Greek Accomplishments

The Greeks were clever people (despite introducing the convoluted geo-centric model). Some of their astronomical triumphs are:
• Aristotle (384-322 B.C.):
  • spherical Earth <===> changing appearance of the sky with latitude, lunar eclipses were "curved."

• Aristarchus (310-230 B.C.):
  • Helio-centric model for the Solar System (not believed because parallax was not observed). We note that that Aristarchus had a physical reason for believing in a helio-centric theory. (Copernicus 1700 years later was driven more by aesthetic arguments.)

    Argument: Aristarchus wanted to show that the Sun was much larger than the Earth and so most likely should be the object in the center of the Solar System.

    The first step was to show that the Sun was much farther from the Earth than was the Moon.



Aristarchus timed how long it took the Moon to go from 3rd to 1st quarter (t) and then from 1st to 3rd quarter (T). If t = T, then the angle A would be 90 degrees. If t less than T, then the angle would be less than 90 degrees. Note that if A ~ 90 degrees this means that the Sun is much much much much further from the Earth than is the Moon. The smaller the angle A is, the smaller the difference between the distances of the Sun and Moon from the Earth. Quantitatvely, the ratio of the distance from the Earth to the Moon (d) to the distance from the Earth to the Sun (D) is given by

(d/D) = sine(90-A)

Aristarchus tried to perform this exercise (it was difficult because A is very nearly 90 degrees). His answer was very inaccurate, but he did find that (d/D) was much smaller than 1, that is, the Sun was much farther away from the Earth than was the Moon!

The next step was to infer the relative size of the Sun and the Earth. To accomplish, Aristarchus used eclipses.



Based on the eclipse geometry shown above, Aristarchus concluded that the Sun must be much larger than the Moon because the angular sizes of the two objects are nearly the same while the Sun is much farther away.

Next, Aristarchus wanted to figure out how large the Moon was compared to the Earth. He decided that the length of the Earth's shadow was much greater than the distance to the Moon and so he could assume that the diameter of the shadow (where the Moon entered it) was roughly the same size as the Earth. Given this, Aristarchus could then simply time how long it took the Moon to pass through the shadow of the Earth and then deduce how large the Moon was compared to the Earth. To see this,


Aristarchus concluded that the Earth was three or so times larger than the Moon! (The Earth is actually around four times larger than the Moon and so his guess wasn't so bad.) Aristarchus thus concluded that the Sun was much larger than the Earth and so it was much more likely that it lived at the center of our Solar System!
• Erastosthenes (273-? B.C.)
  Circumference of the Earth: As you in move in latitude on the Earth, the appearance of the sky will change. Erastosthenes took advantage of this fact to infer the size of the Earth.



On June 21, the Sun casts no shadow at "noon" at Syrene (latitude ~ 23.5 degrees). That is, the Sun is passing directly overhead at Syrene. At Alexandria, the Sun casts a short shadow at "noon" suggesting that the Sun is passing south of the zenith at noon. The length of the shadow suggested that the angle the Sun made with the vertical was 7 degrees. Hmmmm, this means that Alexandria and Syrene are separated by 7 degrees in latitude or that they are 7/360-ths of the circumference of the Earth apart. Since the distance from Syrene to Alexandria could be measured, Erastosthenes deduced the circumference of the Earth. He came within ~2 % of the current estimate!