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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 ($$\text{J}$$).