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

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Answer 1 · 2018-06-26T08:45:33

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

$T^2/R^3=(4pi^2)/(GM_s)$