GRAVITATION VERSUS INERTIA 17 



nicus Ms life, and it was only by the display of equal 

 discretion in retracting his utterances that he escaped 

 the rough logic of the Inquisition. However, one error 

 Copernicus voluntarily carried over from the older 

 theory, namely, the circular form of planetary orbits 

 and with it the tinkering device of epicycles. 



About sixty-five years later (the telescope having 

 in the interim been invented) John Kepler, as the result 

 of years of arduous observation and mathematical toil, 

 announced his three famous laws of planetary motion, 

 which may be paraphrased as follows : 



1. The planets do not revolve in circles at all, but 

 in ellipses. This for all time dispenses with the need 

 of epicycles. Moreover, the sun is not located in the 

 center of the ellipse, but in one of the foci, the focus 

 he occupies being conveniently called the lower to dis- 

 tinguish it from the other. 



2. If we imagine the circulating planet to be 

 joined to the central body by an imaginary straight line 

 which keeps traveling continually around the orbit with 

 it, that line (known as the radius vector) passes over 

 equal areas in equal periods of time. 



8. The cube of the mean distance of any given 

 planet from the sun bears the same ratio to the cube 

 of the mean distance of any other planet, as the square 

 of the time of revolution of the first does to the square 

 of the time of revolution of the second. Example : If a 

 planet B be twice as far as A from the sun, and if B's 

 period of revolution is known to be 24 days, then 



2 3 . is .. 24 2 : X 2 



whence X, A's period, is found to be the square root of 

 72 days. 



Therefore, given the two elements of distance and 

 period of one planet, and the distance or period of 

 another, we can find the missing term. 



