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