Key Equations

Newton’s law of gravitation	${\vec{F}}_{12} = G \frac{m_{1} m_{2}}{r^{2}} {\hat{r}}_{12}$
Acceleration due to gravity at the surface of Earth	$g = G \frac{M_{E}}{r_{}^{2}}$
Gravitational potential energy beyond Earth	$U = - \frac{G M_{E} m}{r}$
Conservation of energy	$\frac{1}{2} m v_{1}^{2} - \frac{G M m}{r_{1}} = \frac{1}{2} m v_{2}^{2} - \frac{G M m}{r_{2}}$
Escape velocity	$v_{esc} = \sqrt{\frac{2 G M}{R}}$
Orbital speed	$v_{orbit} = \sqrt{\frac{{GM}_{E}}{r}}$
Orbital period	$Τ = 2 π \sqrt{\frac{r^{3}}{{GM}_{E}}}$
Energy in circular orbit	$E = K + U = - \frac{G m M_{E}}{2 r}$
Conic sections	$\frac{α}{r} = 1 + e cos θ$
Kepler’s third law	$Τ^{2} = \frac{4 π^{2}}{G M} a^{3}$
Schwarzschild radius	$R_{S} = \frac{2 G M}{c^{2}}$