If the body of mass m is moved from the plane of earth to a point at distance h above the plane of earth, then modification in potential energy or work done against gravity will be

                                 [As r₁ = R and r₂ = R + h]

                                               [As GM/R² = g]

(i) When the height h is not negligible and is comparable to radius of the earth, then we will use above formula.

(ii) If h = nR    then  

(iii) If h = R    then  

(iv) If h is very short as related to radius of the earth then term h/R can be neglected

            From                           [As h/r →o]                     

Gravitational potential and field due toSeveral Objects :

Causing Shape	Gravitational Potential (V)	Gravitational Field (I or E)	Graph V vs R
POINT MASS
	v = -GM/r	I or E = GM/r2
AT A POINT ON THE AXIS OF RING
		E = -GMr/(R2+r2)3/2
ROD: 1. AT AN AXIAL POINT
	V = -(GM/L)ln(1+L/r)	E = GM/r2{1/(1+l/r)}
2. AT AN EQUATORIAL POINT
		E=-dv/dr
CIRCULAR ARC
HOLLOW SPHERE
SOLID SPHERE
LONG THREAD
	V = ∞

Relation between Gravitational potential (v) and Intensity (I or E)

Gravitational potential is a field function. It depends on the position of the point where potential is desired. Gravitational field and the gravitational potential are related by the following relation.

OR     E = -dv/dr  

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