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A unit mass is brought closer to the Earth from infinity, with zero acceleration. The potential energy decreases the kinetic energy does not change, so where is the energy going? Which form of energy is it being converted into?

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Gravity is doing work against whatever force is counteracting it. What the energy is being converted into depends on the nature of this force. Perhaps this force is friction, in which case the energy is converted to heat. Perhaps the mass compresses a series of springs along the way, in which case the energy is stored as potential energy in the springs.

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A unit mass is brought closer to the Earth from infinity, with zero acceleration.

The fact that the acceleration of the mass is always zero implies (by Newton's second law) that there is a force opposing gravity and of equal magnitude acting on the mass at each point on its trajectory.

Indeed, in this case, the kinetic energy does not change because the acceleration is zero (i.e. the two forces cancel each other out). However, these two forces both do work. The work done by gravity is equivalent to the change in potential energy. Hence, this change potential energy is balanced by the work done by the opposing force.

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