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I have a few equations that I need to solve for a specific variable, and I am wondering if anyone would care to look them over.

The first equation is deriving Kepler's equation of orbital period, and solving for mass:

$$\frac{GMm}{r^2}=\frac{m (\large \frac{2 \pi r}{T})^2}{r}$$

solving for $M$: $$M= \large \frac{4 \pi^2 r^3}{T^2G}$$

The second equation is: $$-\frac{Gm_1m_2}{R_E} + \frac{1}{2}m_2v^2= -\frac{Gm_1m_2}{R_E + h}$$

solving for $h$: $$h = \frac{-2R_EGm_1}{-2Gm_1 + V^2R_E} - R_E$$

And the last one: $$-\frac{Gm_1m_2}{R_E}+ \frac{1}{2}m_2v^2=-\frac{Gm_1m_2}{R_E+h}$$

solving for $v$: $$v = \sqrt{\frac{-2Gm_1}{R_E+h}+\frac{2Gm_1}{R_E}}$$

I know that these final results aren't the most pleasing things to look at; but it's simply for a physics lab, so it's not really required for me to fully simplify.

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All look right to me. – Chris Taylor Feb 15 '13 at 12:23
up vote 1 down vote accepted

It all looks OK, except you wrote $V^2$ once where presumably you meant $v^2$.

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Yes, you're right. Thank you very much! – Mack Feb 15 '13 at 21:08

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