Keplers Third Law?

Question

Can someone explain Kepler's Third Law of planetary motion to me? I have the definition but I just don't understand what it is. Help!

Answer 1

Kepler's First Law:
Satellite orbits are elliptical Paths with the Earth at one focus of the ellipse.

Kepler's Second Law:
A line between the center of the Earth and the satellite sweeps out equal areas in equal intervals of time.

Kepler's Third Law:
The square of the orbital period is proportional to the cube of the the orbit's semi major axis.

Kepler's first law simply states that orbits are shaped like ellipses (elongated circles). This can be proven mathematically, once it's understood that the gravitational force between the Earth and the satellite decreases in proportion to the square of distance between the [centers of] the two. This law does not preclude a satellite from orbiting in a circular path since a circle is an ellipse with no elongation (or eccentricity).

Kepler's Second Law is a consequence of the physical law of conservation of angular momentum. This is the same principle that figure skaters use by pulling in their arms to speed up their spin rate and extend them out to slow their spin rate down. This effect is amplified by gravity's inverse square law dictating lower speeds at higher altitudes and vice versa.

Kepler's Third Law states that you can compute the time it takes the satellite to make one complete orbit (the period) from half the longest dimension of the orbital ellipse (the semi major axis). This is also known as the harmonic law.

Answer 2

Kepler's third law states that the squares of the orbital periods of planets are directly proportional to the cubes of their semi-major axes (recall that the first law guarantees that those planetary orbits are elliptical). So planets with larger orbits have quantifiably larger orbital periods, and planets with smaller orbits have higher relative speeds.

Answer 3

Period squared equals average distance to the third power. It means that if you know the average distance from the Sun you can calculate the time required to go once around, and if you know the time to go once around you can calculate the average distance. The larger the distance, the longer it takes to go around.