How can the gravitational potential energy of something be negative?

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Expert Solution

Gravitational potential energy is the work done against the gravitational force to move a point mass from infinite distance to a position in space. Using the inverse square law of gravitational force the gravitational field at infinite separation from the mass is approximately zero and hence gravitational potential energy at infinite distance is zero.

As the object approaches the mass the work done by the gravitational force is positive. Using work-energy theorem we know that,

Change in potential energy= - (Work done)

As work done by the gravitational force is positive therefore change in potential energy is negative.

Change in gravitational potential energy= (Gravitational potential energy at a point) - (GPE at infinite)

Change in gravitational potential energy= (Gravitational potential energy at a point) - 0

Change in gravitational potential energy= Gravitational potential energy at a point= negative

Therefore, Gravitational potential energy at a point is negative.

genius_generous answered 1 year ago

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