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DEFINE GRAVITATIONAL POTENTIAL

Gravitational Potential
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 (where the potential  is zero) to that point that is,

                 
Where V = gravitational potential at some point.
              W = W.D. in bringing mass m from infinity to that point.
 The SI unit of gravitational potential is J kg^-1  and its dimensional formula is [M₀L²T^-2]. Suppose we want to find the gravitational potential at a point P (outside the earth) at a distance r from the centre of the earth. We know that the amount of work done in bringing a body of mass m from infinity to point P is

        
 Gravitational potential at point P in earth’s gravitational field is

       
Or    

Note that gravitational potential is always negative; it is zero at infinity. It follows that a body at infinity would ‘fall’ towards the earth; a body on the earth does not ‘fall’ to infinity.