| 6 | The Solar System |
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.
Thus we have obtained the accompanying plan of the system.
Kepler discovered two more relations: first,Kepler's laws. that the radius vector of any planet swept over equal areas in equal times; and, second, that the cubes of the major axes of the orbits of any two planets were as the squares of their periodic times. The latter is not exactly true, but becomes so if we take the masses at work into account.
From these three "laws," Newton showed that the force governing the motions of the planets was in each case directed to the Sun, and was as the inverse square of the distance from him. Reversely he showed that such being the law of gravitation, the orbits must all be conic sections.
But conic sections are of two kinds,—ellipses Ellipses and hyperbolas. or closed curves, and hyperbolas or curves that do not return into themselves. Clearly permanent members of a system must travel in the first of these two classes of curves, visitors only in the second. Here, then, we have an instant criterion for distinguishing bodies that belong to our system from those that visit it from without.
