Kepler's Third Law

Kepler's Third Law: The square of the orbital period of a planet is proportional to the cube of its average distance from the sun (semi-major axis).

T2= 4?2 a3 / ?  →  T = 2? √(a3/ ?)

T: orbit period

a: semi-major axis of the orbit

?: standard gravitational parameter

Where ? is defined as: ? = G * M

G = universal gravitational constant

M = mass of central body

The orbit period for a central body depends on only one changing variable, the semi-major axis.

Example:

G = 6.674 x 10-11 m3 kg-1 s-2

Mearth = 5.972 x 1024 kg

Thus

?earth = 3.986 x 1014 m3 s-2

= 3.986 x 105 km3 s-2

For a given semi-major axis,

T can be calculated

a = 30,000 km

T = 2? √(a3 / ?earth)

T = 36,566 sec which is

= 609.4 min