if an astronaut in space pushes of to the satellite she is working on, what happens to her if there are no other external forces acting on her ?
If the astronaut pushes off the satellite with enough force, she will start moving away from the satellite in the opposite direction of her push. This is due to Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction.
Since there are no other external forces acting on her, she will continue moving in a straight line at a constant velocity until she reaches another object or is affected by some other force, such as gravity from a nearby planet. If she is far enough away from any other objects in space, she will continue moving in a straight line indefinitely.
In the absence of air resistance or friction, her motion will be perfectly linear and uniform until acted upon by an external force.