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.

 

[PJC01]

Yes, Kepler's three laws of planetary motion and the inverse square law of gravitation are intimately related. Kepler's third law states that the square of a planet's orbital period is directly proportional to the cube of its semi-major axis. This means that the farther a planet is from the sun, the longer it takes to complete one orbit. This law is a consequence of the inverse square law of gravitation, which states that the force between two objects is inversely proportional to the square of the distance between them. This can be derived from Newton's laws of motion and his law of universal gravitation, which states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. So, in short, Kepler's third law is a result of the inverse square law of gravitation.