124 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1936 



minutes of arc. Aristarchus estimated it to be 3°, and so concluded 

 that the sun was only about 20 times as distant as the moon— actually 

 it is 400 times as distant. 



He also made estimates of the actual distances. Thanks to the 

 genius of Anaxagoras, the nature of eclipses was already well under- 

 stood. It was known that the darkness which spreads over the moon 

 at an eclipse is the shadow of the earth. Aristarchus, knowing that 

 the sun was many times more distant than the moon, saw that this 

 shadow must be approximately of the same dimensions as the earth 

 itself — it was a circle of the size of the earth seen at the distance of 

 the moon. Knowing the size of the earth, it was an easy matter to 

 compute the distance of the moon. 



Once again Aristarchus relied on a series of erroneous measures. 

 He estimated that the earth's shadow had only twice the diameter of 

 the moon — actually it has three times this diameter. Also, the moon 

 subtends an angle of half a degree in the sky, but Aristarchus took 

 the angle to be 2°, and so got erroneous values for the moon's distance 

 as well as for its size. Clearly exact measurement was not his strong 

 point, yet he was the first to demonstrate the order of magnitude of 

 astronomical distances. 



Aristarchus made an even more important contribution to the 

 large-scale problems of astronomy. He showed, by reasoning very 

 similar to that used by Copernicus 1,800 years later, that the earth 

 revolved in a circular orbit about the sun. He then argued that, as 

 the fixed stars appeared in spite of this motion to retain fixed places 

 in the heavens, they must be at inuneasurably great distances from 

 the earth, saying that the distances of these stars "bore the same rela- 

 tion to the earth's orbit as the radius of a sphere bears to its center" — 

 in other words, the whole solar system was a mere point in the immen- 

 sity of space. 



I need scarcely remind you how, in the second century after Christ, 

 these enlightened views were challenged and temporarily vanquished 

 by Ptolemy of Alexandria. Ptolemy argued that if the earth were 

 rotating, objects at the Equator would be in the most violent rotation, 

 and so would fly off into space, since "matter which is in violent rota- 

 tion does not seem fit to be massed together, but rather dispersed." 

 He went on to say that "long before now the disintegrated parts of 

 the earth would have been dissipated over the heavens themselves, 

 which is very ridiculous." He also said that, if the earth were rotat- 

 ing, a stone dropped to earth would not reach its destined place, be- 

 cause the earth would be moving eastward under it all the time it 

 was falling. He said further that if the earth were rotating, the 

 clouds would move over our heads from east to west as a consequence 

 of this rotation. Clearly he had never stood in the track of the 



