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The generalizations which can be collected on the subject from direct observation, even such as Kepler's law, are mere approximations: the planets, owing to their perturbations by one another, do not move in exact ellipses.

Jupiter, which shows the greatest effect, makes the circuit of his orbit in 4,333 days instead of 4,335, which it would require if Kepler's law were strictly true.

But in another respect the change is of the utmost importance, since it enables us to extend Kepler's law, which relates solely to the sun and its planets, to other attracting bodies, such as the earth, moon, and stars.

As solar pressure, atmospheric drag and other forces act on them, they obey Kepler's law; their orbit times decrease until they approach the Schuler 84-minute period.

The moon's time of revolution, when so near the earth as barely to escape contact with it, must have been, by Kepler's Law, more than two and less than two and a half hours.