Hi there!
In this instance, the object spinning in a horizontal circle will experience a net force in the horizontal direction due to tension.
The net force is equivalent to the centripetal force, so:
∑F = T
mv²/r = T
Solve for v:
v = √rT/m
v = 13.96 m/s
Answer: The ball would exert and equal force on the astronaut in the opposite direction. Both would move away from each other in a straight path. Hope this helps!