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= 4π 2 a3 / πΒ βΒ T = 2π β(a3/ π)
T: orbit period
a: semi-major axis of the orbit
π: standard gravitational parameter
Where π is defined as: π = 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-1Β s-2
Mearth = 5.972 x 1024 kg
Thus
πearth = 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 = 2π β(a3 / πearth)
T = 36,566 sec which is
= 609.4 min