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Gravitational potential energy

The gravitational potential energy ($E_{\text{p}}$ or $U$) of an object at a point is the work done by a gravitational field in bringing the object from infinity to the point.

$E_{\text{p}}$ itself depends on the object (its mass) and the point of its location (relative to the gravitational field around another object).

The equation for gravitational potential energy $E_{\text{p}}$ is: $$E_{\text{p}}=U =-\frac{GMm}{r}$$$G=$Universal gravitational constant; $m_1$ and $m_2=$two point masses; $r=$distance between the masses.

By convention, $E_{\text{p}}$ is set to be zero at infinity. At a finite distance $E_{\text{p}}$ is negative.

$E_{\text{p}}$ indicates the potential of the object to gain kinetic energy (to accelerate) simply because of its position in the gravitational field of another object.

A body accelerating because of a gravitational force reaches a higher velocity (and kinetic energy) if it starts at an infinite distance than if it starts from closer to the mass that is attracting it.

$E_{\text{p}}$ is often informally abbreviated as PE. The SI unit of gravitational potential energy is the joule ($\text{J}$).