DISTANCES OF HEAVENLY BODIES EICHELBEEGEE. 171 



distance of the sun from the earth by determining the distance or 

 parallax of one of the planets. 



From observations of Mars, Kepler obtained the distance of the 

 sun from the earth as about three times that accepted up to his time. 

 His value, however, was but one-seventh of the true distance. About 

 50 years later Flamsteed and Cassini, working independently and 

 using the same method as that employed by Kepler, obtained for 

 the first time approximately the correct value of the distance of the 

 sun from the earth. In a letter dated November 16, 1672, to the 

 publisher of the Philosophical Transactions, Flamsteed says : 



September last I went to Townley. The first week that I intended to have 

 observed $ there with Mr. Townley, I twice observ'd him, but could not make 

 two Observations, as I intended, in one night. The first night after my return, 

 T had tlie good hap to measure his distances from two Stars the same night; 

 whereby I find, that the Parallax was very small ; certainly not 30 seconds : 

 So that I believe the Sun's Parallax is not more than 10 seconds. Of this 

 trtbservation I intend to write a small Tract, when I shall gain leisure; in which 

 I shall demonstrate both the Diameter and Distances of all the Planets by 

 observations ; for which I am now pretty well fitted. 



During the two and a half centuries since Flamsteed's determina- 

 tion there have been more than a bundled determinations of the 

 solar parallax by various methods. In the method used by Flam- 

 steed the rotation of the earth is depended upon to change the rela- 

 tive position of the observer, the center of the earth, and Mars. 

 Another method is to establish two stations widely separated in lati- 

 tude and in approximately the same longitude. At one station the 

 zenith distance of Mars will be determined as it crosses the meridian 

 north of the zenith; at the other station the zenith distance will be 

 determined as it crosses the meridian south of the zenith. The sum 

 of the two zenith distances minus the diiference in latitude between 

 the two stations will give the displacement of Mars due to parallax. 

 These two methods have been successfully applied to several of the 

 asteroids whose distances from the sun are very nearly that of Mars. 



The nearest approach of Venus to the earth is during her transit 

 across the face of the sun, and these occasions — four during the 

 last two centuries — have been utilized to determine the solar paral- 

 lax. Here, as in the case of Mars, two different methods may be 

 used, either by combining observations at two stations widely sepa- 

 rated in latitude or at two stations widely separated in longitude. 



The methods just described for obtaining the solar parallax, the 

 geometrical methods, were made available, as has been said, by 

 the discovery of Kepler's laws of planetary motion. Newton's dis- 

 covery of the law of gravitation gave rise to another group of 

 methods, designated as gravitational methods. The best of these 

 is probably that in which the distance of the sun from the earth 

 is determined from the mass of the earth, which in turn is deter- 



