Gravitational Work: Ball & Earth Interaction Analysis

[Squoe]

If an object (a ball) begins at rest and falls a distance (h) there is a transformation of gravitational potential energy into kinetic energy (the ball is moving at time-final for my analysis), resulting in a zero net change of total energy for this ball. But, gravity was doing positive work over the distance h. Is it correct to view this scenario as an expression of Newton's third law of motion in that the ball also does gravitational work on the Earth; hence, the work of the ball on the Earth cancels the work of the Earth on the ball. It is insufficient to only analyze the ball. In terms of energy, you must recognize the interaction (transfer of energy) of the two objects. Is my thinking accurate?

 

[mfb]

Gravitational potential is a property of the whole system (ball plus earth). It is not a property of an object, although that is a good approximation if you have a ball and Earth (as the displacement of Earth is negligible while the force is the same).