One may well ask how our sophisticated modern view of the universe arose. As far as we can tell, it was Parmenides of Elea who 2,500 years ago ennunciated for the first time the notion that the earth is a sphere. This idea was based upon Parmenides' feeling that a body of any other shape would fall inwards on itself. Considering the fact that there was no theory of gravitation at that time, this line of argument was quite prophetic.
Plato (427-347 B.C.) had a great deal of influence, so his support of the spherical earth hypothesis did much to acquire general acceptance of that notion, even though his reasoning was further removed from modern scientific thought.
Aristotle (384-322 B.C.) developed a line of reasoning which is very modern. He pointed out that during lunar eclipses the shadow of the earth upon the moon is always circular, no matter whether the moon is high overhead or closer to the horizon. If the earth were of some other shape than a sphere, for example, if it were shaped like a tin can, then its shadow on the moon would depend very much upon the relative orientation of the Sun, earth and moon.
The first accurate determination of the size of the earth was made by Eratosthenes (276-195 B.C.). The summer solstice is that day upon which the Sun attains the greatest altitude above the horizon in northern skies. At the time of the summer solstice it was known to Eratosthenes that the Sun appeared directly overhead at noon in the city of Syene, Egypt. This ancient city corresponds to the modern city of Aswan, the location of the famous Aswan dam. Now, Alexandria, on the shore of the Mediteranean Sea was supposed to be due north of Syene. Actually, it lies a couple hundred miles to the west of due north, as you can tell from a modern map of the area. Fortunately for Eratosthenes the fact that the two cities do not fall precisely upon a north-south line introduced a relatively small error in his determination of the size of the earth.
At noon during the summer solstice the Sun was not directly overhead in Alexandria, but instead it was found to be about 7 degrees 12 minutes south of the zenith (overhead). Note that one degree may be divided into 60 minutes, and one minute of arc may be divided into 60 seconds. So we are talking about 7.2 degrees.
In the time of Eratosthenes, one common method for measuring great
distances was by runners, who acquired great skill in estimating the
distances they covered. From the distance between Syene and
Alexandria determined in this manner, Eratosthenes concluded that
the radius of the earth must be about 3925 miles. Of course, the
Greeks didn't use miles. I just translated from one archaic system
of units to another. In any event this estimate of the earth's size
is remarkably accurate. I suspect that if I requested members of
this class to measure the size of the earth, many would not do as
well as Eratosthenes.
The idea that the earth rotates daily upon its axis was first ennunciated by Heraclides during the fourth century B.C. Do not confuse him with the philosopher Heraclitus, who lived much earlier. About 260 B.C. Aristarchus took the further step of placing the Sun at the center of the solar system, with the earth revolving about the Sun. Not only did Aristarchus originate the heliocentric model, but he inferred from this model that the stars must be very far from the earth, for no parallax had been observed for any star as the earth revolves about the Sun.
Aristarchus was the first to make a serious attempt to determine the
size of the solar system, a task which was not to be completed in
a satisfactory manner until the eighteenth century. The attempt of
Aristarchus was based upon simultaneous consideration of the Sun and
moon. In essence his idea was to measure the angle between the moon
and the Sun when the moon is at quadrature, i.e., first quarter or
last quarter. If you should have the opportunity, try to make this
measurement yourself. You should then appreciate the difficulty of
the task. Nevertheless, Aristarchus concluded that the angle was
about 87 degrees. Since one is dealing with a long skinny triangle,
it is clear that the distance to the Sun must be very great compared
to the distance to the moon. If Aristarchus's estimate were correct,
the Sun would be about 20 times further than the moon. Actually, the
angle is more like 89 degrees 50 minutes, corresponding to an even
longer and skinnier triangle, with the Sun actually 345 times as far
as the moon.
The distance to the moon was determined by Hipparchus (160-125 B.C.) by comparing the radius of curvature of the earth's shadow with the radius of the moon during a lunar eclipse. From the observed ratio the size of the moon could be inferred, since the size of the earth was already known from the work of Eratosthenes. If you ever have the opportunity to witness a lunar eclipse, try measuring the radius of curvature of the earth's shadow as Hipparchus did.
Knowing the size of the moon and being well aware that the apparent
diameter of the moon is about 1/2 degree, Hipparchus was able to
calculate the distance to the moon, getting a value within 1 percent
of the value which is currently accepted. The distance is about 1/4
million miles. This means, of course, that the Sun must be at least
5 million miles away, 20 times the distance to the moon.
Hipparchus also discovered the precession of the equinoxes. This refers to the fact that the positions of the vernal and autumnal equinoxes in the sky change, albeit very slowly. Polaris was not always the pole star! The rate of change, however, is so slow that one must marvel at the fact that ancient men were aware of the change. Of course, the point is that the effect is cumulative. Therefore, it is only necessary to have access to historical records, and curiosity. Hipparchus went further. He was able to demonstrate the precession of the equinoxes over a short period of time. To accomplish this he developed a simple apparatus, which we refer to as the Hipparchus ring. The ring was set up very carefully so that its plane was perpendicular to the earth's axis. Only on two days of the year did the Sun cast a shadow of the ring upon the ring itself; namely, on the days of the vernal and autumnal equinoxes. On these days, all day long the shadow of the ring was cast upon the ring itself. After a number of years it was observed that the position of the equinoxes, which could be determined accurately with the Hipparchus ring, had changed by a small but significant amount. The rate of precession is so slow that 26,000 years is required for the equinoxes to return to their original positions. Someday the star Vega will be regarded as the north star, if anyone is still around and curious about the heavens.
The impressive discoveries of men like Aristarchus and Hipparchus should not cause one to believe that genius is infallible. In spite of his own great contributions to astronomy, Hipparchus, it should be noted, abandoned the idea of Heraclides that the earth rotates daily. As the centuries passed, it seemed that Greek science tended to move ever further from what has become our modern point of view. Thus, in the 2nd century A.D., Ptolemy rejected Aristarchus's notion that the Sun is at the center of the solar system. Nevertheless, it would be foolish to ignore Ptolemy's great contributions in the area of the prediction of planetary motions. Using his geocentric theory, men were able to predict with reasonable accuracy such astronomical events as eclipses and conjunctions of the planets. The latter term refers to a situation where two planets have approximately the same direction as viewed from earth.
I should like to present the point of view that while the heliocentric model of Aristarchus is closer to contemporary lay knowledge of physics than is the geocentric model of Ptolemy, both models are equally far from the viewpoint of a modern physicist, conditioned to think in terms of Einstein's theory of relativity. We no longer think of objects moving through an immutable three-dimensional Euclidean space. Thus, we now regard the distinction between a heliocentric and a geocentric viewpoint as one of computational ease versus computational difficulty. Unfortunately the philosophically appealing notion of relativity often goes hand in hand with an extraordinary degree of mathematical complexity. It is not surprising; only in an exceedingly complicated theory could it be irrelevant what "actually" moves.
An example such as this should make one wonder how many of the crucial problems facing science today will turn out centuries hence to be meaningless questions within the framework of some theory which is as yet not even a gleam in some physicist's eye. It is a very strange and confusing notion, but in a sense a question cannot be formulated succinctly until the answer is known, and then the question may turn out to be meaningless. Meanwhile, a number of people may be ridiculed or burned at the stake for advocating one or another unorthodox opinion concerning the question.
