136. The Sidereal Period of a Superior Planet.—The sidereal period of a superior planet is found by a method of computation similar to that for finding the sidereal period of an inferior planet:—
Let a denote the synodical period of the planet,
Let b denote the sidereal period of the earth,
Let x denote the sidereal period of the planet.
Then will 360°/b = daily motion of the earth,
And 360°/x = daily motion of the planet;
Also 360°/b - 360°/x = daily gain of the earth.
But 360°/a = daily gain of the earth:
Hence 360°/b - 360°/x = 360°/a
1/b - 1/x = 1/a