momentum in space?

Question

I have a physics question:
Two astronauts outside a space capsule decided to play catch with a third astronaut. All the astronauts weigh the same on earth and are equally strong. The first astronaut throws the second toward the third and the game begins. Describe the motion of the astronauts as the game proceeds. How long will the game last?

I have to explain this question using momentum. Please help!!!

Answer 1

When the first astro throws the second astro, to conserve momentum, as the third approaches the second, the first moves away in the opposite direction (away from the second). Both the first and the third move with the same speed. When the first hits the second, they become one for some time. During that period, they both move in the direction of the third at half the speed of the first since their mass has double (mv3 + m*0 = (m+m)v or v = 0.5v3). When the second throws the third back toward the first, the third will travel with half the speed of the first, and hence, will never reach him. The second will travel away from the first with 1.5 the speed of the first. They will never touch each other again.