In empty space probably means, there is no force on the ball.
(This assumption is not quite correct since there is still the force of gravity between the ball and the astronaut, but this force is very very small and can be neglected.)
Assuming there is no force on the ball, Newtown's 1st law says: When viewed in an internal frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.
This means: If there is no force on the ball, there will be no acceleration on the ball either. If the acceleration is zero, the velocity of the ball never changes.
I'm pretty sure it's the<span> impact of the air molecules on the outside of the stopper. They exert a net inward force, which is not resisted by anything on the other side.</span>
