Corroboration Of Simple Algebra For A Physics Lab 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.

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