Conservation of momentum astronauts question

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SUMMARY

The discussion centers on the conservation of momentum among three astronauts playing catch in space. When the first astronaut throws the second, the momentum is conserved, meaning the total momentum before and after the throw remains constant. As all astronauts have equal mass and start from rest, the motion of the astronauts will result in the third astronaut moving in the opposite direction of the throw, while the thrower will move in the opposite direction to conserve momentum. The game can continue indefinitely as long as they maintain their throws without external forces acting on them.

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cali_sk8er205
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Suppose there are three astronauts outside their spaceship and that two of them decide to play catch with the third. This means the first two astronauts are attempting to throw the third back and forth. All astronauts weigh the same on Earth and are equally strong. The first throws the second and the game begins. Describe the motion of the astronauts as the game proceeds. How long will the game last (i.e. how many throws) ?
 
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It would help to show what you've tried so far,

We know that momentum is conserved (mass * velocity) within a system. Initially I assume that none of the astronauts are moving. What does this tell you about the motion of the astronauts after the first throw?
 

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