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

M_earth = 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