A rocket moves away from the surface of the earth. As the distance r from the center of the planet increases, what happens to the force of gravity on the rocket?

The further the rocket travels from the Earth, the force of gravity decreases. The equation under Newtonian laws is F = G (M1-M2) / r^2. This equation states that as the radius (distance) gets larger, the divisor gets larger, the force becomes smaller.