"Proof" is hardly the term. You are deriviving Keplers law from the universal law of gravitation.
Remember that Kepler's law applies to things in orbit, where the force of gravity supplies enough pull to keep it in orbit,or forcegravity=forcecentripetal.
GMm/r^2= mv^2/r= m (2pi r/T)^2/r
= m (4PI^2 r/T^2)
GM=4PI^2 r^3/T^2
or r^3/T^2= GM/4PI^2 = constant.
Then, since this is a constant for any orbit, any orbiting mass, then for anything,
(r1/r2)^3= (T1/T2)^2
That is one law. Now for equal areas, for circles, the proof is trivial, for areas swept it is a bit more complicated.
I'm trying to prove Kepler's equations
the proof is in my book but I don't understand it
(T1/T2)^2 = (s1/s2)^3
ok first what allows us to rewrite that formula as so???
(s1^3/T1^2)=(s2^3/T2^2)
my book goes about the proof as
m1 ((4 pi^2 r1)/T1^2)
which I get but then
where does this come fromg
it says rearange this to get..
T1^2/r1^3 = ((4 pi^2)/(GMs))
thats don't understand the proof of keplers laws
also what allows us to state that centripetal acceleration is the same thing as gravity???
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As a sidenote, your algebra skills are weak, and you would do well to do a number of exercies (workbooks for various skills are readily available at any bookstore) to improve those skills.
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