A 400 kg satellite is in a circular orbit of radius `2R_(E)` about he Earth. How much energy is required to transfer it to a circular orbit of radius `rR_(E)`? What are the changes in the kinetic and potential energies?

Explanation

Initial total energy is `-(GMm)/(2r_(2)) = -(GMm)/(8R) = E_(2)`
Final total energy is `-(GMm)/(2r_(2)) = -(GMm)/(8R) = E_(2)`
The change in the total energy is
`Delta E = E_(2) - E_(1) = (GMm)/(8R) rArr Delta R = ((GM)/(R^(2))) (mR)/(8)`
`Delta R = (gmR)/(8) = (9.8 xx 400 xx 6.37 xx 10^(6))/(8) = 3.13 xx 10^(9)J`
Change in kinetic energy = `K_(2) - K_(1) = -3.13 xx 10^(9)J`
Change in potential energy `= U_(2) -U_(1) = -6.25 xx 10^(9)J`