# What is the Newton's version of Kepler's third law?

Jun 26, 2018

Newton's law F_g=G·(M_s·M_p)/R^2 where ${M}_{s} , {M}_{p}$ are the

mass of Sun and a planet, $G$ is a constant value and $R$ is the distance between Sun and Planet.

Kepler's Law is ${T}^{2} / {R}^{3} = K$ constant and T is period of traslation in orbit and R again, distance between Sun and Planet.

We know that centrifuge force is given by

F_c=M_p·a=M_p(2pi/T)^2·R where a is acceleration in orbit

Then combining both expresions

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