An artificial satellite of mass m is moving round the earth in an orbit of radius 2R. How much work is to be done to transfer the satellite to an orbit of radius 4R ? How will the potential energy of the satellite change ? (R=Radius of earth)

Explanation

If mass of the earth =M , potential energy of artificial satellite at distance `2R=-(GMm)/(2R)`
Total energy `=-(GMm)/(2*2R)=-(GMm)/(4R)`
Potential energy at a distance `4R=-(GMm)/(4R)`,
Total energy `=-(GMm)/(2*4R)=-(GMm)/(8R)`
So, work done
= increase in energy `=-(GMm)/(8R)-(-(GMm)/(4R))`
`=(GMm)/(4R)(1-1/2)=(GMm)/(8R)`
Change in potential energy
`=-(GMm)/(4R)-(-(GMm)/(2R))=(GMm)/(2R)(1-1/2)=(GMm)/(4R)`