Two astronauts in space with a baseball decide to play catch to pass the time. In the language of conservation of momentum, describe what happens to each astronaut as they start to toss the ball back and forth

As the first astronaut throws the ball, lets assume it goes with v velocity and the mass of the ball be m

the momentum comes out be mv, thus to conserve that momentum the astronaut will move opposite to the direction of the ball's motion with the velocity mv/M (where M is the mass of the astronaut).