The Story of Astronomy (3 page)

The Egyptians by their astronomy discovered the solar year and were the first to divide it into twelve parts—and in my opinion their method of calculation is better
than the Greek; for the Greeks, to make the seasons work out properly, intercalate a whole month every other year, while the Egyptians make the year consist of twelve months of thirty days each and every year intercalate five additional days, and so complete the regular circle of the seasons.

Herodotus describes here a calendar that had been in use for several millennia. The Egyptians introduced a year with 12 months each of 30 days, following the calendar of the Sumerians. Then they simply added an extra five feast days to make the year up to 365 days. They knew that this made the length of their year correct to the nearest day, but it was still too short by a little over a quarter of a day. They stuck faithfully to their 365-day calendar, however, allowing their months to migrate to different seasons as the missing leap year days accumulated. Every four years their calendar lost another day until after the incredible span of 1460 years—that is, four cycles of 365 years—it was back to where it had started! This cycle was known as the Cycle of Sothis. It does not seem logical that a civilization as advanced as Egypt's would allow this to happen when they knew the exact nature of the error in their calendar. It made nonsense of the dates for planting the seed and reaping the crop, but the Cycle of Sothis was executed at least twice before the Egyptian calendar was reformed.

Herodotus also knew something of astronomy in his own country of Greece. Early Greek civilization does not have the antiquity of ancient Egypt, but it still has a lineage dating back to the eighth century
BC
. We are very fortunate that Hesiod, the earliest of the Greek poets, gives us a wonderful description of the skies from his poem “Works and Days,” where he describes the life of the agricultural peasant:

When the Pleiades rise it is time to use the sickle, but the plough when they are setting; forty days they shall stay away from heaven; when Arcturus ascends from the sea and, rising in the evening, remains visible for the entire night, the grapes must be pruned; but when Orion and Sirius come in the middle of heaven and the rosy fingered Eos sees Arcturus, the grapes must be picked; when the Pleiades, the Hyades, and Orion are setting, then mind the plough; when the Pleiades, fleeing from Orion, plunge into the dark sea, storms may be expected; fifty days after the Sun's turning is the right time for man to navigate; when Orion appears, Demeter's gift has to be brought to the well-smoothed threshing floor.

It is said that the Greek astronomer Thales (
c
.624–546
BC
) predicted an eclipse of the Sun in about 600
BC
. Greek astronomy was not sufficiently advanced for him to have made a long-range prediction of an eclipse at that time, but if he had been observing the Moon closely he may well have been able to make the prediction just a few days before the event. Alternatively, he may have had access to Babylonian or Egyptian records.

Life changed only slowly in the long centuries of the ancient world, and at that time astronomy also advanced slowly. Thales was a contemporary of the mathematician and philosopher Pythagoras (
c
.580–
c
.500
BC
), famous for proposing his theorem concerning the square of the hypotenuse of a right-angled triangle. Pythagoras argued that the Earth was a sphere. He must have seen and wondered at the sight of a ship falling below the horizon, but his reasoning was that of the philosopher rather than the astronomer—he thought the Earth must be spherical simply because in his opinion the sphere was the perfect shape. There was a significant advance in the middle of the next century (
c
.450
BC
) when Oenopides (
c
.490–420
BC
) discovered that the Sun seemed to orbit the Earth in a plane inclined at 23 degrees to the rotation of the stars about the pole. It is this angle that determines the position of the tropics and also the Arctic and Antarctic circles.

The fourth century
BC
brings us to the time of Alexander the Great (356–323
BC
) and his tutor Aristotle (384–322
BC
). Alexander, in his conquest of the world, founded many cities bearing his name. The most famous and successful was Alexandria in Egypt, founded in the year 332
BC
. It became a meeting point for Greek and Egyptian ideas and learning, as well as becoming a great trading center. The city named after him was Alexander's greatest contribution to culture and his most important legacy. The city grew quickly in size and status and for centuries it was the greatest center of science and culture in the ancient world. It boasted the greatest library in the world, with scrolls and documents collected from every known civilization.

While Alexander's contribution to astronomy was that he carried the learning and philosophy of the Greek world to all the countries he conquered, there was one downside—Alexander was tutored by Aristotle, a great philosopher but a very poor scientist. Aristotle considered that to actually go out and measure something was an activity more suited to a craftsman or a slave. He asserted that gentlemen could reach their conclusions just by thinking through a problem or by arguing their case in the market place or the forum. It was Aristotle who wrote that
“It does not necessarily follow that, if the work delight you with its grace, the one who wrought it is worthy of esteem.”

He is also credited with saying
“What are called the mechanical arts carry a social stigma and are rightly dishonoured in our cities.”
By sitting in his armchair and thinking, Aristotle had decided that it was impossible for the Earth to move. We have to conclude that Aristotle was one of the men mainly responsible for the “snobbish” attitude of Greek philosophers toward practical science; he would look down his nose with disdain at the astronomer measuring angles in the skies. His philosophy did much to delay scientific progress, not just for centuries but for millennia, and his negative influence in fields like technology and mechanics was not fully overthrown until the time of Isaac Newton.

In the Aegean Sea, very near the mainland cities of Ephesus and Miletus, lay the small Greek island of Samos. It was here in the sixth century
BC
that Pythagoras had developed his philosophy and mathematics. It was here, too, in the third century
BC
that the astronomer Aristarchus (
c
.310–230
BC
) was born. Aristarchus later moved from Samos to Alexandria, where it would be easier for him to follow his interests in astronomy. In the third century
BC
every educated person knew that when there was an eclipse of the Sun the event was the result of the Moon passing across the face of the Sun. But there was another
kind of eclipse, less spectacular but more common than the solar eclipse, and it happened when the Earth passed between the Sun and the Moon. When the shadow of the Earth fell upon the Moon, the latter could still be seen during the eclipse, but with much reduced brightness. On the assumption that the Earth was at the center of the universe, it was not difficult to explain the lunar eclipse in terms of the shadow of the Earth. But Aristarchus had his own thoughts about the nature of the Earth itself, and his ideas were very advanced for his time. He had no doubt that the Earth was a sphere, a view endorsed by the curved shape of the Earth's shadow, but he also proposed the heretical idea that the sphere of the Earth was much smaller than the sphere of the Sun. He formulated a set of six hypotheses before setting out to prove his revolutionary theories. Here for the first time we have a record of an astronomer using the elements of geometry to calculate astronomical distances, in particular the distance to the Sun.

1. The Moon receives its light from the Sun.
This was Aristarchus' way of pointing out that the phases of the Moon are a result of the illumination it received from the Sun. It was obvious to him that the Moon was a sphere in space, with the Sun shining on it.

2. The Earth has a relation of both point and center to the orbit of the Moon.
Here Aristarchus was careful not to place the Earth at the center of the Moon's orbit. He knew that the orbit was not quite a circle, but he also knew that the Earth somehow controlled the Moon's motion and that it lay at a key point in the Moon's orbit.

3. Whenever the Moon appears divided in half, the great circle between light and dark is inclined to our sight.
The great circle was the divider between light and dark on the Moon; in modern parlance it is called the “terminator.” Aristarchus meant that at half-moon the observer on Earth was in the same plane as the circle that divided the bright side of the Moon from the dark side.

4. Whenever the Moon appears divided in half, the angle between Earth and Moon seen from the Sun is 1/30th of a quadrant.
Aristarchus attempts to measure the distance to the Sun. This is a very clumsy way to describe an angle. The Babylonians had used the system of dividing the circle into 360 degrees long before Aristarchus, but in the third century
BC
the Greeks did not use it. A quadrant is 90 degrees. And 1/30th of a quadrant is 1/30th of a right angle, or 3 degrees. This was the angle Aristarchus used to calculate the solar distance. His method was correct
but the true value of the angle was very much smaller than he thought—it was only about 9 minutes of arc.

5. The width of the Earth's shadow is that of two Moons.
If we could stand on the Moon during a lunar eclipse, we would see part of the Sun cut away by the Earth. We would be standing in the Earth's penumbra or partial shadow. When the Earth completely covered the Sun we would be in the umbra, the complete shadow. The umbra can be thought of as a cone that varies from the width of the Earth at its base to zero at the apex. During a lunar eclipse the Moon passes through this shadow cone. It has an angle of about half a degree and a length, the “height” of the cone, of about 869,400 miles (1.4 million km).

What Aristarchus meant by his statement was that the width of the shadow cone, at the point where the Moon entered and passed through, was twice the diameter of the Moon itself. His estimate of two Moons was very crude—an estimate of three Moons would have been more accurate. What we must admire, however, is the ingenuity of his method and the fact that his logic was correct.

6. The Moon subtends 1/15th part of a sign of the zodiac.
There are 12 signs of the zodiac and each one spans 30 degrees of sky. Therefore 1/15th of a zodiac gives an angle of 2 degrees. If Aristarchus means that the angular diameter
of the Moon is 2 degrees then he is wrong by a factor of four. This error is just not possible for an astronomer with the status of Aristarchus. A 1/60th part of a sign of the zodiac would be correct. We can only conclude that “1/15th” is a simple error of transcription.

Using these six hypotheses Aristarchus tried to measure the distance to the Moon. The shadow of the Earth resembled a great cone, and Aristarchus knew that the angle of this cone was half a degree, exactly the same as the angular diameter of the Sun. When the Moon passed through the shadow cone he calculated that the distance it traveled in passing through was equal to two lunar diameters. This implied that the distance from Earth to Moon was one-third of the length of the shadow cone. The shadow cone was about 230 Earth radii, and he was able to calculate from this figure that the distance to the Moon was about 72 Earth radii. This was a good approximation, but he could not complete his calculation because he did not have an accurate figure for the radius of the Earth.

Aristarchus went on to estimate the distance to the Sun. Once again his method was very ingenious. He knew that the Moon was illuminated by the light of the Sun and that therefore when the phase of the Moon, seen from the Earth, was exactly half, then the angle of the
Sun–Moon–Earth triangle was exactly 90 degrees. The angle between the Sun and the Moon could easily be measured from the Earth. If the distance from Earth to Moon was known, then the triangle could be solved and the distance from Earth to Sun could be calculated.

But the experiment was a failure. We can see from hypothesis 4 that he calculated the angle between the Sun and the Moon to be 87 degrees, when in fact it was less than one-sixth of a degree. The heavily cratered lunar surface made it impossible for him to decide when the Moon was exactly at half phase, and because of this he was only able to obtain the crudest figure of 20 lunar distances for the distance to the Sun. The lunar distance was again expressed in terms of the Earth's radius but this, too, was an unknown quantity.

It would appear from this that all the efforts of Aristarchus came to nothing. He did not leave behind a measure of the Earth's radius, nor of the lunar distance or the distance to the Sun. But in spite of these failures Aristarchus is remembered as one of the greatest astronomers of all time. He was an excellent practical astronomer and he was also a great theorist. His lasting claim to fame is that he was the first to propose a world model with the Sun at the center of the solar system and the planets orbiting around it. His distances may have been wrong, but he knew that the Earth was a revolving
globe following an orbit around the Sun. Aristarchus was a thousand years ahead of his time, and there is a strong case for calling the Copernican System the Aristarchian System.

Later in the same century a man called Eratosthenes (
c
.276–194
BC
) arrived in Alexandria to take up his post as the new librarian. He was born in the town of Cyrene in the upper reaches of the River Nile, about 500 miles (800 km) to the south of Alexandria. Eratosthenes remembered when, as a child, he and his playmates peered down into the darkness of a deep well. It was possible, for a short time at noon on just one day of the year, to see a brilliant light at the bottom of the dark well. The light was the reflection of the Sun on the surface of the water far below. In fact, the light could be seen only at noon on midsummer's day when the Sun was directly overhead. Eratosthenes knew that on the same day of the year the Sun in Alexandria did not reach the zenith. He could not repeat his childhood observations in Alexandria, but he could measure the height of the Sun at noon and show that it was an angle of 7.5 degrees away from the vertical. He knew that the Earth was a sphere and that this angle was the difference in latitude on the surface of the Earth between Alexandria and the town of Syene.
The ratio of 7.5 degrees to the full circle was the same as the ratio of the distance between the two places to the circumference of the whole Earth. If, therefore, Eratosthenes could measure the distance between Alexandria and Syene, he could easily calculate the circumference of the Earth. He estimated the distance in units called stadia—each unit being the length of a games stadium, although we cannot be sure of the exact value. Using modern units, the stadium is thought to have been about 80 meters (263 ft), and the distance from Alexandria to Syene was 10,000 stadia. This gives a value for the circumference of the Earth of 23,846 miles (38,400 km)—a very accurate determination, although we have to ask if the length of the stadium has perhaps been calculated retrospectively from the known circumference of the Earth!