Walker, Halliday & Resnick — Gravitation: Problem 2

2 Two neutron stars are separated by a distance of \(1.0 \times 10^{11} \text{ m}\). They each have a mass of \(1.0 \times 10^{30} \text{ kg}\) and a radius of \(2.0 \times 10^5 \text{ m}\). They are initially at rest with respect to each other. As measured from that rest frame, how fast are they moving when (a) their separation has decreased to one-half its initial value and (b) they are about to collide?