Floating in deep space, you find yourself at rest next to a small asteroid. You reach out and tap the asteroid with a hammer. What happens to you in this process?

There is a force that has the same magnitude as that of the hammer applied on the astronaut and with direction away from the asteroid, movement is given by

F_hammer - F_Gravitation = m a

Explanation:

For this exercise we will propose its solution from Newton's third law, which states that every action has a reaction of equal magnitude, but felt different.

As it is in space, we must assume that it is not subject to the gravitational attraction of nearby bodies, except the asteroid that attracts it. When he extends his hand and hits the asteroid, he exerts a force on him, by Newton's third law he responds with a force of equal magnitude applied to the astronaut, therefore without the two they are not united they could separate if this force is greater than the force of universal attraction between the two.

In summary There is a force that has the same magnitude as that of the hammer applied on the astronaut and with direction away from the asteroid, movement is given by

F_hammer - F_Gravitation = m a