The gravitational potential at a point in a gravitational field is defined as the amount of work done in bringing a body of unit mass from infinity to that point without acceleration.

Gravitational potential at a point,

Gravitational intensity (I) is related to gravitational potential (V) at a point by the relation,

Gravitational potential energy of a body

### Gravitational potential energy of a body

at a point in the gravitational field of another body is defined as the amount of work done in bringing the given body from infinity to that point without acceleration.

**Gravitational potential energy U = gravitational potential × mass of body**

where U is taken to be zero at *r *→ ∞. The total potential energy of a system of particles is the sum of energies for all pairs of particles, with each pair represented by a term of the form given by above equation. This prescription follows from the principle of superposition.

If an isolated system consists of a particle of mass *m *moving at a speed *v *in the vicinity of a massive body of mass *M*, the total mechanical energy of the particle is given by

E = K.E + P.E

That is, the total mechanical energy is the sum of the kinetic and potential energies. The total energy is a constant of motion.

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