Newton's Law: F = 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^2/(R+h)^2 (≈ g(1-2h/R) for h<<R)
• Depth: g_d = g(1-d/R)
• Latitude: g_eff = g - Romega^2cos^2(lambda)

Velocities:

• Orbital: v_o = sqrt(GM/r) = sqrt(gR^2/r)
• Escape: v_e = sqrt(2GM/R) = sqrt(2gR) = sqrt(2)*v_o

Satellite (radius r):

• KE = GMm/(2r), PE = -GMm/r, E = -GMm/(2r)
• T = 2pisqrt(r^3/(GM))

Kepler's 3rd Law: T^2 = 4pi^2a^3/(GM)