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phosgene
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Homework Statement
In the diagram below, masses m and Me are in circular orbit about Ms with the same period.
http://min.us/i/lprtU83D9cGR
Derive an expression for the equilibrium position r of mass m.
Homework Equations
For a circular orbit, the eccentricity, e = 0.
[itex]e=\sqrt{1+2mEh^{2}k^{-2}}=\frac{mrv^{2}}{GMm}-1[/itex]
Where [itex]h=\frac{L}{m}, k=-GMm[/itex]
The Attempt at a Solution
So, I'm kind of assuming that I simply set one of these equations to zero and solve for r, to get something like:
[itex]r=\sqrt{\frac{-G^{2}M_{s}^{2}m}{2Ev^{2}}}[/itex] (which will not be imaginary because in an elliptical orbit E<0)
or
[itex]r=\frac{GM_{s}}{v^{2}}[/itex]
Is it really that simple though? It's a 4 mark question.
**EDIT** I think the above is wrong. I think I should have calculated the period of the mass m in terms of the two other masses, then equated it with the period of the other mass. I think I've got it now!
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