Ancient civilizations began to create calendars as a way of reminding them about important annual events, such as the times to plant and then to store crops. As cultures developed, the calendars became more sophisticated. Later, observations from eclipses led philosophers and early astronomers to develop ways of measuring the distance from the Earth to the Sun, and even the size of the Earth itself. However, for many millennia the belief that the Earth was at the center of the universe held back the advancement of our understanding of the true nature of the solar system.
In the fertile plain between the great rivers of the Tigris and the Euphrates there developed the ancient civilizations of Sumeria and Babylon. The Sumerian civilization, which was even older than the first Egyptian dynasty, dates back to about 8000 BC. The Sumerians developed a form of writing executed with a stylus on a clay tablet. The writing became known as “cuneiform” text, with the symbols written with the stylus representing either nouns or verbs.
In addition to this early form of writing, the Sumerians were also the first civilization to develop a working calendar. Like all who followed them they wanted to bring together the cycles of both the Sun and the Moon into their calendar. The Moon took 30 days, measured to the nearest day, to go through all its phases, and thus the Sumerian year consisted of 12 months of 30 days, giving a total of 360 days. The fourth month was written in cuneiform as the character for “seed”; the 11th month, the harvest month, was written as the character for “grain”; and it was followed by the character for “house” or “barn.” The Sumerian calendar thus predicted and noted the season to sow the seed, the season to harvest the crops, and when to store them in the barn for the winter.
For a while the calendar served them well, but after a few years they found that the harvest did not ripen by the 11th month because their year was too short by just over five days. So the Sumerians simply added an extra month to their calendar every six or seven years. They knew that their year was too short, but a year of 360 days had one great advantage. It was a number that divided exactly by 60, and because of this the complete circle of the heavens was seen as divided into 360 equal parts that we now call degrees. The base of 60 was used for both angular measure and time intervals—thus 60 seconds became one minute and 60 minutes made an hour. Eventually the angular measure of the degree was also divided into the 60 parts that we know as minutes, and the minutes themselves were divided into 60 seconds of arc. The confusion between minutes and seconds of arc, and minutes and seconds of time, still remains, however.
In the dynasty of the emperor Hammurabi (1792–1750 BC) the capital of the Sumerian kingdom moved to Babylon and the area became known as Babylonia. Much of the ancient calendar was retained, and every lunar month began on the first appearance of the crescent Moon. The astronomers went on to divide the stars into a zodiac of six houses of unequal portions.
The Babylonians were not only great astronomers, they were also very able mathematicians. We see many examples of geometry and trigonometry appearing in their work, as well as advances in astronomy. Their calculation of pi, the ratio of the circumference of a circle to its diameter, was given as three and one eighth; it was in error by a few percent, but it shows that they knew the importance of this ratio. One of the surviving cuneiform scripts shows that the Babylonians knew how to solve the quadratic equation. They were the first civilization to introduce a seven-day week and they named the seven days after the Sun and the Moon followed by the five known planets, to give the sequence Sun, Moon, Mercury, Venus, Mars, Jupiter and Saturn. (This naming is still very evident in languages such as French and Spanish, but in English the Norse gods have supplanted all the original names except for Sunday, Monday and Saturday.)
The Earth was often imagined by many ancient peoples as a hollow hemispherical shell floating on the world-waters—the idea of the Earth as boat-shaped is one of the oldest images of the Earth. In the Babylonian conception of the universe the Earth occupied the central place and was the accepted center of their planetary system.
According to the Babylonian system the sky forms a hollow vault above which reside the gods. In the east (left) is a door out of which the Sun rises each day, and a similar door is in the west (right) through which it returns. In the sky there are fixed stars, meteors and moving planets. The Earth is round in the form of a large hollow mountain, which rests on water. In the east is the bright mountain of the rising Sun and in the west the dark mountain of the sunset. The sea extends over the sky and in the southwest lies the island of the blessed. Under the ground is the region of the dead, consisting of seven concentric areas.
At about the time the Babylonians were devising their calendars, the ancient Egyptians also made valuable contributions to the calendar. For the Egyptians, the annual flooding of the Nile was their lifeblood, and to be able to predict the flooding was of great significance to them. Their calendar evolved with only three seasons, which they called the flooding, the subsistence of the river and the harvesting. Each of these three seasons was divided into four lunar months, making a total of 12 months in all. The Egyptians instigated a calendar based on their 12 lunar months. This calendar remained in use for approximately 3000 years, but like the Babylonians the Egyptians needed to insert extra months every six or seven years to maintain its accuracy. In later years they simply added five or six days at the end of the year. This was the system they used in 440 BC when the Greek traveler and historian Herodotus (484–420 BC) gave a description of the Egyptian calendar:
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!
Eratosthenes’ work was only a generation later than that of Aristarchus. His result would have enabled Aristarchus to calculate the distance to the Moon with tolerable accuracy. By this time Aristotle’s assertion that the Earth did not move had been rejected by a few enlightened people, but it was many centuries before the negative influence of Aristotle was completely overthrown.
Eratosthenes was the first person to measure the size of the Earth to any degree of accuracy, but it is worth mentioning that there were prior claims to this measurement. The Chaldeans of ancient Babylon had a tradition that a person could walk 30 stadia in an hour; this equates to a distance of about 1.5 miles (2.4 km) per hour. In a day, therefore, a well-organized relay team could easily cover a distance of about 37 miles (60 km). The Chaldeans claimed that if a person could walk steadily at this speed for a year then they would encompass the whole Earth. The calculation gives a figure for the circumference of the Earth of about 13,000 miles (21,000 km). In fact, this figure is only just over half the true distance, but it is of little matter for the method is very unsound scientifically and the measurement could not possibly have been carried out by marching around the Earth.
There is another much later claim. In the first century BC, the astronomer Poseidonius (c.135–51 BC) measured the circumference of the Earth. His method was very similar to that of Eratosthenes, but he made use of the stars rather than the Sun. He made observations of the star Canopus as seen from Rhodes and from Alexandria. From the elevation of the star he was able to measure the difference in latitude between the two places, and he arrived at a figure usually quoted as 240,000 stadia or 11,923 miles (19,200 km). Again, this figure was far too low, and indeed it was disputed by the Greek geographer Strabo (63 BC–AD 23). It appears from one account that when Poseidonius made his measurement on Canopus the star grazed the horizon at Rhodes. Poseidonius probably knew nothing of atmospheric refraction, so this factor would create a substantial error in his measurements. Despite the erroneous calculations often made by ancient scientists, we must nevertheless admire the ingenuity of some of the methods they used.