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This question already has an answer here:

I learn that any work needs a source of energy, the work of gravity force (like keeping the Moon in the orbit by the Earth gravity force) comes from where? Can we find any mass reduction (transform to energy source) during the time?

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marked as duplicate by Daniel Griscom, Norbert Schuch, ACuriousMind, Kyle Kanos, dmckee Jan 4 '16 at 0:59

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ well you are questioning on the very basics of how the nature work? $\endgroup$ – Anni Jan 3 '16 at 12:39
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    $\begingroup$ Just a note - the moon being kept in orbit by the Earth's gravity needs no energy (on average over an orbit at least). Since gravity is a conservative force, no energy is expended on moving in a path that ends up at the same point. $\endgroup$ – Chris Cundy Jan 3 '16 at 13:05
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    $\begingroup$ Possible duplicate of Where does gravity get its energy from? $\endgroup$ – Sathyam Jan 3 '16 at 18:36
  • $\begingroup$ Not sure that the duplicate fully answers this question - I think the question here is "if you moved two large objects closer together, thus changing the potential energy stored, would their total mass change in accordance with $E=mc^2$". If that is indeed the question, then the suggested duplicate is not a duplicate. For now I vote to keep this open, until HRT clarifies. $\endgroup$ – Floris Jan 3 '16 at 21:27
  • $\begingroup$ But this question and the duplicate suffer from a deep misunderstanding to the point that the question isn't even remotely sensible as asked. Start by patching up your understanding of "work" and proceed from there. $\endgroup$ – dmckee Jan 4 '16 at 1:01
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But work is the integral f ds
If the orbit is not decaying then no work is performed

If the orbit were to degrade then the moon would have less potential energy

Think of putting a satellite in orbit. The potential energy is the work against gravity to get it to that altitude and the work to get it up to speed for orbit.

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