Question

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

Answer 1

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=(4pi^2)/(GM_s)`