Conservation of momentum astronauts question

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In the scenario where three astronauts are playing catch in space, the conservation of momentum principle applies, meaning the total momentum before and after each throw remains constant. Initially, all astronauts are at rest, so their combined momentum is zero. When one astronaut throws the second, the momentum from the throw will result in the third astronaut moving in the opposite direction to maintain the overall momentum balance. The game will continue until the astronauts can no longer throw effectively, which depends on their relative positions and the forces exerted during each throw. The discussion emphasizes the importance of demonstrating work to understand the physics involved in the motion of the astronauts.
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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?
 
Rake-MC said:
It would help to show what you've tried so far

https://www.physicsforums.com/showthread.php?t=268214

(Reposting the same question without showing any work, having been asked to show some work, by the looks of it.)
 

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