$ 8 7 ] The Motion of the Planets 115 



as seen from the sun, an interval of time known as the 

 sidereal period. This can evidently be calculated by a 

 simple rule-of-three sum from the data given. For Venus 

 has in 584 days gained a complete revolution on the 

 earth, or has gone as far as the earth would have gone in 

 584 + 365 or 949 days (fractions of days being omitted for 

 simplicity) ; hence Venus goes in 584 x |ff days as far 

 as the earth in 365 days, i.e. Venus completes a revolution 

 in 584 x Iff or 225 days. This is therefore the sidereal 

 period of Venus. The process used by Coppernicus was " 

 different, as he saw the advantage of using a long period of 

 time, so as to diminish the error due to minor irregularities, 

 and he therefore obtained two observations of Venus at 

 a considerable interval of time, in which Venus occupied 

 very nearly the same position both with respect to the sun 

 and to the stars, so that the interval of time contained very 

 nearly an exact number of sidereal periods as well as of 

 synodic periods. By dividing therefore the observed 

 interval of time by the number of sidereal periods (which 

 being a whole number could readily be estimated), the 

 sidereal period was easily obtained. A similar process 

 shewed that the synodic period of Mercury was about 116 

 days, and the sidereal period about 88 days. 



The comparative sizes of the orbits of Venus and 

 Mercury as compared with that of the earth could easily 

 be ascertained from observations of the position of either 

 planet when most distant from the sun. Venus, for 

 example, appears at its greatest distance from the sun when 

 at a point v t (fig. 44) such that v x E, touches the circle in 

 which Venus moves, and the angle E, v, s is then (by 

 a known property of a circle) a right angle. The angle 

 s E! v t being observed, the shape of the triangle s E, v t is 

 known, and the ratio of its sides can be readily calculated. 

 Thus Coppernicus found that the average distance of 

 Venus from the sun was about 72 and that of Mercury 

 about 36, the distance of the earth from the sun being 

 taken to be 100; the corresponding modern figures are 

 72-3 and 387. 



87. In the case of the superior planets, Mars, Jupiter, 

 and Saturn, it was much more difficult to recognise that 

 their motions could be explained by supposing them to 



