shapley. Curtis argued that nebulae are island universes similar to but separate from our own galaxy; Shapley included the nebulae in our galaxy. The controversy was settled when E. P. Hubble detected Cepheid stars in the Andromeda nebula and used them in a new method of distance determination, demonstrating that Andromeda and many other nebulae are far outside the Milky Way. Thus the universe was found to consist of a large number of galaxies, spread like islands through infinite space.

Such was the progress of astronomy from the time of the Babylonian observations of planetary motions to within a few degrees accuracy, to the Greek determinations of positions within a few minutes of arc, to the 19th-century measurements of parallax and proper motions in fractions of a second of arc. The concern of astronomers evolved from the determination of apparent motions to the observation of planetary surfaces, and ultimately to the measurement of the motions of the stars themselves, and of galaxies and systems of galaxies.

RELATIVITY

Albert Einstein's theory of relativity has caused major revolutions in physics and astronomy during the 20th century. It introduced to science the concept of "relativity"--the notion that there is no absolute motion in the universe, only relative motion--thus superseding the 200-year-old theory of mechanics of Isaac Newton. Einstein showed that we reside not in the flat, Euclidean space and uniform, absolute time of everyday experience, but in another environment: curved space-time. The theory played a role in advances in physics that led to the nuclear era, with its potential for benefit as well as for destruction, and that made possible an understanding of the microworld of elementary particles and their interactions. It has also revolutionised our view of cosmology, with its predictions of apparently bizarre astronomical phenomena such as the big bang, neutron stars, black holes, and gravitational waves. The theory of relativity is a single, all-encompassing theory of space-time, gravitation, and mechanics. It is popularly viewed, however, as having two separate, independent theoretical parts--special relativity and general relativity. One reason for this division is that Einstein presented special relativity in 1905, while general relativity was not published in its final form until 1916. Another reason is the very different realms of applicability of the two parts of the theory: special relativity in the world of microscopic physics, general relativity in the world of astrophysics and cosmology.

A third reason is that physicists accepted and understood special relativity by the early 1920s. It quickly became a working tool for theorists and experimentalists in the then-burgeoning fields of atomic and nuclear physics and quantum mechanics. This rapid acceptance was not, however, the case for general relativity. The theory did not appear to have as much direct connection with experiment as the special theory; most of its applications were on astronomical scales, and it was apparently limited to adding minuscule corrections to the predictions of Newtonian gravitation theory; its cosmological impact would not be felt for another decade. In addition, the mathematics of the theory were thought to be extraordinarily difficult to comprehend. The British astronomer Sir Arthur Eddington, one of the first to fully understand the theory in detail, was once asked if it were true that only three people in the world understood general relativity. He is said to have replied, "Who is the third?"

This situation persisted for almost 40 years. General relativity was considered a respectable subject not for physicists, but for pure mathematicians and philosophers. Around 1960, however, a remarkable resurgence of interest in general relativity began that has made it an important and serious branch of physics and astronomy. (By 1977, Eddington's remark was recalled at a conference on general relativity attended by more than 800 researchers in the subject.) This growth has its roots, first, beginning around 1960, in the application of new mathematical techniques to the study of general relativity that significantly streamlined calculations and that allowed the physically significant concepts to be isolated from the mathematical complexity, and second, in the discovery of exotic astronomical phenomena in which general relativity could play an important role, including quasars (1963), the 3-kelvin microwave background radiation (1965), pulsars (1967), and the possible discovery of black holes (1971). In addition, the rapid technological advances of the 1960s and '70s gave experimenters new high-precision tools to test whether general relativity was the correct theory of gravitation.

The distinction between special relativity and the curved space-time of general relativity is largely a matter of degree. Special relativity is actually an approximation to curved space-time that is valid in sufficiently small regions of space-time, much as the overall surface of an apple is curved even though a small region of the surface is approximately flat. Special relativity thus may be used whenever the scale of the phenomena being studied is small compared to the scale on which space-time curvature (gravitation) begins to be noticed. For most applications in atomic or nuclear physics, this approximation is so accurate that relativity can be assumed to be exact; in other words, gravity is assumed to be completely absent. From this point of view, special relativity and all its consequences may be "derived" from a single simple postulate. In the presence of gravity, however, the approximate nature of special relativity may manifest itself, so the principle of equivalence is invoked to determine how matter responds to curved space-time. Finally, to learn the extent that space-time is curved by the presence of matter, general relativity is applied.

SPECIAL RELATIVITY

The two basic concepts of special relativity are the inertial frame and the principle of relativity. An inertial frame of reference is any region, such as a freely falling laboratory, in which all objects move in straight lines with uniform velocity. This region is free from gravitation and is called a Galilean system. The principle of relativity postulates that the result of any physical experiment performed inside a laboratory in an inertial frame is independent of the uniform velocity of the frame. In other words, the laws of physics must have the same form in every inertial frame. A corollary is that the speed of light must be the same in any inertial frame (because a speed-of-light measurement is a physical experiment) regardless of the speed of its source or that of the observer. Essentially all the laws and consequences of special relativity can be derived from these concepts.

The first important consequence is the relativity of simultaneity. Because any operational definition of simultaneous events at different locations involves the sending of light signals between them, then two events that are simultaneous in one inertial frame may not be simultaneous when viewed from a frame moving relative to the first. This conclusion helped abolish the Newtonian concept of an absolute, universal time. In some ways the most important consequences and confirmations of special relativity arise when it is merged with quantum mechanics, leading to many predictions in agreement with experiments, such as elementary particle spin, atomic fine structure, antimatter, and so on. The mathematical foundations of special relativity were explored in 1908 by the German mathematician Hermann Minkowski, who developed the concept of a "four-dimensional space-time continuum," in which time is treated the same as the three spatial dimensions--the fourth dimension of Minkowski space-time.

THE PRINCIPLE OF EQUIVALENCE

The exact Minkowski space-time of special relativity is incompatible with the existence of gravity. A frame chosen to be inertial for a particle far from the Earth where the gravitational field is negligible will not be inertial for a particle near the Earth. An approximate compatibility between the two, however, can be achieved through a remarkable property of gravitation called the weak equivalence principle (WEP): all modest-sized bodies fall in a given external gravitational field with the same acceleration regardless of their mass, composition, or structure. The principle's validity has been checked experimentally by Galileo, Newton, and Friedrich Bessel, and in the early 20th century by Baron Roland von Eotvos (after whom such experiments are named). If an observer were to ride in an elevator falling freely in a gravitational field, then all bodies inside the elevator, because they are falling at the same rate, would consequently move uniformly in straight lines as if gravity had vanished. Conversely, in an accelerated elevator in free space, bodies would fall with the same acceleration (because of their inertia), just as if there were a gravitational field.

Einstein's great insight was to postulate that this "vanishing" of gravity in free-fall applied not only to mechanical motion but to all the laws of physics, such as electromagnetism. In any freely falling frame, therefore, the laws of physics should (at least locally) take on their special relativistic forms. This postulate is called the Einstein equivalence principle (EEP). One consequence is the gravitational red shift, a shift in frequency f for a light ray that climbs through a height h in a gravitational field, given by (delta f)/f = gh/c(2) where g is the gravitational acceleration. (If the light ray descends, it is blue shifted.) Equivalently, this effect can be viewed as a relative shift in the rates of identical clocks at two heights. A second consequence of EEP is that space-time must be curved. Although this is a highly technical issue, consider the example of two frames falling freely, but on opposite sides of the Earth. According to EEP, Minkowski space-time is valid locally in each frame; however, because the frames are accelerating toward each other, the two Minkowski space-times cannot be extended until they meet in an attempt to mesh them into one. In the presence of gravity, space-time is flat only locally but must be curved globally.

Any theory of gravity that fulfils EEP is called a "metric" theory (from the geometrical, curved-space-time view of gravity). Because the equivalence principle is a crucial foundation for this view, it has been well tested. Versions of the Eotvos experiment performed in Princeton in 1964 and in Moscow in 1971 verified EEP to 1 part in 10(12). Gravitational red shift measurements using gamma rays climbing a tower on the Harvard University campus (1965), using light emitted from the surface of the Sun (1965), and using atomic clocks flown in aircraft and rockets (1976) have verified that effect to precision's of better than 1 percent.

GENERAL RELATIVITY

The principle of equivalence and its experimental confirmation reveal that space-time is curved by the presence of matter, but they do not indicate how much space-time curvature matter actually produces. To determine this curvature requires a specific metric theory of gravity, such as general relativity, which provides a set of equations that allow computation of the space-time curvature from a given distribution of matter. These are called field equations. Einstein's aim was to find the simplest field equations that could be constructed in terms of the space-time curvature and that would have the matter distribution as source. The result was a set of 10 equations. This is not, however, the only possible metric theory. In 1960, C. H. Brans and Robert Dicke developed a metric theory that proposed, in addition to field equations for curvature, equations for an additional gravitational field whose role was to mediate and augment the way in which matter generated curvature. Between 1960 and 1976 it became a serious competitor to general relativity. Many other metric theories have also been invented since 1916.

An important issue, therefore, is whether general relativity is indeed the correct theory of gravity. The only way to answer this question is by means of experiment. In the past scientists customarily spoke of the three classical tests proposed by Einstein: gravitational red shift, light deflection, and the perihelion shift of Mercury. The red shift, however, is a test of the equivalence principle, not of general relativity itself, and two new important tests have been discovered since Einstein's time: the time-delay by I. I. Shapiro in 1964, and the Nordtvedt effect by K. Nordtvedt, Jr., in 1968.

The confirmation of the deflection of starlight by the Sun by the solar eclipse expedition of 1919 was one of the triumphant moments for general relativity and brought Einstein world-wide fame. According to the theory, a ray of light propagating through the curved space-time near the Sun should be deflected in direction by 1.75 seconds of arc if it grazes the solar surface. Unfortunately, measurements of the deflection of optical starlight are difficult (in part because of need for a solar eclipse to obscure the light of the Sun), and repeated measurements between 1919 and 1973 yielded inaccurate results. This method has been supplanted by measurements of the deflection of radio waves from distant quasars using radio-telescope interferometers, which can operate in broad daylight. Between 1969 and 1975, 12 such measurements ultimately yielded agreement, to 1 percent, with the predicted deflection of general relativity.

The time-delay effect is a small delay in the return of a light signal sent through the curved space-time near the Sun to a planet or spacecraft on the far side of the Sun and back to Earth. For a ray that grazes the solar surface, the delay amounts to 200 millionths of a second. Since 1964, a systematic program of radar ranging to the planets Mercury and Venus, to the spacecraft Mariners 6, 7, and 9, and to the Viking orbiters and landers on Mars has been able to confirm this prediction to better than half of 1 percent.

Another of the early successes of general relativity was its ability to account for the puzzle of Mercury's orbit. After the perturbing effects of the other planets on Mercury's orbit were taken into account, an unexplained shift remained in the direction of its perihelion (point of closest approach to the Sun) of 43 seconds of arc per century; the shift had confounded astronomers of the late 19th century. General relativity explained it as a natural effect of the motion of Mercury in the curved space-time around the Sun. Recent radar measurements of Mercury's motion have confirmed this agreement to about half of 1 percent.

The Nordtvedt effect is one that does not occur in general relativity but is predicted by many alternative metric theories of gravity, including the Brans-Dicke theory. It is a possible violation of the equality of acceleration of massive bodies that are bound by gravitation, such as planets or stars. The existence of such an effect would not violate the weak equivalence principle that was used as a foundation for curved space-time, as that principle applies only to modest-sized objects whose internal gravitational binding is negligible. One of the remarkable properties of general relativity is that it satisfies EEP for all types of bodies. If the Nordtvedt effect were to occur, then the Earth and Moon would be attracted by the Sun with slightly different accelerations, resulting in a small perturbation in the lunar orbit that could be detected by lunar laser ranging, a technique of measuring the distance to the Moon using laser pulses reflected from arrays of mirrors deposited there by Apollo astronauts. In data taken between 1969 and 1976, no such perturbation was detected, down to a precision of 30 cm (1 ft), in complete agreement with the zero prediction of general relativity and in disagreement with the prediction of the Brans-Dicke theory. A number of secondary tests of more subtle gravitational effects have also been performed during the last decade. General relativity has passed every one, while many of its competitors have failed. Tests of gravitational radiation and inertial frame-dragging are now being devised. One experiment would involve placing spinning objects in Earth orbit and measuring expected relativistic effects.

COSMOLOGY

One of the first astronomical applications of general relativity was in the area of cosmology. The theory predicts that the universe could be expanding from an initially condensed state, a process known as the big bang. For a number of years the big bang theory was contested by an alternative known as the steady state theory, based on the concept of the continuous creation of matter throughout the universe. Later knowledge gained about the universe, however, has strongly supported the big bang theory as against its competitors. Such findings either were predicted by or did not conflict with relativity theory, thus also further supporting the theory. Perhaps the most critical piece of evidence was the discovery, in 1965, of what is called (Background Radiation). This "sea" of electromagnetic radiation fills the universe at a temperature of about 2.7K (2.7 degrees C above absolute zero). Background radiation had been proposed by general relativity as the remaining trace of an early, hot phase of the universe following the big bang. The observed cosmic abundance of helium (20 to 30 percent by weight) is also a required result of the big-bang conditions predicted by relativity theory.

In addition, general relativity has suggested various kinds of celestial phenomena that could exist, including neutron stars, black holes, gravitational lenses, and gravitational waves. According to relativistic theory, neutron stars would be small but extremely dense stellar bodies. A neutron star with a mass equal to that of the Sun, for example, would have a radius of only 10 km (6 mi). Stars of this nature have been so compressed by gravitational forces that their density is comparable to densities within the nuclei of atoms, and they are composed primarily of neutrons. Such stars are thought to occur as a by-product of violent celestial events such as supernovae and other gravitational implosions of stars. Since neutron stars were first proposed in the 1930s, numerous celestial objects that exhibit characteristics of this sort have been identified. In 1967 the first of many objects now called pulsars was also detected. These stars, which emit rapid regular pulses of radiation, are now taken to be rapidly spinning neutron stars, with the pulse period represent the period of rotation.

Black holes are among the most exotic of the predictions of general relativity, although the concept itself dates from long before the 20th century. These theorised objects are celestial bodies with so strong a gravitational field that no particles or radiation can escape from them, not even light--hence the name. Black holes most likely would be produced by the implosions of extremely massive stars, and they could continue to grow as other material entered their field of attraction. Some theorists have speculated that supermassive black holes may exist at the centres of some clusters of stars and of some galaxies, including our own. While the existence of such black holes has not been proven beyond all doubt, evidence for their presence at a number of known sites is very strong.

In theory, even a relatively small mass could become a black hole. The mass would have to be compressed to higher and higher densities until it diminished to a certain critical radius, the so-called "event horizon," named the Schwarzschild Radius because it was first calculated in 1916 by German astronomer Karl Schwarzschild. (His calculations apply to a non rotating object. The figures for a rotating object were developed in 1963 by New Zealand mathematician Roy Kerr.) For an object having the mass of the Sun the event horizon would be approximately 3 km (2 mi). Scientists such as the English theoretical physicist Stephen Hawking have speculated that tiny black holes may indeed exist.

The concept of gravitational lenses is based on the already discussed and proven relativistic prediction that when light from a celestial object passes near a massive body such as a star, its path is deflected. The amount of deflection depends on the massiveness of the intervening body. From this came the notion that very massive celestial objects such as galaxies could act as the equivalent of crude optical lenses for light coming from still more distant objects beyond them. An actual gravitational lens was first identified in 1979.

One phenomenon predicted by general relativity has not yet been substantially verified, however: the existence of gravitational waves. Gravitational waves would be produced by changes in gravitational fields. They would travel at the speed of light, transport energy, and induce relative motion between pairs of particles in their path (or produce strains in more massive objects). Astrophysicists think that gravitational waves should be emitted by dynamic sources such as supernovae, massive binary (or multiple-star) systems, and black holes or collisions between black holes. Various attempts, unsuccessful thus far, have been made to observe such waves. A more fundamental matter confronting general relativity is that of the attempt being made by physicists to unite gravitation with Quantum Mechanics, the other paradigm of modern physics. This search for some Unified Field Theory is the major task of workers in Quantum Cosmology.

PULSARS

Compact Stars

Red dwarfs, white dwarfs, neutron stars, black holes: this is a list of objects in which each is smaller, denser and more extreme in its physical conditions than the one before. The compaction is a result of the familiar force of gravity, but the condensed stars which result are outside our common experience. A matchbox size piece of white dwarf material would contain the same mass as a battleship, while the same mass of neutron star material occupies the space of a pinhead. A black hole is so collapsed that size and density no longer have any meaning.

A white dwarf, which is a star about the size of the Earth but with a mass similar to that of the Sun, is prevented from shrinking further by `degenerate electron pressure' --- free electrons cannot be packed more closely together. In some stars, usually more massive than white dwarfs, this barrier is overcome by the combination of the electrons with protons to form neutrons, which pack together even more closely, giving a neutron star. A neutron star has about the same mass as the Sun, but is only about 30 kilometres across. So small a star has a tiny surface area, and cannot emit much of the thermal radiation which makes normal stars shine: nevertheless some neutron stars can be observed at great distances by an entirely different kind of radiation, a regularly pulsating radio signal. These are the pulsars.

What Are Pulsars?

Pulsars were discovered in 1967 by Anthony Hewish and Jocelyn Bell at the radio astronomy observatory (now the Nuffield Radio Astronomy Observatory) at Cambridge. Their characteristic radio emission is a uniform series of pulses, spaced with great precision at periods between a few milliseconds and several seconds. Over 300 are known, but only two, the Crab Pulsar and the Vela Pulsar, emit detectable visible pulses. These two are also known to emit gamma--ray pulses, and one, the Crab, also emits X--ray pulses. The regularity of the pulses is phenomenal: observers can now predict the arrival times of pulses a year ahead with an accuracy better than a millisecond. How can a star behave as such an accurate clock? The only possibility for so rapid and so precise a repetition is for the star to be rotating rapidly and emitting a beam of radiation which sweeps round the sky like a lighthouse, pointing towards the observer once per rotation. The only kind of star which can rotate fast enough without bursting by its own centrifugal force is a neutron star.

Pulsars are very strongly magnetised neutron stars, with fields of strength reaching 100 million tesla (1 million, million gauss, compared with less than 1 gauss for the Earth's magnetic field). The rapid rotation therefore makes them powerful electric generators, capable of accelerating charged particles to energies of a thousand million, million volts. These charged particles are, in some way as yet unknown, responsible for the beam of radiation in radio, light, X--rays and gamma--rays. Their energy comes from the rotation of the star, which must therefore be slowing down. This slowing down can be detected as a lengthening of the pulse period. Typically a pulsar rotation rate slows down by one part in a million each year: the Crab Pulsar, which is the youngest and most energetic known, slows by one part in two thousand each year.

How Many Pulsars In Our Galaxy?

Pulsars are found mainly in the Milky Way, within about 500 light--years of the plane of the Galaxy. A complete survey of the pulsars in the Galaxy is impossible as weak pulsars can only be detected if they are nearby. Radio surveys have now covered almost the whole sky, and over 300 pulsars have been located. Their distance can be measured from a delay in pulse arrival times observed at low radio frequencies; the delay depends on the electron density in interstellar gas and on the distance travelled. Extrapolating from this small sample of detectable pulsars it is estimated that there are at least 200,000 pulsars in the whole of our Galaxy. Allowing for those whose lighthouse beams do not sweep across in our direction, the total population must reach one million.

Each pulsar radiates for about four million years; after this time it has lost so much rotational energy that it cannot produce detectable radio pulses. If we know the total population (1,000,000) and the lifetime (4,000,000 years), we can deduce that a new pulsar must be born every four years (assuming that the population remains steady). Very recently pulsars have been found in globular clusters. They are believed to have been formed there by accretion of matter onto white dwarf stars in binary systems. Other pulsars are born in supernova explosions. If all pulsars were born from supernovae explosions we can predict that there should a supernova in our galaxy every four years. These are spectacular events, and we would expect to see more of them if one occurs every four years. The last directly observed supernova in our galaxy was Kepler's supernova of AD 1604, but we do know that others occur which are less spectacular or which are hidden from us by interstellar dust clouds. It is not yet clear whether the birth-rate of pulsars and the rate of supernovae can be fully reconciled or how many outside globular clusters may be formed in binary systems.

The Crab Pulsar

The Crab Nebula is the visible remnant of a supernova explosion which was witnessed in AD 1054 by Chinese and Japanese astronomers. Near the centre of the Nebula is the Crab Pulsar, which is the most energetic pulsar known. It rotates 30 times per second, and it is very strongly magnetised. It therefore acts as a celestial power station, generating enough energy to keep all the Nebula radiating over practically the whole of the electromagnetic spectrum. The Crab Pulsar radiates two pulses per revolution: this double pulse profile is similar at all radio frequencies from 30 MHz upwards, and in the optical, X--ray and gamma--ray parts of the spectrum, covering at least 49 octaves in wavelength. The visible light is powerful enough for the pulsar to appear on photographs of the Nebula, where it is seen as a star of about magnitude 16. Normal photographs smooth out the pulses, but stroboscopic techniques can show the star separately in its `off' and `on' conditions.

The Binary Pulsar and General Relativity

Many stars are members of binary systems, in which two stars orbit around each other with periods of some days or years. If one of the stars is a neutron star, the orbiting pair can be so close that the gravitational attraction between them is very high, and some unusual effects can be observed. Several binary systems are known in which the other star is a giant; in these cases the neutron star can attract gas from the outer parts of its companion, and a stream of gas falls with great energy on to the surface of the neutron star. These systems are observed as X--ray sources. Some of the X--ray sources show periodic variations as the neutron star rotates: these are the so--called `X--ray pulsars'. One binary system, known as PSR 1913+16, consists of two neutron stars, so close together that their orbital period is only 775 hours. No gas streams between these stars, which interact only by their mutual gravitational attraction. The orbit of one of them can be described in great detail, because it is a pulsar. The period of this pulsar is 59 milliseconds, and it produces a very stable series of pulses with an unusually low slow--down rate. It is, in fact, an accurate clock moving very rapidly in a strong gravitational field, which is the classical situation required for a test of Einstein's General Theory of Relativity.

According to non--relativistic, or Newtonian, dynamical theory, the orbits of both stars should be ellipses with a fixed orientation, and the orbital period should be constant. Measurements of the arrival time of the pulses have shown significant differences from the simple Newtonian orbits. The most obvious is that the orbit precesses by 42 degrees per year. There is also a small, but very important, effect on the orbital period, which is now known to be reducing by 89 nanoseconds (less than one ten--millionth of a second) each orbit. The reducing orbital period represents a loss of energy, which can only be accounted for by gravitational radiation. Although gravitational radiation itself has never been observed directly, the observations of PSR 1913+16 have provided good proof of its existence. It is appropriate that this discovery, which is a further confirmation of the predictions of the General Theory of Relativity, was announced in 1979, which was the centenary of Einstein's birth.

WHAT ARE THE STARS?

The basic difference between a star and a planet is that a star emits light produced in its interior by nuclear `burning', whereas a planet only shines by reflected light. There seem to be an enormous number of stars that are visible to the naked-eye at a really dark site but, in fact, the eye can only see about two thousand stars in the sky at one time. We can see the unresolved light of many thousands more when we look at the Milky Way and the light of the Andromeda galaxy which can be seen by the eye comes from thousands of millions of stars. The Sun is our own special star yet, as stars go, it is a very average star. There are stars far brighter, fainter, hotter and cooler than the Sun. Basically, however, all the stars we can see in the sky are objects similar to the Sun. The Sun (and any other star) is a great ball of gas held together by its own gravity. The force of gravity is continually trying to force the Sun towards its centre and if there were not some other force counteracting it the Sun would collapse. The necessary outward pressure is produced by the radiation from the nuclear energy generation in the Sun's interior.

How do stars originate?

Stars form from concentrations in huge interstellar gas clouds. These contract due to their own gravitational pull. As the cloud gets smaller it loses some of the energy stored in it as potential gravitational energy. This is turned into heat which in the early days of the embryo star can easily escape and so the gas cloud stays cool. As the cloud's density rises it gets more and more difficult for the heat to get out and so the centre gets hot. If the cloud is big enough, the temperature rise is sufficient for nuclear reactions to take place. This generates more heat and the `burning' of hydrogen into helium takes place, as in the Sun. The object is then a star.

The Early Evolution of a Star.

In its early stages the embryo star is still surrounded by the remains of the original gas cloud, from which it formed. By this stage the cloud remnant takes the form of a disk around the star. The radiation from the star gradually dissipates this disk, possibly leaving behind a system of smaller objects, planets.

The Main-Sequence.

The star now settles down to a long period of stability while the hydrogen at its centre is converted into helium with the release of an enormous amount of energy. This stage is called the main-sequence stage, a reference to the classical Hertsprung-Russell diagram. Most stars lie in a well defined band in the diagram and the only parameter that determines where in the band they lie is the star's mass. The more massive a star is the quicker it `burns' up its hydrogen and hence the brighter, bigger and hotter it is. The rapid conversion of hydrogen into helium also means that the hydrogen gets used up sooner for the more massive stars than for the smaller ones. For a star like the Sun the main-sequence stage lasts about 10,000,000,000 years whereas a star 10 times as massive will be 10,000 times as bright but will only last 100,000,000 years. A star one tenth of the Sun's mass will only be 1/10,000th of its brightness but will last 1,000,000,000,000 years.

Post Main-Sequence Evolution.

Stars do not all evolve in the same way. Once again it is the star's mass that determines how they change.

Medium mass stars: Stars similar in mass to the Sun `burn' hydrogen into helium in their centres during the main-sequence phase but eventually there is no hydrogen left in the centre to provide the necessary radiation pressure to balance gravity. The centre of the star thus contracts until it is hot enough for helium to be converted into carbon. The hydrogen in a shell continues to `burn' into helium but the outer layers of the star have to expand. This makes the star appear brighter and cooler and it becomes a red giant. During the red giant phase a star often loses a lot of its outer layers which are blown away by the radiation coming from below. Eventually, in the more massive stars of the group the carbon may be `burnt' to even heavier elements but eventually the energy generation will fizzle out and the star will collapse to what is called a `degenerate white dwarf'.

Small mass stars: Our knowledge of the evolution of these stars is purely theoretical because their main sequence stage lasts longer than the present age of the Universe, so none of the stars in this mass range has evolved this far We believe that the evolution will proceed as for the medium mass stars except that the temperature in the interior will never rise high enough for helium `burning' to start. The hydrogen will continue to `burn' in a shell but will eventually be all used up. The star will then just get cooler and cooler ending up after about 1,000,000,000,000 years as a `black dwarf'.

High mass stars: There are very few stars with masses greater than five times the mass of the Sun but their evolution ends in a very spectacular fashion. As was said above, these stars go through their evolutionary stages very quickly compared to the Sun. Like medium mass stars, they `burn' all the hydrogen at their centres and continue with a hydrogen `burning' shell and central helium `burning'. They become brighter and cooler on the outside and are called red supergiants. Carbon `burning' can develop at the star's centre and a complex set of element `burning' shells can develop towards the end of the star's life. During this stage many different chemical elements will be produced in the star and the central temperature will approach 100,000,000 K.

For all the elements up to iron the addition of more nucleons to the nucleus produces energy and so yields a small contribution to the balance inside the star between gravity and radiation. To add more nucleons to the iron nucleus requires energy and so once the centre of the star consists of iron no more energy can be extracted. The star's core then has no resistance to the force of gravity and once it starts to contract a very rapid collapse will take place. The protons and electrons combine to give a core composed of neutrons and a vast amount of gravitational energy is released. This energy is sufficient to blow away all the outer parts of the star in a violent explosion and the star becomes a supernova. The light of this one star is then as bright as that from all the other 100,000,000,000 stars in the galaxy. During this explosive phase all the elements with atomic weights greater than iron are formed and, together with the rest of the outer regions of the star are blown out into interstellar space. The central core of neutrons is left as a neutron star which could be a pulsar.

What is remarkable about this is that the first stars were composed almost entirely of hydrogen and helium and there were no oxygen, nitrogen, iron, or any of the other elements that are necessary for life. These were all produced inside massive stars and were all spread throughout space by such supernovae events. We are made up of material that has been processed at least once, and probably several times, inside stars.

Royal Greenwich Observatory.

TELESCOPES

In everyday life we use a telescope or a pair of binoculars when we want to see a distant object in greater detail. The size of the telescope used determines how much detail we can see with it and how bright the image looks. Astronomical telescopes are also used to do these two things. They are big so that they can collect a lot of light from a faint star or galaxy and so that their resolution, the ability to see small detail, is as good as possible.

The Refractor.

Most everyday telescopes and binoculars use lenses to gather the light which we see through an eyepiece. Astronomical telescopes which use lenses in this way are called Refracting Telescopes because the objective lens (at the end furthest from the eye) refracts (bends) the light to a focus which is magnified by the eyepiece. Astronomers do not use refractors very much nowadays because if we wished to collect a lot of light from a faint object we would need a very large objective lens. The only way to support a large lens is around its edge. The force of gravity would bend the lens away from its design shape when we moved the telescope around the sky. The biggest refractor in the World is the 40-inch Yerkes refractor near Chicago in the USA. The largest in Britain is the 28-inch at the Old Observatory in Greenwich.

The Reflector.

The problems inherent in supporting the lens in a refractor and the light losses due to the light passing through thick pieces of glass are overcome in the reflecting telescope by using a mirror instead of a lens to collect the light. The mirror of a reflector is at the bottom end of the telescope tube. It consists of a fairly thick, rigid disk of glass whose top surface has been accurately ground and polished so as to reflect all the light falling on it to a focus near the top end of the telescope tube. This mirror can be supported, not only around its edge, but also all over its back surface. The top surface is made highly reflecting by evaporating onto it, in a vacuum, a thin film of aluminium.

The Classical Cassegrain.

In the classical Cassegrain telescope the primary mirror takes a paraboloid shape. This brings the light of any object in the field of the telescope to a focus near the top end of the tube, called the prime focus. This is used on big telescopes to take pictures of small areas of the sky. This used to be done using photographic plates but these are rapidly being replaced by more efficient television type detectors called CCDs. (See the pamphlet on Detectors.) As any instrument at the prime focus will obstruct the light on its way towards the primary mirror, we can not put large instruments there. Instead we place a smaller curved mirror, called the secondary, just inside the telescope focus where it reflects the light down the telescope tube and through a hole in the primary mirror to a focus just behind it, called the Cassegrain focus. Large instruments, such as a spectrograph, can be placed there.

Unfortunately the field of a classical Cassegrain telescope is rather small. This problem can be tackled by putting a complex lens system, called a corrector, into the light beam or by changing the classical design by altering the curvature of the primary mirror.

The Schmidt Telescope.

For photography of large areas of the sky the primary mirror is made with spherical curvature and an aspheric `corrector plate' is placed at the top end of the telescope tube. There are three large Schmidt telescopes in the world with fields about 6" across (the Moon's apparent diameter in the sky is half a degree). The oldest of these is the Palomar schmidt (not to be confused with the Palomar 200-inch) and the other two are the ESO Schmidt in Chile and the United Kingdom Schmidt in Australia. These have been used to produce photographic charts of the whole sky.

Radio Telescopes.

Most radio telescopes work in the same way as an optical reflecting telescope except that the mirror is made of metal, which reflects the radio waves up to a detector at the prime focus. Some radio telescopes are single, large, steerable dishes, like the Jodrell Bank telescope, others are used as arrays whose signals can be linked together to act as a single very large telescope with very high resolution. There are large radio telescopes at Jodrell Bank, in Cheshire, and at Cambridge.

Telescope Mountings.

The classical mounting for an astronomical telescope is to have an axis parallel to the Earth's north-south axis. As the Earth rotates once a day about its axis the telescope is rotated, in the opposite direction, at the same rate. This results in the telescope remaining pointing at a star in the sky as long as it is above the horizon. This is called an equatorial mounting. The making of a drive to work at a constant speed about one axis with small corrections when necessary is a simple problem but the mechanical design of the mounting, with no axis vertical, is neither simple nor cheap.

Many different forms of equatorial mounting have been devised; the Northumberland telescope in Cambridge, the Isaac Newton and the Jacobus Kapteyn in the Canary Islands all have different types of equatorial mountings. Now that computer controlled drive systems can be made which allow constantly varying drive rates to be used on two axes, we can use the much simpler Alt-Az mounting, which has a vertical and a horizontal axis. The William Herschel telescope in the Canary Islands has such a mounting.

Why do Astronomers always want bigger telescopes?

The size of the primary mirror of a telescope determines the amount of light that is received from a distant, faint object. Some of the most important astronomical problems are, today, in cosmology. Astronomers want to know how the galaxies, of which the Milky Way is our galaxy, were formed, when, how and why. In order to try to solve problems like these we need to be able to analyse the light coming from the furthest and the faintest objects in the sky. The light from these objects must be fed into instruments attached to the telescopes so that the light can be analysed. (See the pamphlet on Spectroscopy.) For such objects we need very big telescopes.

Observing from space.

We have mentioned radio telescopes, these like optical telescopes can be used from the ground because the atmosphere transmits these sorts of radiation. There are other wavelengths, however that are absorbed by the atmosphere and do not reach the ground. These include X-rays, the ultraviolet and the far infrared. The atmosphere also stops us from seeing very sharp detail. When you look at the stars at night you see them twinkle. This is the effect of layers in the atmosphere of different temperature bending the light towards and away from your eyes. The same bending affects optical telescopes and results in stars appearing, not as pin-points, but as fuzzy blobs. Astronomers go to great lengths to put their telescopes where the atmosphere is most stable but to get the best results we must go outside the atmosphere.

The Hubble Space Telescope was designed to give us this excellent resolution and to be able to work in the ultraviolet. Unfortunately a mistake was made with its primary mirror and during its first months of service it did not perform as well as it should have. Recently, a special Shuttle mission was launched successfully by NASA to correct this fault, and now the images it routinely captures are nothing short of breathtaking. The Hubble Space Telescope (HST) is giving us pictures better than any seen before and has changed our ideas about many things.

Yet other satellites measure in the ultraviolet, the infrared, X-rays and gamma-rays. They have revealed objects that we did not know existed and have resulted in an even greater demand for large ground-based optical telescopes to study these interesting objects.

TERRESTRIAL IMPACT CRATERS

Introduction

Impact craters are geologic structures formed when a large meteoroid, asteroid or comet smashes into a planet or a satellite. All the inner bodies in our solar system have been heavily bombarded by meteoroids throughout their history. The surfaces of the Moon, Mars and Mercury, where other geologic processes stopped millions of years ago, record this bombardment clearly. On the Earth, however, which has been even more heavily impacted than the Moon, craters are continually erased by erosion and re deposition as well as by volcanic resurfacing and tectonic activity. Thus only about 120 terrestrial impact craters have been recognised, the majority in geologically stable cratons of North America, Europe and Australia where most exploration has taken place. Spacecraft orbital imagery has helped to identify structures in more remote locations for further investigation.

Meteor Crater (also know as Barringer Crater), Arizona, was the first-recognised terrestrial impact crater. It was identified in the 1920s by workers who discovered fragments of the meteorite impactor within the crater itself. Several other relatively small craters were also found to contain impactor fragments and for many years these remnants were the only accepted evidence for impact origin. However, scientists have come to realise that pieces of the impactor often do not survive the collision intact.

In massive events caused by a large impactor, tremendous pressures and temperatures are generated that may vaporise the meteorite altogether or may completely melt and mix it with melted target rocks. Over several thousand years, any detectable meteoritic component may erode away. In some cases, non terrestrial relative abundance's of siderophile elements can be detected in the impact melt rocks within large craters - a chemical signature of the meteorite impactor.

Since the 1960s, numerous studies have uncovered another physical marker of impact structures, shock metamorphism. Certain shock metamorphic effects have been shown to be uniquely and unambiguously associated with meteorite impact craters; no other earthly mechanism, including volcanism, produces the extremely high pressures that cause them. They include shatter cones, multiple sets of microscopic planar features in quartz and feldspar grains, diaplectic glass, and high-pressure mineral phases such as stishovite. All known terrestrial impact structures exhibit some or all of these shock effects.

Impact craters are divided into two groups based on morphology: simple craters and complex craters. Simple craters are relatively small with depth-to-diameter ratios of about 1:5 to 1:7 and a smooth bowl shape. In larger craters, however, gravity causes the initially steep crater walls to collapse downward and inward, forming a complex structure with a central peak or peakring and a shallower depth compared to diameter (1:10 to 1:20). The diameter at which craters become complex depends on the surface gravity of the planet: The greater the gravity, the smaller the diameter that will produce a complex structure. On Earth, this transition diameter is 2 to 4 km (depending on target rock properties); on the Moon, at 1/6 Earth's gravity, the transition diameter is 15 to 20 km.

The central peak or peak ring of the complex crater is formed as the initial (transient) deep crater floor rebounds from the compressional shock of impact. Slumping of the rim further modifies and enlarges the final crater. Complex structures in crystalline rock targets will also contain coherent sheets of impact melt atop the shocked and fragmented rocks of the crater floor. On the geologically inactive lunar surface, this complex crater form will be preserved until subsequent impact events alter it. On Earth, weathering and erosion of the target rocks quickly alter the surface expression of the structure; despite the crater's initial morphology, crater rims and ejecta blankets are quickly eroded and concentric ring structures can be produced or enhanced as weaker rocks of the crater floor are removed. More resistant rocks of the melt sheet may be left as plateaus overlooking the surrounding structure.

Large terrestrial impacts are of greater importance for the geologic history of our planet than the number and size of preserved structures might suggest. For example, recent studies of the Cretaceous/Tertiary boundary, which marks the abrupt demise of a large number of biological species including dinosaurs, revealed unusual enrichments of siderophile elements and shock metamorphic features that are markers of meteorite impact events. Most researchers now believe that a large asteroid or comet hit the Earth at the end of the Cretaceous Period 66 million years ago. An environmental crisis triggered by the gigantic collision contributed to the extinctions of more than 95% of the species -- animal and plant -- then inhabiting the Earth. Based on apparent correspondences between periodic variations in the marine extinction record and the impact record, some scientists suggest that large meteorite impacts might be the metronome that sets the cadence of biological evolution on Earth - an unproven but intriguing hypothesis.

The origin of this classic simple meteorite impact crater was long the subject of controversy. The discovery of fragments of the Canyon Diablo meteorite, including fragments within the breccia deposits that partially fill the structure, and a range of shock metamorphic features in the target sandstone proved its impact origin. Target rocks include Paleozoic carbonates and sandstones; these rocks have been overturned just outside the rim during ejection. The hummocky deposits just beyond the rim are remnants of the ejecta blanket.

The information presented here was taken from, Terrestrial Impact Craters, compiled by Christian Koeberl and Virgil L. Sharpton of the Lunar and Planetary Institute.

SUNDIALS

History of the Sundial

From time immemorial Man must have realised that the changing length of the shadow of an object indicated the time of day - that the shadow shortened towards noon and lengthened again towards evening. No doubt the first crude sundial consisted of no more than a vertical stake in the ground. Eventually Man must have realised that the changing length of the shadow could be used, probably with stone markers, in the same manner as we use the hands of a clock today. This notable step forward in Man's attempt at measuring time was at least 3,500 years ago as the earliest known sundial, found in Egypt, dates from that time. The day was then subdivided into 12 parts which we refer to as `temporary hours'. Of course the temporary hours would vary in length, being longest in summer and shortest in winter, although in the Mediterranean lands the difference is nothing like as noticeable as it would be in the British Isles. In the latter case an `hour' in summer would have been twice as long as an `hour' in winter!

It was not until the 13th century that an Arab named Abul-Hassan introduced the idea of making all hours of equal length, and it was not until the 15th century that these equal hours were in general use. During the Renaissance period the development of sundials proceeded rapidly and many varied and ingenious designs were produced. In addition to having hour and minute marks for telling the time, other features were often incorporated. Thus the `furniture' of a dial might also consist of markings to indicate the seasons, the calendar date, times of sunrise and sunset, the signs of the Zodiac and the dates of the Sun's entrance into each sign, the position of the Sun relative to the horizon (azimuth and altitude), and the points of the compass. A few dials were made which also carried a crude form of tide table indicating the time of high tide at certain named ports when the Moon was observed in a particular direction.

However, sundials were gradually superseded by clocks though it is recorded that the French railways regulated their clocks by sundials right up to the end of the nineteenth century.

Sundial Theory

Sundials are naturally limited in their usefulness and a cynic might complain that they are of little more than academic interest in a climate such as that `enjoyed' in the British Isles. Nevertheless the study of sundials, or gnomonics as it is sometimes called, will also provide a good understanding of some fundamental astronomical principles. As the Earth rotates on its axis, so the Sun appears to move uniformly across the sky and if a rod is placed parallel to the Earth's axis its shadow will naturally move uniformly around itself. In other words, as the Sun moves through an arc of 15 in the sky in one hour so will the shadow move at the same rate. This is the principle on which most (but not all) sundials are based, and in fact the same idea is used with telescopes which are then said to be `equatorially mounted'.

Because the Earth's distance from the Sun varies throughout the year and also because its equator is inclined to its orbit is a difference between apparent solar time (time told by the Sun) and mean solar time which is the time kept by mechanical and electrical clocks. In fact it is possible for the Sun to be as much as a quarter of an hour fast or slow when compared with a clock which keeps mean solar time (i.e. Greenwich Mean Time). This difference is called the equation of time and is described in `The Equation of Time'.

If we know this correction as a function of the date it is possible to adjust certain types of sundial (those where equal intervals of time are indicated by equal angles) to allow for the change in the equation of time; or alternatively, for any type of dial, to apply a correction to the time read from the dial.

Another correction that has to be made is to allow for the longitude of the place. We are all familiar with the fact that `New York is five hours behind Greenwich' meaning, for example, that when it is midday at Greenwich it is only 7am in New York. This is because New York is 5 hours of longitude west of Greenwich. Even if we move only as far west as Bristol we find that this town is 10 minutes of time west of Greenwich so that the Sun crosses the meridian 10 minutes later than it does at Greenwich. Therefore if you had a sundial in Bristol and wanted to find the Greenwich Mean Time, you would have to add 10 minutes to the time from the dial, unless this longitude correction had already been allowed for in the construction of the dial.

Types of Sundial

Most sundials have the gnomon lying parallel to the Earth's axis. If the dial plate lies in the equatorial plane then the time scale is equiangular (all the hour lines are exactly 15 apart). If the dial is placed in any other plane then the time scale is no longer equiangular and the angles between the time marks have to be calculated using trigonometrical formulae. Dials can be classified according to the plane in which the dial lies as shown in the following table:

Another type of dial depends on the fact that the Sun's altitude (angular height above the horizon) changes with time. The dial has to be calibrated with date marks as well as time marks. These dials can be carried around and used anywhere within a few degrees of the latitude for which they were constructed, merely by pointing the gnomon in the direction of the Sun. An altitude dial inscribed on a cylinder, with a horizontal gnomon, was used by shepherds in the Pyrenees.

Portable dials were made in large numbers in the 16th--19th centuries and a fine selection of them is on display at the Old Royal Observatory at Greenwich, now part of the National Maritime Museum.

Another type of dial is the equiangular dial although it is not mentioned as such in the literature. It is defined as one which is constructed so that equal intervals of time are indicated by equal angles. Equiangular dials can be horizontal, vertical or reclining.

Sundials in Cambridge

There are many interesting sundials in Cambridge. There is only space here to mention three. In Senate House Passage a gateway to Gonville and Caius has a group of simple vertical dials mounted about an hexagonal tower whereas the beautiful example in Queen's college is a vertical reclining dial with additional markings to indicate, not only the time, but also the altitude and azimuth of the Sun, its zodiacal position, the date and sunrise time. It is also a moondial, a notoriously inaccurate

Construction.

The dial chosen to commemorate the Tercentenary of the founding of the Observatory at Greenwich (in 1675) is called a reclining equiangular sundial. The dial is situated in the grounds to the east of the new RGO building. It was designed so that the viewer can read the time to within one minute of GMT. This necessitates regular adjustment of both the rotation of the dial and the position of the gnomon. Unfortunately there is not sufficient manpower available to do this on a regular basis.

Royal Greenwich Observatory.

The Kuiper Belt and the Oort Cloud

Careful orbital calculations done in 1950 by Jan Oort indicate that a huge "cloud" (now called the Oort Cloud) of perhaps a trillion (1e12) comets orbit the Sun far beyond the orbit of Pluto from about 30,000 AU to a or more. This is the source of the long-period comets. The Oort Cloud may account for a significant fraction of the mass of the solar system, perhaps nearly as much as Jupiter.

The Kuiper Belt is a region past the orbit of Neptune roughly 30 to 100 AU from the Sun containing many small icy bodies. It is now considered to be the source of the short-period comets. Occasionally the orbit of a Kuiper Belt object will be disturbed by the interactions of the giant planets in such a way as to cause to cross the orbit of Neptune. It will then very likely have a close encounter with Neptune sending it out of the solar system or into an orbit crossing those of the other giant planets or even into the inner solar system.

There are presently six known objects orbiting between Jupiter and Neptune including 2060 Chiron (aka 95 P/Chiron) and 5145 Pholus. The IAU has designated this class of objects as Centaurs. These orbits are not stable. These objects are almost certainly "refugees" from the Kuiper Belt. Their future fate is not known. Curiously, it seems that the Oort Cloud objects were formed closer to the Sun than the Kuiper Belt objects. Small objects formed near the giant planets would have been ejected from the solar system by gravitational encounters. Those that didn't escape entirely formed the distant Oort Cloud. Small objects formed farther out had no such interactions and remained as Kuiper Belt.

Several Kuiper Belt objects have been discovered recently including 1992 QB1 and 1993 SC. They appear to be small icy bodies similar to Pluto and Triton (but smaller). As of 1995 there are 21 known trans-Neptunian objects (not counting Pluto and Charon. Nine of these have distances between 31 and 36 AU, the other eight between 40 and 45 AU. None have so far been found in the gap in between; this may be an effect of Neptune's gravitational attraction. Colour measurements of some of the brightest have shown that they are unusually red. It is estimated that there are at least 35,000 Kuiper Belt objects greater than 100 km in diameter, which is several hundred times the number of similar sized objects in the Main asteroid belt.

A team of astronomers led by Anita Cochran report that the Hubble Space Telescope has detected extremely faint Kuiper Belt objects. The objects are very small and faint perhaps only 20 km or so across. There may be as many as 100 million such comets in low-inclination orbits and shining brighter than the HST's magnitude-28 limit. Spectra and photometric data have been obtained for 5145 Pholus. Its albedo is very low (less than 0.1). Its spectra indicates the presence of organic compounds, which are often very dark (e.g. the nucleus of Comet Halley.

Chiron is by far the largest known object of this type. It is about 170 km in diameter, 20 times larger than Halley. If it ever is perturbed into an orbit that approaches the Sun it will be a truly spectacular comet. Some believe that Triton, Pluto and its moon Charon are merely the largest examples of Kuiper Belt objects. But these are more than distant curiosities. They are almost certainly pristine remnants of the solar nebula from with the entire solar system was formed. Their composition and distribution places important constraints of models of the early evolution of the solar system.

What's New on the Moon?

THE SUN

What is the Sun?

The diameter of the Sun is 1,400,000 km (840,000 miles) which is more than 100 times the diameter of the Earth. Its mass is more than 300,000 times that of the Earth. The Sun is a very hot gaseous body composed of nearly 75% hydrogen, 25% helium, less than 1% oxygen and all the other elements constituting less than 1%. Its surface temperature is about 6,000 C. The source of energy in the Sun is the fusion of hydrogen nuclei (protons) into helium nuclei. In this process a small amount of mass is lost and transformed into energy. This nuclear reaction can only take place in the very hot (15,000,000 C) and dense centre of the Sun. The Sun loses half a million tons every second in this destruction of mass to give energy but will maintain its present output of energy for about 5,000 million years.

For this long period of time the Sun is called a main-sequence star but eventually the hydrogen in the centre will all have been converted into helium. The balance between the force of gravity pulling all the Sun's mass towards its centre, and the force due to the energy in the Sun which pushes matter outwards, will then be upset. The centre will contract and become even hotter while the outer part will expand and become cooler. The Sun will then be brighter, cooler and bigger -- a red giant star. Ultimately all sources of energy production will come to an end and the Sun will collapse to become a very small hot object called a white dwarf.

The Solar Cycle

The Sun, as seen from the Earth, rotates about its axis once in just over 27 days and its activity rises and falls over an approximately 11 year cycle, producing variations in the Earth's magnetic field and changes in our upper atmosphere (the ionosphere) affecting the transmission of radio waves and therefore world-wide telecommunications. This cycle of activity was discovered by a German amateur astronomer Heinrich Schwabe as a result of observations carried out between 1826 and 1843; within ten more years a relationship had been established. At the beginning of each cycle, sunspots occur in high latitudes on the Sun (about 40 " from its equator) and in the course of about 11 years, occur in lower and lower latitudes and even on the equator itself. If the latitudes and duration's of these sunspot groups are plotted against time.

The period of rise from minimum phase (when sunspots may be absent for several weeks) to maximum phase (when 20 or more groups may be present at one time) takes on average four years, and the fall to the next minimum seven years. In the last 100 years the period of rise has ranged between 3.3 and 5.0 years and the period of fall between 5.7 and 8.3 years, so it is difficult to make predictions over any length of time.

Sunspots

These disturbed regions are seen as dark markings on the Sun's surface. Having a temperature of about 4,800C, they appear dark by contrast with the brighter surrounding surface, the temperature of which is 6,000 C. The life of a sunspot can be as short as a few hours or as long as several months. Some are seen over several revolutions of the Sun about its axis and in such cases are actually observed for only about half their duration, because for 13 or 14 days of the 27 day revolution they are on the hemisphere facing away from the Earth. Sunspots can occur singly and in groups and they can be of very different sizes. Large sunspots are sometimes visible to the naked eye when seen through fog or when the Sun is dim and red at sunrise or sunset. At other times the disk is too bright to be looked at directly. Sunspots with areas of only one millionth represent the other end of the scale.(See Read: Sunspots)

WARNING: NEVER LOOK DIRECTLY AT THE SUN: it is extremely dangerous to use binoculars or a telescope to look at the Sun as this can cause permanent blindness.

The Photosphere, Chromosphere and Corona.

The apparent disk of the Sun is called the "photosphere". The disk can be seen to get less bright at its edge. This is called limb darkening. At times near sunspot maximum bright areas can be seen near the limb, often near sunspot groups. These are called "faculae". The surface of the Sun can be seen, through a telescope ( See Warning), to have a granular appearance. These granules are the convection cells that carry the energy from below the apparent surface.

Outside the photosphere are the solar chromosphere and corona which can only be seen with special equipment or at a total solar eclipse. The "chromosphere" is slightly cooler than the photosphere but is more active as the solar prominences pass through it. These take two forms `quiescent', large arched structures associated with the magnetic fields around groups of sunspots, and `active', which are more violent events associated with solar flares. The "corona" is a very hot (a million degrees) extension of the Sun out towards the Earth. It is the corona that gives the totally eclipsed Sun its beautiful appearance.

Solar Flares

Usually associated with sunspots, these are observed as an increase in brightness of areas of hydrogen (known as Flocculi) and can give rise to bursts of intense radiation in the ultraviolet region of the Sun's spectrum which cause sudden ionospheric disturbances and radio fadeouts, leading to disruption of telecommunications on the Earth's sunlit hemisphere. Flares also eject streams of electrically charged particles which affect the Earth's magnetic field and cause geomagnetic `storms': disturbances affecting the compass needle. These `storms' are sometimes accompanied in our latitudes by the "aurora borealis" (See Read List), or Northern Lights. Solar flares vary in size and intensity, the smallest lasting only a few minutes before the brightness begins to fade. These small flares produce negligible effects, but a large flare may last for several hours and produce partial or complete radio fadeouts for a corresponding period.

Royal Greenwich Observatory.

The Equation of Time

The measurement of time no longer uses sundials but relies on devices, such as clocks, to determine a uniform rate. This rate is calibrated using astronomical observations so that clock time is equivalent to time determined by the mean motion of the Earth. We know, from modern astronomical observations and from observations of artificial satellites, that the Earth's rotation rate is not constant but varies both over the short term and over centuries. These small variations are due to real variations in the rotation of the Earth and are compensated for by inserting leap-seconds as appropriate.

If a sundial is used to determine the time it rapidly becomes apparent that it does not indicate the same time as clock time. The difference amounting to some 16 minutes at certain times of year. This difference is also seen as an asymmetry in the times of sunrise and sunset. It is called the Equation of Time. The Equation of Time has two causes. The first is that the plane of the Earth's Equator is inclined to the plane of the Earth's orbit around the Sun. The second is that the orbit of the Earth around the Sun is an ellipse and not a circle.

The Equation of Time due to Obliquity.

The angle between the planes of the Equator and the Earth's orbit around the Sun is called the angle of Obliquity. If we assume that the orbit of the Earth is circular then the apparent motion of the Sun along the great circle, that is the Ecliptic, will be regular covering equal angles in equal time. We measure apparent solar time, however, as a projection of this movement onto the Equator. This projection will be a maximum when the great circles of the Equator and the Ecliptic are parallel (at the summer and winter solstices) and will be a minimum where the great circles are at their largest angle (at the equinoxes). The Sun will be on the meridian at noon at both solstices and equinoxes and so the Equation of Time due to Obliquity will be zero at these times. Between the solstices and the equinoxes the Sun will be slow relative to clock time with minima near Feb. 5 and Aug. 5. Between equinoxes and solstices the Sun will be fast relative to clocks with maxima near May 5 and Nov. 5.

The Equation of Time due to Unequal Motion.

The orbit of the Earth around the Sun is an ellipse. The distance between the Earth and the Sun is a minimum (perigee) on Dec. 31 and is greatest (apogee) on July 1. The Sun's apparent longitude changes fastest when the Earth is closest to the Sun. The Sun will appear on the meridian at noon on these two dates and so the Equation of Time due to Unequal Motion will then be zero. Between Dec. 31 and July 1 the Sun will be slow relative to clock time with a minimum around March 31. Between July 1 and Dec. 31 the Sun will be fast relative to clock time with a maximum around Sep 30.

TIME

What Time Is It?

There are many methods used to keep time, each having its own special use and advantage. Until recently, when atomic clocks became available, time was reckoned by the Earth's motions: one rotation on its axis was a "day" and one revolution about the Sun was a "year". An hour was one twenty-fourth of a day, and so on. It was convenient to use the position of the Sun in the sky to measure the various intervals.

Apparent Time

This is the time kept by a sundial. It is a direct measure of the Sun's position in the sky relative to the position of the observer. Since it is dependent on the observer's location, it is also a local time. Being measured according to the true solar position, it is subject to all the irregularities of the Earth's motion. The reference time is 12:00 noon when the true Sun is on the observer's meridian.

Mean Time

Many of the irregularities in the Earth's motion are due to its eccentric orbit and tidal effects. In order to add some consistency to the measure of time, we use the concept of mean time. Mean time uses the position of a fictious "mean Sun" which moves smoothly and uniformly across the sky and is insensitive to the Earth's irregularities. A mean solar day is 24 hours long. The "Equation of Time", is tabulated in almanacs and represented on maps by the Analemma, provides the correction between mean and apparent time to allow for the eccentricity of the Earth's orbit.

Local Mean Time (LMT)

Local mean time is determined by the mean Sun's position relative to the local meridian of the observer. As with any "local" time, it depends on the observer's geographic location. The reference time is 12:00 noon when the mean Sun is on the local meridian.

Mean Civil Time (LCT)

Also called clock time or zonal time, this is the standard time by which most of our non-astronomical activities are measured. The Earth's surface is divided into 24 time zones, each spanning 15 degree of longitude with some variance to accommodate political boundaries. The central meridian of each zone is precisely defined, however, to be an integral multiple of 15 degrees longitude. The reference time for the entire zone is 12:00 noon when the mean Sun is on the central meridian of the time zone.

Universal Time (UT or GMT)

This is the basis for all civil time keeping and is very close to the LMT at 0 degrees longitude at Greenwich Observatory. hence, it is sometimes called Greenwich Mean Time or GMT. The military often uses the term "zulu" to refer to universal time.

Standard time broadcast by radio stations such as WWV or CHU is Coordinated Universal Time (UTC or UT1). This time is based on an atomic clock and is "corrected" by adding occasional "leap seconds" to keep it in reasonable agreement with universal time.

International Atomic Time (IAT)

International atomic time is the time kept by atomic clocks. The Systemme International (SI) second is defined so that the frequency of a certain resonance of the cesium atom is 9,192,631,770 herz.

Sidereal Time

Sidereal Time is measure relative to the stars and is based on the true rotation period of the Earth. Since the Sun appears to move relative to the stars, a sidereal day is 3 minutes and 56 seconds shorter than a solar day. Sidereal time is measure by the position of the vernal equinox relative to the meridian. Depending on the exact reference used, sidereal time may be local (LST) or mean (MST). We use sidereal time to adjust our setting circles.

Ephemeris Time (ET)

As the name implies, this is the time upon which the ephemeris is based. It is reckoned by the orbital periods of the moon and the planets and, therefore, is not subject to the irregularities of the Earth's rotation. It is a uniform measure which forms the basis of the theories of celestial dynamics. It was chosen to be close to UT during the 19th century. By the end of the 20th century, ephemeris time will differ from UT by some 50 seconds. While some almanacs list an estimated correction factor for the current year, the true correction is always determined after the fact by comparing measured planetary positions to the predicted positions.

Hour Angle

An object's hour angle is the difference between the local sidereal time and the object's right ascension. The difference is taken in such a manner that an object west of the meridian has a positive hour angle, while an object east of the meridian has a negative hour angle.

THE TIDES

Tides are due to the gravitational attraction of one massive body on another. We commonly think of the tides as being a phenomenon that we see in the sea. There are other instances of the effects of tidal forces such as the drastic effect that a Black Hole has on matter in its close vicinity. The effect of the tidal forces of a white dwarf star on its close companion are sufficient to drag matter away from the companion onto the surface of the white dwarf where is can cause a sudden, drastic increase in brightness seen as a Nova explosion. Other binary stars also show the effects of tidal forces and these are also exhibited by close pairs of galaxies where the effects of the gravitational pull are sufficient to distort the shapes of the galaxies into weird and wonderful shapes.

The Law of Gravity.

Isaac Newton showed that the pull of gravity depended on three things; the masses of the two bodies and their distance apart. He showed that the force was inversely proportional to the square of the distance. This means that if we consider the gravitational pull of the Earth on a satellite, the force will be only a quarter if we double the distance from the centre of the Earth. The Sun is far more massive than the Moon yet, because it is much further away, its gravitational pull is less than half the Moon's.

Ocean Tides.

The tides which we see in the oceans are due to the pull of the Moon and the Sun. The simplest explanation is that the water on the side of the Earth closest to the Moon is pulled, by the Moon's gravitational force, more strongly than is the bulk of the Earth; whereas the water on the side furthest from the Moon is pulled less strongly than the Earth. The effect is to make bulges in the water on opposite sides of the Earth. The effect of the Sun's pull is similar and the tides that we see are the net effect of both pulls.

When the pull from the Sun adds to that of the Moon the tides are large and we call them Spring tides whereas when the pulls are at 90 degrees the tides are small and we call them Neap tides. The heights of spring tides are governed by the distance of the Moon from the Earth, being largest at Perigee (when the Moon is closest to the Earth) and smallest at Apogee (when the Moon is at its furthest). Because the Sun's pull is aligned with that of the Moon at New Moon and Full Moon these are the times when Spring Tides occur. The pull of the Sun is less than half that of the Moon and so the frequency of the tides is determined by the apparent passage of the Moon around the Earth which takes just over a day. We, therefore, in most places on the Earth have two tides a day with the time of each becoming later from one day to the next by just under an hour a day. (The actual period is, of course, determined by the rotation of the Earth and the orbit of the Moon.)

The height of the tide at any one place is determined by the shape of the coastline and of the nearby continental shelf. The presence of shelving land masses and bays gives much greater range to the tides than is seen in mid-ocean. A phenomenon which is generally not realised is that the air and solid land-masses also move up and down due to the tidal forces. Although the movement is much less in the land than that in the sea it can amount to a metre of vertical shift. It might be expected that the time of high tide would be when the Moon is on the meridian. This is not so. The reason is that, because of the Earth's rotation and friction, the tidal bulge gets left behind a little. The effects near complex coastlines such as in Britain are very difficult to compute.

The Earth-Moon System.

The long term effect of the tides is that energy is dissipated by friction in the oceans and the land and in the distortion of the Moon by the tidal pull of the Earth. This slows down the rotation speed of the Earth and moves the Moon further away from the Earth. The Earth loses rotational energy which is given to the Moon. Eventually the Earth's rotation rate will be slowed so that it is the same as that of the orbital period of the Moon. The Earth will then always keep the same face towards the Moon in the same way that the Moon already keeps the same face towards the Earth. After that the system will slowly lose energy so that the Moon will come closer to the Earth again. This is, of course, a very slow effect. The present rate of change is that the Earth's rotation rate is slowing by 16 seconds every million years and the distance of the Moon is increasing by 120 cm each year.

Satellites of other Planets.

In the same way the tidal forces of the Earth on the Moon have caused it to rotate in synchronism with its orbital period (it keeps the same face towards the Earth as it goes around), almost all of the satellites of the planets do the same. The exceptions are believed to be satellites which are ex-asteroids captured by the planet where the tidal forces have not yet had time to equalise the two periods. Even the planet Mercury has suffered from such tidal forces and its rotational period is two-thirds of its orbital period due to the tidal force of the Sun. Jupiter's satellite Io has an eccentric orbit. Tidal forces from Jupiter are trying to remove this eccentricity and force the orbit to be circular but the eccentricity is caused by tidal forces from the satellite Europa. This means that Io is suffering considerable distorting forces. These generate heat inside Io which is sufficient to power the active volcanoes that were seen by the Voyager spacecraft.

Close Binary Stars.

It is believed that at least half the stars, which look to us to be single, are in fact two, or more, stars in binary or multiple systems. It is clear, from analogy with the Earth-Moon system that such pairs of stars will exert tidal pulls on one another. These tidal pulls become very important when we consider pairs of stars which are close together. If one star is much bigger than the other it is possible to think of situations where the gravitational pull of the smaller star on the closest part of the big star is greater than the pull of the big star.

In these circumstances the big star will lose matter towards the small star. We see this happening in many binary systems where the big star has reached the point in its evolution where it increases markedly in size. This leads to many interesting objects, the most notable being when the smaller star is a compact object. Novae are stars that suddenly appear where there was apparently no star, or only a very faint star, before. We know that what has happened is that the tidal forces have stripped material from the larger star of a pair and deposited it onto a smaller white-dwarf companion.

This material, when it reaches the surface of the white-dwarf, is `burnt up' in a very rapid and explosive thermonuclear reaction. This raises the brightness of the white-dwarf to be one of the brightest stars in the whole galaxy, whereas before the explosion it was one of the faintest. Another example of this phenomenon is where the small companion is a neutron star or a black-hole. Then the matter transferred from the larger star gives up so much energy that it emits intense X-radiation which can be seen by X-ray satellites as an x-ray transient. Such sources are the best way in which we can `see' evidence for black holes.

Royal Greenwich Observatory.

Unless otherwise indicated, all text Copyright ) 1999 Swimming Elk Software.