Kepler's planetary motion and inverse square law

[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.

 

[HomogenousCow]

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

 

[jtbell]

Is it from [Kepler's] third law that the derivation of inverse sq.law of G=M.m/R2 is derived?

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

https://www.physicsforums.com/showthread.php?t=399797

 

[raopeng]

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.