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jackrc11
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Homework Statement
In our unit on centripetal force, a large portion of the unit has been focusing on gravity and how the orbit is related to centripetal force. Our teacher told us to prove t^2/r^3 using F=(mv^2)/r and F=G(mM/r^2) as a small side part of our homework
Homework Equations
t^2/r^3
F=(mv^2)/r
F=G(mM/r^2)
where G = 6.67*10^-11
M and m are the objects' masses
The Attempt at a Solution
(mv^2)/r = G(mM/r^2)
mv^2 = G(mM/r)
v^2 = GM/r
giving
4(pi^2)(r^2)/t^2 = GM/r
and
GM = v^2 / r = 4(pi^2)r
GM/r = (4pi^2)r / r = 4pi^2
4(pi^2)(r^2)/t^2 = (4pi^2)
leaving the ratio
r^2 / t^2
When it should be r^2 / t^3. What did I do wrong? Was there something I forgot?