# Explain briefly about the Gravitational potential

Gravitational Potential-

In a gravitational field potential V at a point, P is defined as negative of work done per unit mass in changing the position of a test mass from some reference point to the given point.

Note-usually reference point is taken as infinity and potential at infinity is taken as Zero.

and it is given as

$V=-\int \overrightarrow{I}\cdot \overrightarrow{dr}$

where

$V\rightarrow$ Gravitational potential

$I\rightarrow$ Field Intensity

$dr\rightarrow$ small distance

We can also write $I=-\frac{dV}{dr}$

This means a negative gradient of potential gives the intensity of the field.

The negative sign indicates that in the direction of intensity the potential decreases.

• It is a scalar quantity.

• $Unit \to \; Joule/kg \; or \; m^{2}/sec^{2}$

• $Dimension\: :\; \left [ M^{0}L^{2}T^{-2} \right ]$

• Gravitational Potential at a distance 'r'

If the field is produced by a point mass then

$I= \frac{GM}{r^{2}}$

So $V=-\int \overrightarrow{I}\cdot \overrightarrow{dr}$

$V=-\frac{GM}{r}$

at $r=\infty$       $V=0=V_{max}$

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