172 OUTLINES OF NATURAL PHILOSOPHY. 



or the planet's distance from the Sun, is found. 

 The position of PS, relatively to NS, is also thus 

 determined ; for, in the right-angled spherical tri- 

 angle, of which the base is the arch that mea- 

 sures the angle OSN, and the perpendicular the 

 arch which measures the angle PSO, the hypothe- 

 nuse is the measure of the angle PSN, which the 

 radius vector makes with the given line SN. 



b. Thus also, EP, the planet's distance from the 

 Earth, is found. If, then, by observations made 

 a little before and after the opposition, the diur- 

 nal motion of the planet in its own orbit, relative- 

 ly to E, be determined, the same may be found 

 relatively to S, being to the other in the inverse 

 ratio of SP to EP, 



When many oppositions of a planet are thus obser- 

 ved, many different radii of the planetary orbits 

 are determined, as well as the angular motions 

 corresponding to them. 



170. It appears, on laying down the radii 

 determined as above, that the orbits of the pla- 

 nets are ellipses, having the Sun in their com- 

 mon focus ; and that the angular motions of a 

 planet round the Sun, are inversely as the 

 squares of its distances from the Sun ; so that 

 the sectors described by the radius vector, are 

 proportional to the time. 



These 



