162 eichelberger: distances of heavenly bodies 



arranging these bodies in order of distance very much as we 

 know them to-day, assuming that the more rapid the motion 

 of a body among the stars the less its distance from the Earth ; 

 the stars, that were supposed to have no relative motions, were 

 assumed to be the most distant objects. 



The first attempt to assign definite relative distances to any 

 two of the bodies was probably that of Eudoxus of Cnidus who, 

 about 370 B.C., supposed, according to Archimedes, that the 

 diameter of the Sun was nine times greater than that of the Moon, 

 which is equivalent to saying that, since the Sun and the Moon 

 have approximately the same apparent diameter, the distance 

 of the Sun from the Earth is nine times greater than that of the 

 Moon. 



A century later, about 275 B.C., Aristarchus of Samos gave 

 a method of determining the relative distances of the Sun and 

 Moon from the Earth as follows: When the Moon is at the 

 phase first quarter or last quarter, the Earth is in the plane of 

 the circle which separates the portion of the Moon illuminated 

 by the Sun from the non-illuminated part, and the line from the 

 observer to the center of the Moon is perpendicular to the line 

 from the center of the Moon to the Sun. (Diagram shown.) 

 If, at this instant, the angular separation of the Sun and Moon 

 is determined, one of the acute angles of a right-angle triangle — 

 Sun, Moon, and Earth — is known, from which can be deduced 

 the ratio of any two of the sides, as, for instance, the ratio of the 

 distance from the Earth to the Moon to that from the Earth 

 to the Sun. Aristarchus gives the value of this angle as differ- 

 ing from a right angle by only one-thirtieth of that angle, i.e. 

 it is an angle of 87°, from which it follows that the distance from 

 the Earth to the Sun is nineteen times that from the Earth to 

 the Moon. This method of Aristarchus is theoretically correct, 

 but in determining the angle at the Earth as being 3° less than a 

 right angle, he made an error of about 2° 50'. 



Hipparchus, who lived about 150 B.C. and was called by 



Delambre the true father of astronomy, attacked the problem 



of the distances of the Sun and Moon through a study of eclipses. 



Assuming in accordance with the result of Aristarchus that the 



