Newton's Law: F = $\frac{GMm}{r}$^2, G = 6.674 x 10^{-11} N*$m^2$/$kg^2$

Field & Potential:

• E = -GM/$r^2$ (toward mass), V = -GM/r
• E = -dV/dr

g Variation:

• Height: $g_h$ = gR^$\frac{2}{R+h}$^2 (≈ g(1-2h/R) for h<<R)
• Depth: $g_d$ = g(1-d/R)
• Latitude: $g_{eff}$ = g - R*$omega^2$*$cos^2$(lambda)

Velocities:

• Orbital: $v_o$ = sqrt$\frac{GM}{r}$ = sqrt($gR^2$/r)
• Escape: $v_e$ = sqrt$\frac{2GM}{R}$ = sqrt(2gR) = sqrt(2)*$v_o$

Satellite (radius r):

• KE = $\frac{GMm}{2r}$, PE = -GMm/r, E = -$\frac{GMm}{2r}$
• T = 2pisqrt(r^$\frac{3}{GM}$)

Kepler's 3rd Law: $T^2$ = 4*$pi^2$*a^$\frac{3}{GM}$