Page:A short history of astronomy(1898).djvu/164

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 11/2, 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 Mercury 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 m₁ and m₂, 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 Merqury appears to be moving towards the left,