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=U_{1}−U_{2}=−RGMm −(−2RGMm )=−2RGMm $ work done in lifting body from $2R$ to $4R$ $W_{′}=−ΔU=U_{1}−U_{2}=−2RGMm −(−4RGMm )=−4RGMm =2W $