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The law of conservation of energy, which states that the amount of energy in a system is constant. For questions about Earth's environment, see the climate-science tag instead.
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Is conservation of energy violated when two bodies move closer due to gravitational pull?
The answer to the question is in the question itself. You wrote:
Suppose 2 objects are placed not too far away from themselves. These objects start moving towards each other due to gravity.
Then …