In a deep space, a ring of static massive dust of radius R=6000 km and mass M = 1024 kg, has a uniform density ρ and zero velocity. Assume the ring is fixed in space. A broken spaceship of mass m = 2 x106 kg is released from rest on the axis of the ring at a distance x=100000 km from the plane of the ring.
a) With what speed does the spaceship pass through the center of the ring?
b) After some time the space ship will begin to oscillate, in and out of the ring, with a small amplitude of oscillation. What is the frequency of this oscillation?