Two planets, each with a mass of 4.990E+27 kg, are released from rest some 2.850E+11 m apart. What are their speeds (in m/s) as they crash together? Assume that the planets have a diameter of 1.40E+08 m.
Potential Energy change = Final kinetic energy
G M^2[1/D1 - 1/D2] = 2*(1/2)M Vf^2, where
G = universal gravity constant
M = mass of either planet
D1 = initial separation = 2.85*10^11 m
D2 = final separation = 1.40*10^8 m
Solve for final velocity Vf
Vf^2 = G M [1/D1 - 1/D2]