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= 4𝝅2 a3 / 𝝁  β†’Β  T = 2𝝅 √(a3/ 𝝁)

T: orbit period

a: semi-major axis of the orbit

𝝁: standard gravitational parameter

Where 𝝁 is defined as: 𝝁 = 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.


G = 6.674 x 10-11 m3 kg-1Β s-2

Mearth = 5.972 x 1024 kg


𝝁earth = 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 √(a3 / 𝝁earth)

T = 36,566 sec which is

= 609.4 min