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# Keplers laws deduced from newtons law of gravitation watch

1. Can someone give a link for this, or give a proof?

thanks
2. F= G Mm / ( r^2)

F=mv^2 / d

Speed = dinstance / time

U basicaully have to combine those three eqations because you can think of the force as a gravitational force and a centripetal force and it leads to keplers laws
3. (Original post by kingmonkeywoman)
F= G Mm / ( r^2)

F=mv^2 / d

Speed = dinstance / time

U basicaully have to combine those three eqations because you can think of the force as a gravitational force and a centripetal force and it leads to keplers laws

yeah, but is that the only law that can be deduced?

cant the 1st and 2nd law?
4. wouldn't u just equate F=GMm/r^2 and F=mv^2/r ???

using: v= angular velocity X r

and: angular velocity = 2 pi / T
5. (Original post by Mathemagician)
yeah, but is that the only law that can be deduced?

cant the 1st and 2nd law?

Erm, i dunno, i dont think they can no.

I mean how can u use it to show the orbit in an ellipse when u have to assume its a circle to prove his third law....

This kepler just came up with it because he couldnt fit mars into a circular orbit even when he used epicycles

So u dont think you can prove the other three laws, but maybe u can in some complicated way i dont know about, you definately dont need to know about that for cosmology exam though
6. ok in free fall mv^2/r=GMm/r^2
so V^2/r=GM/r^2
V^2/r=w^2r
but w=2pi/T
so (2pi/T)^2 x r=GM/r^2
so thus 4(pi)^2 r^3=GMT^2
so 4pi^2/GM=T^2
so

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