Gravitational potential energy

Gravitational energy or gravitational potential energy is the potential energy a massive object has in relation to another massive object due to gravity. It is the potential energy associated with the gravitational field, which is released (converted into kinetic energy) when the objects fall towards each other. Gravitational potential energy increases when two objects are brought further apart.
For two pairwise interacting point particles, the gravitational potential energy



U


{\displaystyle U}
is given by




U
=
−



G
M
m

R


,


{\displaystyle U=-{\frac {GMm}{R}},}
where



M


{\displaystyle M}
and



m


{\displaystyle m}
are the masses of the two particles,



R


{\displaystyle R}
is the distance between them, and



G


{\displaystyle G}
is the gravitational constant.Close to the Earth's surface, the gravitational field is approximately constant, and the gravitational potential energy of an object reduces to




U
=
m
g
h


{\displaystyle U=mgh}
where



m


{\displaystyle m}
is the object's mass,



g
=
G

M

E



/


R

E


2




{\displaystyle g=GM_{\text{E}}/R_{\text{E}}^{2}}
is the gravity of Earth, and



h


{\displaystyle h}
is the height of the object's center of mass above a chosen reference level.

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