The Story of Astronomy

by Peter Aughton

  From the outset Ptolemy assumed that the Earth was at the center of the universe. He showed how to predict the position of the Sun in the sky with great accuracy and how to predict the position of the Moon—a far more difficult problem—with tolerable accuracy. His methods were certainly good enough to enable his successors to predict both solar and lunar eclipses from his tables. The motions of the planets were very complex on account of their retrograde motion. They passed from west to east across the night sky, but at some point in their orbit they would move backward for a few months before going forward again. Ptolemy did not try to find a physical reason for the retrograde motion, but he had an excellent method of simulating it so that the positions of the planets could be predicted well in advance. Everything was based on circular motion, because the circle was seen to be the perfect figure. To find the path of a planet he used a system that we call deferents and epicycles, a very ingenious system of circles within circles that predicted the orbits with great precision. It was originally devised by Apollonius of Perga (c.262–190 BC), a brilliant Greek mathematician who lived several centuries before Ptolemy. A deferent was a large circle centered on the Earth, and an epicycle was a small circle whose center moved around the circumference of the deferent.

  Ptolemy deemed it necessary to try to explain the mechanism that held the stars and the planets in the sky. Gravitation in the Newtonian sense was not understood, but everybody knew that all solid bodies fell toward the Earth and that something in the heavens must therefore be preventing the stars from falling. The device that had been suggested by Eudoxus and others was that of a great crystal sphere rotating daily about the Earth and carrying the stars around with it. The sphere of the stars did not carry the planets, for it was well known that they did not remain at the same point in the sky. It was therefore necessary to introduce the clumsy device of an extra sphere for every planet, and yet another two crystal spheres to explain the motion of the Sun and the Moon.

  An Immovable Earth, and the Motions of the Moon and the Sun

  In the first book of the Almagest Ptolemy described his geocentric system and gave various arguments to prove that, in its position at the center of the universe, the Earth must be immovable. He showed that if the Earth moved, as earlier astronomers like Hipparchus had suggested, then certain phenomena should be observed. He argued, for example, that since all bodies fall to the center of the universe, the Earth must be fixed at the center, otherwise falling objects would not be seen to drop toward the center of the Earth. He also showed that when a body was thrown vertically upward it always returned to the point on the Earth from where it was launched. He claimed that if the Earth rotated once every 24 hours, as suggested by Hipparchus, this would not happen.

  In his second book Ptolemy described the diurnal motion of all the objects in the skies. He calculated the time that they rose over the horizon and the time when they set below it. Book three described the motion of the Sun through the zodiac.

  In books four and five he demonstrated the motion of the Moon and what he called the lunar parallax. All this was taken from the work of Hipparchus. He also went on to calculate the sizes and distances of the Sun and Moon, again following the work of Hipparchus. The figures for the Moon were fairly accurate, but the Sun was taken to be only about 20 times further away than the Moon; this was the distance calculated by Aristarchus. The system still made the Sun much larger than the Earth, but Ptolemy did not see this as a good enough reason to put the Sun at the center of the universe.

  Eclipses and Star Motions

  Book six of the Almagest was dedicated to eclipses, both of the Sun and the Moon. The eclipses were seen as major events, and it was very important for an astronomer to be able to predict them well in advance. The Ptolemaic system was quite capable of doing this, for the motions of both the Sun and the Moon were accurately described. The most difficult problem was finding the longitude of the Moon. Although the method could predict an eclipse, it did not give the correct distance of the Moon. If the lunar distance calculation had been correct, then at some points in its orbit the Moon would be seen in the sky at up to four times the size of the Sun.

  In books seven and eight Ptolemy considered the motion of the stars. He described the precession of equinoxes that had been carefully measured by Hipparchus. His work was not all plagiarism, however, and Ptolemy made his own estimate of 36 seconds of arc per century for the precession. This was poor compared with Hipparchus’ estimate of 45 or 46 seconds per year, and indicates that Hipparchus was the more skillful observer. (Today’s figure for the precession of the equinoxes is 50.25 seconds per year.)

  Planetary Motions

  In book nine Ptolemy showed how to model the motions of the planets. It has long been known that the true orbits of the planets are ellipses with the Sun at one focus. There is, therefore, some irony in the fact that it was Apollonius—who wrote a brilliant treatise on the conic sections and who knew the properties of the ellipse, the parabola and the hyperbola better than anybody else before him—who also produced the ingenious but incorrect system of cycles and epicycles for the motions of the planets.

  Ptolemy’s next three books gave more details of the planets with accurate figures for their orbits and their constants of motion. On Ptolemy’s system the Sun and the planets all moved in the same plane, called the plane of the ecliptic, but he knew there were minor deviations from his system and his final book was dedicated to what he called motion in latitude and the apparent path of the Sun against the stars.

  The Ptolemaic system was not perfect, but with so many variables to choose from it was able to give a good approximation for all the planetary orbits. Ptolemy realized that the planets were much closer to the Earth than were the fixed stars. He believed in the physical existence of crystalline spheres to which the stars and the planets were attached. The sphere of the stars was not quite the outer limits of his universe, however; he suggested that there were other spheres, ending with what he called the “prime mover,” and it was this that provided the motive power for all the other spheres in his concept of the universe. Furthermore, the universe was considered to be eternal. In the Middle Ages there was some concern about how the spheres could continue to drive the solar system without running down, but medieval thought had a simple answer to the problem. Manuscripts of the time show angels turning handles on the spheres to keep the heavens rotating.

  The system of Ptolemy survived the fall of Rome and the Dark Ages. The Almagest, or Great Work, was a very apt name for a system of the world that was not bettered for 13 centuries.

  Chinese Astronomy and Calendar

  From earliest times the Chinese astronomers kept detailed records of sunspots, eclipses, novae and—especially—comets, whose unpredicted appearance they viewed as bad omens. Star tables were produced by the 4th century BC, with a continuous record being kept from 70 BC.

  The Chinese believed that the emperor must preserve a harmonious relationship with the cosmic order by means of virtuous living and the correct performance of rituals and ceremonies. This required a reliable calendar. The present calendar emerged in the 14th century BC, having evolved in the centuries before. A year had 12 months of 29 or 30 days beginning at the new Moon, with an additional month every two or three years to reconcile the lunar year with the solar year. The calendar marked predictable astronomical events such as lunar eclipses and the positions of the planets, as well as equinoxes, solstices and agricultural seasons.

  4

  ASTRONOMY IN THE DARK AGES

  The fall of the Roman empire ushered in the period known as the Dark Ages—a time of great change and uncertainty, with new empires created in the aftermath. Much of the original scientific knowledge from the ancient world was lost to the West, but kept alive by Islamic astronomers in the East. The period also saw new advances in astronomy and mathematics, thanks to enlightened scientists such as Omar Khayyam.

  In 1900 the wreck of a Greek ship was discovered off the island of Antikyth
era. The vessel was dated to about 80 BC. The ship alone was a valuable archaeological find, but amongst the cargo was an object that has puzzled scientists and archaeologists for years. It consisted of a frame containing a set of brass wheels, very similar to the mechanism of a clock but a thousand years before its time, and quite unlike anything else ever discovered. The best explanation so far is that the mechanism was an astronomical device used to calculate the positions of the planets—an advanced version of an instrument known as the astrolabe, which was also used to predict eclipses and to follow the motion of the Moon. The device was an isolated find, but if we accept the antiquity of the Antikythera instrument then we must accept that Greek and Roman technology in the ancient world was far in advance of what had previously been thought.

  A Divided Empire

  The traditional date for the fall of the Roman empire is usually cited as 476 when Romulus Augustus (reigned 475–76), the de facto emperor of the Western Roman empire, was deposed by Odoacer (435–93). The mighty Roman empire that had lasted so long and that had eventually brought Christianity to the Western world, was finally overthrown by people the Romans called the barbarians. The centuries that followed became known as the Dark Ages. Rome became divided into two empires: the East and the West. The Western empire fared badly; it became a feudal, agrarian society, and after a few generations much of the knowledge passed down from the ancient world was never used and in many cases was lost. The Eastern empire, the Byzantine empire centered on Constantinople, fared much better. Manuscripts and other forms of knowledge from the library at Alexandria found their way to the East where many scripts were copied and translated into Arabic so that they could be studied by Islamic scholars.

  For more than a century after the fall of Rome the Islamic empire seemed content with its boundaries, but after the flight of the prophet Mohammed (570–632) from Mecca in 622 the empire began to expand. The city of Alexandria survived Rome by nearly two centuries, but in 641 it finally succumbed to the Arabian invaders. The sacking and burning of the great library, the greatest store of knowledge in the world, is often quoted as the barbaric work of Islam, but centuries later it transpired that this was not quite the case. Many of the manuscripts resurfaced, sometimes as the originals in Greek or Latin, sometimes as Arabic translations. When the period of military expansion was complete, the Islamic scholars became great admirers of the civilizations of the past, and were keen to retrieve as much knowledge as they could from the ancient world. Within a hundred years the Islamic empire dominated the whole of the Middle East. The empire spread westward across Asia Minor, into Egypt, and across the north of India as far as the border of China. It also spread to the west along the southern shores of the Mediterranean, and in 771 the Moors crossed the Straits of Gibraltar and settled in the region called Andalusia in southern Spain.

  Andalusia was once part of the Roman empire. Scipio Africanus (236–183 BC) conquered the region in 210–206 BC, and it eventually became the Roman province of Baetica. This province flourished under Roman rule and was the birthplace of the emperors Trajan (c.56–117) and Hadrian (76–138) and the writers Lucan (39–65) and Seneca (c.3 BC–AD 65). Roman rule lasted there until the Vandals, closely followed by the Visigoths, overran the region in the fifth century. Thus when the Moors arrived in the eighth century Andalusia already had an impressive Roman history—but it was not a history well known to the local people; it had all happened long before living memory.

  Arabian and Persian Astronomers

  Very little is known about the state of astronomy in the centuries immediately after the fall of Rome, but by the ninth century we see the first appearance of the fruits of Arabian knowledge. The earliest-known astrolabes, for example, appear in Islam, and an example from Damascus still survives from about 830. One of the astrolabe’s uses was to determine the elevation of celestial objects above the horizon. It comprised two or more flat metal discs with calibrated scales, attached so that both, or all, the discs could rotate independently. For early navigators and astronomers it served as a star chart, a compass, a clock and a calendar. It survived for centuries and it had no equal as a navigational device until the introduction of the sextant in the 18th century. The Danjon astrolabe is what is known as a portable solstitial armillary, modified for observations of the stars. The instrument is suspended by a small hook or eye, and it consisted initially of a single ring that hung in a vertical plane. Pivoted at the center of the ring was a rod equal in length to the ring diameter, carrying sights at either end. It could be aligned on a star or a planet, with an angular scale inscribed on the armillary ring to show the object’s altitude.

  Many important advances in the field of mathematics were made in the Islamic world. One of the simplest, but most significant, ideas was the introduction of a symbol for the number zero, making possible the Arabic system of numerals with a base of ten. It is the system used almost exclusively today. To appreciate what a great step forward this represents we need only look at the problems of multiplication and division thrown up by the Roman numeral system that was widely used in the West at that time. Arabian mathematics went much further than just devising the numerical system we use today. They also introduced algebra, the system of mathematics where unknown quantities are represented by symbols. Equations could be manipulated algebraically to simplify many mathematical calculations.

  We know the names of many of the early Islamic astronomers, and we even know a little about their work, but it is not until the ninth century that we can identify individual astronomers and their contributions to knowledge. Albategnius (c.850–929) was one of the earliest of the Islam school. He was an Arabian nobleman born in Batan in Mesopotamia, and he became the leading astronomer and mathematician of his time. He drew up improved tables for the motion of the Sun and the Moon. He knew that the Earth’s orbit around the Sun was an ellipse, and he measured its eccentricity. He also measured the inclination of Earth’s equator to its orbital plane and he made an estimate of the number of days in the year. Albategnius made his observations over a period of 40 years from his observatory in Rakku, and they were summarized in his book Movements of the Stars, published in Europe long afterward in 1537. His estimate of the year was so accurate that it was used by European astronomers in the 16th century for the Gregorian reform of the Julian calendar.

  Albategnius was followed two generations later by the astronomer Al Sufi Abd al-Rahman. He was born in 903 and lived for 83 years. He was another Persian nobleman, also known by the Latinized name Azophi. He published a work called the Book of the Fixed Stars, which first appeared in about 964. It included a catalog of 1018 stars, giving their approximate positions, magnitudes and colors. It obviously owed much to Ptolemy’s Almagest, but it also contained many Arabic star names that are still in use today, although sometimes in a corrupted form. An interesting entry is the earliest-known reference to the Andromeda Galaxy, our closest galaxy. It was also at about this time that a Persian mathematician and astronomer called Abul Wafa (940–97) studied and described geometrical constructions using only a straight edge and a fixed compass. He later dubbed his instrument a “rusty compass” because it never changed its radius. Wafa also pioneered the use of the trigonometrical functions; he compiled tables of sines and tangents at intervals of 15 arc-minutes, and he seems to be the first to have used the secant and cosecant functions. Much of his work was carried out as part of an investigation into the complex orbit of the Moon.

  Astrologer al-Birini

  In the early centuries it is always difficult, and usually impossible, to differentiate between astronomers and astrologers because there was only a fine boundary between them. Astrologers were keen to know the positions of the planets as accurately as possible in order to help them formulate their predictions. The astrologer al-Birini flourished at the end of the first millennium. He was born just before sunrise on September 4, 973 at the city of Kath on the River Oxus, in what is now Uzbekistan. He was interested in all branches of learning and
was fluent in six languages. In 998 he moved to Gurgan on the Caspian Sea where he completed his first major work called The Chronology of Ancient Nations. He also wrote a Book of Instruction in the Elements of the Art of Astrology, dedicated to a high-ranking woman called Rayhanah. It begins with sections on geometry and arithmetic, then describes the astronomy of Ptolemy and also includes a detailed section on the use of the astrolabe. The remainder of the book concentrates on astrology and shows how many of the world’s events and disasters were forecast in the stars.

  A New Work on Optics

  In about 1000 the Arab mathematician and physicist Alhazen (c.945–c.1040) wrote the first important book on optics since the time of Ptolemy. He rejected the older notion that light was emitted by the eye in favor of the view accepted today—that light is emitted from a source like the Sun, or reflected from an object, and then gathered into the eye. His Treasury of Optics was written at the end of the first millennium, but it was not published in Latin until 1572, over 500 years later, giving another example of how long some of the Arabic texts survived and how they came to be known in Europe. He described lenses, plane and curved mirrors and colors. Alhazen was also an engineer. He made an expedition to southern Egypt, sponsored by the caliph al-Hakim (985–1021), where his mission was to study possible ways of controlling the waters of the Nile. He soon realized that what he had undertaken was impossible and that the Nile could not be easily tamed. He also realized that when the bad news reached the caliph he would be executed for having failed in his task. Alhazen feigned madness upon his return. He kept up the pretense for many years until the death of the caliph in 1021.