Kepler’s Laws Simplified

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Kepler’s Laws of Planetary Motion

Originally, Kepler’s three laws were established empirically from actual data but they can be deduced (not so trivially) from Newton’s laws of motion and gravitation.

Kepler’s laws simplified:

Kepler’s First Law

The orbits of planets around the Sun are in general ellipses, with the Sun positioned at one of the foci of the ellipse for each orbit.

Kepler’s Second Law

The area swept out by a line joining the centers of a planet and the Sun is the same in equal units of time.

Kepler’s Third Law

The square of the orbital period of a planet in orbit around the sun is proportional to the cube of the semimajor axis of the orbit. (The semimajor axis is equal to half of the largest symmetry axis of the ellipse that constitutes the orbit.)

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The relation between the orbital period and the orbit’s semimajor axis according to Kepler’s third law.