Gravitational Potential Energy

Gravitational potential energy, U of a point mass m, in a gravitational field, is the work done by an external force in bringing that point mass from infinity to that point.

$U \, = \, G \frac{Mm}{r}$

Units of U is Joules (J).

Reasons for a negative sign in the equation:

  • Zero (reference point) for gravitational potential energy is set to be at infinity.
  • The gravitational pull is an attractive force. Since gravitational potential is defined to be work done per unit mass by an external force to bring a mass from infinity to a point, the external force has to do work against the attractive field. As external force is opposite to the direction of displacement, values of gravitational potential are negative.


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