Two hypothetical planets of masses m1 and m2 and radii r1 and r2, respectively, are nearly at rest when they are an infinite distance apart. Because of their gravitational attraction, they head toward each other on a collision course. (a) When their center-to-center separation is d, find expressions for the speed of each planet and for their relative speed. (b) Find the kinetic energy of each planet just before they collide, if m1 = 2.00 X 1024 kg, m2 = 8.00 X 1024 kg, r1 = 3.00 X 106 m, and r2 = 5.00 X 106 m. (Note: Both energy and momentum of the system are conserved.)