Kepler's laws of planetary motion

Johannes Kepler's primary contributions to astronomy/astrophysics were his three laws of planetary motion. Kepler, a nearly blind though brilliant German mathematician, derived these laws, in part, by studying the observations of the keen-sighted Danish astronomer Tycho Brahe. The article on Johannes Kepler gives a less mathematical description of the laws, as well as a treatment of their historical and intellectual context.

Kepler's third law

The square of the sidereal period of an orbiting planet is directly proportional to the cube of the orbit's semimajor axis.

Related Topics:
Square - Sidereal period - Proportional - Cube - Semimajor axis

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:P2 propto a3

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:P = object's sidereal period in years

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:a = object's semimajor axis, in AU

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Thus, not only does the length of the orbit increase with distance, also the orbital speed decreases, so that the increase of the sidereal period is more than proportional.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

See the actual figures: attributes of major planets.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

This law is also known as the harmonic law.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~