1 1 8 A Short History of Astronomy [Cn. IV. 



values for the synodic and sidereal periods, viz. 780 days 

 and 687 days respectively for Mars, 399 days and about 

 12 years for Jupiter, 378 days and 30 years for Saturn 

 (cf. fig. 40). 



The calculation of the distance of a superior planet 

 from the sun is a good deal more complicated than that 

 of Venus or Mercury. If we ignore various details, the 

 process followed by Coppernicus is to compute the position 

 of the planet as seen from the sun, and then to notice 

 when this position differs most from its position as seen 

 from the earth, i.e. when the earth and sun are farthest apart 

 as seen from the planet. This is clearly when (fig. 46) 

 the line joining the planet (P) to the earth (E) touches the 

 circle described by the earth, so that the angle s P E is 

 then as great as possible. The angle P E s is a right 

 angle, and the angle s P E is the difference between the 

 observed place of the planet and its computed place as 

 seen from the sun ; these two angles being thus known, the 

 shape of the triangle s P E is known, and therefore also 

 the ratio of its sides. In this way Coppernicus found 

 the average distances of Mars, Jupiter, and Saturn from the 

 sun to be respectively about i|, 5, and 9 times that of the 

 earth ; the corresponding modern figures are 1*5, 5*2, 9*5. 



88. The explanation of the stationary points of the 

 planets (chapter i., 14) is much simplified by the ideas of 

 Coppernicus. If we take first an inferior planet, say Mercury 

 (fig. 47), then when it lies between the earth, and sun, as 

 at M (or as on Sept. 5 in fig. 7), both the earth and Mer- 

 cury are moving in the same direction, but a comparison 

 of the sizes of the paths of Mercury and the earth, and of 

 their respective times of performing complete circuits, shews 

 that Mercury is moving faster than the earth. Consequently 

 to the observer at E, Mercury appears to be moving from 

 left to right (in the figure), or from east to west ; but this 

 is contrary to the general direction of motion of the planets, 

 i.e. Mercury appears to be retrograding. On the other 

 hand, when Mercury appears at the greatest distance from 

 the sun, as at M, and M , its own motion is directly towards 

 or away from the earth, and is therefore imperceptible ; 

 but the earth is moving towards the observer's right, and 

 therefore Mercury appears to be moving towards the left, 



