Kepler's laws

Kepler's laws (i.e., Kepler's laws of planetary motion) are three laws that cover the basic kinematics (description of rules governing the motions) of the solar system's planets, and are useful for many cases of orbiting bodies. Johannes Kepler worked them out in the early 17th century in his effort to find a mathematical basis for the known astronomy.

1. The orbits are elliptical, with the Sun at a focus of the ellipse.
2. The orbital speed is such that a line between planet and Sun sweeps out the same area over any equal time-intervals.
3. The square of the orbital period is proportional to the cube of the orbit's semi-major axis.

An orbit that follows these laws is termed a Keplerian orbit. Considering a circle to be a special case of an ellipse, the laws do say a circular orbit's speed is constant.

The laws are now used regarding other host-bodies than the Sun, e.g., the Moon orbiting the Earth, yielding very good approximations given some assumptions, among them that the primary body is by far the most massive, that the bodies are basically spherical, that gravitational interactions between bodies orbiting the central body are minimal, and that relativistic speeds and strong-field gravity are not involved. Orbits that do not match these laws yield information when analyzed to uncover which assumptions don't hold and to what degree. Modifications to the laws to take into account some of these factors are also currently used. A very common modification (often the modified laws simply cited as Kepler's laws) is to use the barycenter of the two bodies as the foci rather than the exact center of the more massive body, and applying the resulting laws to each body: by doing so, the laws are more exact, and handle orbits of bodies with mass ratios closer to or equal to 1:1.