A spacecraft of mass m describes a circular orbit of radius r1, around the earth of mass M. Calculate the additional energy to be imparted to the spacecraft to transfer it to a circular orbit of larger radius r2,

For a satellite, orbiting in a circular orbit or radius r,We have,GMmr2=mv2r  or  mv2=GMmr K.E. =12GMmr and P.E. =−GMmrTotal energy E =−GMm2rTotal energy of the satellite orbiting in circular orbit of radius r1 is given byE1=−GMm2r1Similarly, for an orbit or radius r2E2=−GMm2r2So, additional energy imparted will beE2−E1=−GMm2r2−−GMm2r1=GMm21r1−1r2=GMmr2−r12r1r2