# How is Kepler's Law used to find the period of orbit for earth?

Dec 5, 2015

${T}^{2} = \frac{4 {\pi}^{2}}{G M} {R}^{3}$

#### Explanation:

Kepler's 3rd Law of Planetary Motion states that the square of the period T of revolution for any planet (mass M) around the sun is directly proportional to the cube of the semi-major axis R of the orbit.

If one uses physics principles and derives the equation and fills in the relevant constants of proportionality, we may then make the period T the subject of the formula to obtain

${T}^{2} = \frac{4 {\pi}^{2}}{G M} {R}^{3}$

(Let me know if you want a precise derivation of this formula using physics methods and I will upload it for you as well).

G is Newton's Universal Gravitational constant and has value $6 , 67 \times {10}^{- 11} N . {m}^{2} / k {g}^{2}$