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Q:

When a rocket flies away from Earth, why does the force needed to keep it accelerating decrease?

A:

Something’s acceleration depends on the net force acting on it and the object's mass. Gravity and drag act against thrust. That means that they cancel out some of the thrust. The net force then is the amount of thrust that isn’t cancelled out. Both drag and gravity decrease as a rocket gets further from the Earth. The rocket's mass decreases as it uses fuel. Therfore, thrust can also decrease and the rocket can have the same net force and acceleration.