This is a hypothetical question, a brain experiment, thought someone might be able to answer it for me, someone who has a good understanding of general relativity etc.
Assume I take an object and instantaneously place it 300km above earth's surface (stationary not in orbit) As soon as I release this object it immediately accelerate towards earth at 9.81m/s^2.
Now I take an identical object to the same point in space, an identical scenario, however this object has a rocket engine mounted on it such that the rocket engine alone will apply the exact thrust required to accelerate the object directly towards earth at 9.81m/s^2 as soon as I release it.
My question is does the second object accelerate towards earth at 19.62m/s^2 (acceleration from gravitational force + acceleration thrust from rocket engine)? Or does the object still accelerate at 9.81m/s^2, but the gravitational force applied to it is zero?