To find the path of a planet, we first get its synodic period, or period with regard to the Sun. Then, from a sufficient number of observations of synodic periods to give their mean, we obtain the sidereal period, or period with reference to the stars.

By considering the angular motions, the two periods are easily seen to be connected by the following equation: —

Where	E = the Earth's period;
 	S = the Planet's synodic period;
 	P = the Planet's sidereal period.

From two bearings separated by a sidereal period, we get a quadrilateral, of which, knowing parts enough to solve, we derive the planet's distance from the Sun at the moment. We now have for the planet what we had for the Sun, —direction and distance at a given time. Dotting these data upon the apparent path, Kepler proved that the orbit of Mars was an ellipse. Mars was the first of the planets thus to have its orbit found; following it the others yielded similarly to the genius of the man. All the planets, then, move in ellipses about the Sun.
