derive an expression for the gravitational potential energy of body mass m located at distance r from centre of the - Physics - Work Energy And Power

Question

derive an expression for the gravitational potential energy of body
mass m located at distance r from centre of the earth

Akansha Tyagi · Accepted Answer

Consider two particles of masses m1 and m2 are at distance r 
Now one of the particle is taken at someother point Now their separation becomes r'Force on second particle,F=Gm1m2r2The Workdone by the gravitational force in displacementdW=-Gm1m2r2drIncrease in Potential Energy,dU=-dW=Gm1m2r2Increase in Energy,=∫dUin moving from r to r',dU=Gm1m2[1r-1r']Let distance between them is infinity,u(r)=-Gm1m2r

derive an expression for the gravitational potential energy of body mass m located at distance r from centre of the earth.