Kepler's planetary motion and inverse square law

1. Mar 11, 2013

shounakbhatta

Hello,

The inverse square law of Newton's gravitational force, is it somehow related to each other?

I mean to say P^2 is directly prop.a^3. Is it from the third law that the derivation of inverse sq.law of G=M.m/R2 is derived?

Thanks.

2. Mar 11, 2013

HomogenousCow

You can derive all of Kepler's laws from the inverse square law of gravitation.

3. Mar 11, 2013

Staff: Mentor

Basically, yes. This old thread has a couple of links to files that have more details. See posts #9 and #10.

But I think the second law is not only for inverse square rule, in fact it holds true for any centre field force($\vec{F}= f(r)\vec{r}$) because $\dot{S}= \frac{1}{2}r^2 \frac{dw}{dt}$ where $r^2 \frac{dw}{dt}$ is consevative in any central force field.