The gravitational potential (V) is the gravitational potential energy (U) per unit mass: where m is the mass of the object. Potential energy is equal (in magnitude, but negative) to the work done by the gravitational field moving a body to its given position in space from infinity.
example
Change in gravitational potential energy as work done by gravitational force
Example: If R is radius of the earth and W is work done in lifting a body from the ground to an altitude R, the calculate the amount of work which should be done in lifting it further to twice that altitude?
Solution: work done is equal to change in PE W=−ΔU=U1−U2=−RGMm−(−2RGMm)=−2RGMm work done in lifting body from 2R to 4R W′=−ΔU=U1−U2=−2RGMm−(−4RGMm)=−4RGMm=2W