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 M_{1} and M_{2}, 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, or from west to east. Hence between M_{1} and M its motion has changed from direct to retrograde, and therefore at some intermediate point, say _m_{1}_, (about Aug, 23 in fig. 7), Mercury appears for the moment to be stationary, and similarly it appears to be stationary again when at some point _m_{2}_ between M and M_{2} (about Sept. 13 in fig. 7). [Illustration: FIG. 47.—The stationary points of Mercury.] In the case of a superior planet, say Jupiter, the argument is nearly the same. When in opposition at J (as on Mar. 26 in fig. 6), Jupiter moves more slowly than the earth, and in the same direction, and therefore appears to be moving in the opposite direction to the earth, _i.e._ as seen from E (fig. 48), from left to right, or from east to west, that is in the retrograde direction. But when Jupiter is in either of the positions J_{1} or J (in which the earth appears to the observer on Jupiter to be at its greatest distance from the sun), the motion of the earth itself being directly to or from Jupiter produces no effect on the apparent motion of Jupiter (since any displacement directly to or from the observer makes no difference in the object’s place on the celestial sphere); but Jupiter itself is actually moving towards the left, and therefore the motion of Jupiter appears to be also from right to left, or from west to east. Hence, as before, between J_{1} and J and between J and J_{2} there must be points _j_{1}_, _j_{2}_ (Jan. 24 and May 27, in fig. 6) at which Jupiter appears for the moment to be stationary. [Illustration: FIG. 48.—The stationary points of Jupiter.] The actual discussion of the stationary points given by Coppernicus is a good deal more elaborate and more technical than the outline given here, as he not only shews that the stationary points must exist, but shews how to calculate their exact positions.