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

1 Answer
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=(4pi^2)/(GM_s)#