There is no physical object in space upon which a rocket is able to push off of. nonetheless a rocket is able to accelerate in space. how can this be? explain.

The rocket does not push off the ground. solid or liquid fuel is burnt which results in emission of gases from the nozzle at the bottom. We know from Newton's third law of motion that for every action, there is equal and opposite reaction. The force with which gasses emit leads to an equal amount of force acting on the rocket in opposite direction causing its acceleration.