When we calculate Gravitational Potential energy of the two masses, we fix one mass and calculate the force acting on the other mass. Work done by the the force which is acting on the fixed mass is zero. But Suppose both Mass acted upon by a conservative force (gravitational force on each other) so both the conservative force is doing work as both masses are moving so dont the potential energy= -Work done by conservative force of 1st mass + (- work done by the conservative force of 2nd mass). But in book this case has also the same formula for change in potential energy= -GMm/R which is the formula when one mass is fixed and other mass moving?
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It appears that this question can be answered by a strict application of Newton's gravitational law, undisturbed by any intuition.
F=Gm1m2/r2 where r is the distance between the two objects translates into F=mgh, and "height" becomes distance. Both work and potential energy are to be calculated as you describe. In the case you describe - both moving - that is not different. It's a choice you make considering the planet, the apple, or the earth as "conservative", as point of reference. The formula disrepects the movements of both objects. The formula applies in both ways, and the work or force only depends on height which is distance. Distance may change if the conservative mass is seen as being moved. Even this is not different from the non-conservative mass being moved. Both changes distance, and the formula is to be applied anew. When calculating the acceleration of the apple, the acceleration of the earth must be counted out; I think that's what the word conservative is about. It's either the apple or the earth that is taken for the conservative part, and - "it works".
