**Gravitational potential energy**

Hello everyone as we know that the object thrown vertically upwards come backs towards the earth’s surface due to gravitational potential energy. This energy decreases with increase in height from the surface of earth. The work done during change in the position of object from the point of lower altitude to the point of higher altitude or vice versa is nothing but the potential energy, here it is termed as gravitational potential energy.

**Derivation of formula for gravitational potential energy **

Let us find the formula for energy of orbiting satellite

Negative sign indicates that the displacement is opposite to direction of gravitational force.

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Using the formula for integration as,

We know that this work is nothing but the energy stored in the form of potential energy, here it is termed as gravitational potential energy.

This is gravitational potential energy of the system of object of mass m and Earth of mass M at distance r.

**Numerical for explanation of gravitational potential energy**

**Ex:1 **Find the change in potential energy of a body of mass 60 kg when it is raised from height r_{1}= 2R to r_{2}= 5R above the Earth’s surface from the centre of earth.

**Solution: **

Here the distances are from the centre of earth then,

r_{i}= 2R+R=3R, r_{f}= 5R+R=6R,