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

Quote by shounakbhatta

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.

http://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([itex]\vec{F}= f(r)\vec{r}[/itex]) because [itex]\dot{S}= \frac{1}{2}r^2 \frac{dw}{dt}[/itex] where [itex]r^2 \frac{dw}{dt}[/itex] is consevative in any central force field.

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shounakbhatta	Kepler's planetary motion and inverse square law Tweet 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.

raopeng	Kepler's planetary motion and inverse square law But I think the second law is not only for inverse square rule, in fact it holds true for any centre field force([itex]\vec{F}= f(r)\vec{r}[/itex]) because [itex]\dot{S}= \frac{1}{2}r^2 \frac{dw}{dt}[/itex] where [itex]r^2 \frac{dw}{dt}[/itex] is consevative in any central force field.