Question

By what percent the energy of the satellite has to be increase d to shift it from orbit of radius 'r' to '3r/2'.
1)66.7% 2)33.3% 3)15% 4)20.3%

please help me tell me the answer step by step

Answer 1

energy of satellite in the first case

E1=GMm2rE1=GMm2r

energy in the second case is

E2=GMm2(32r)E2=GMm2(32r)

ΔE=GMmr(12−13)=GMm6ΔE=GMmr(12−13)=GMm6

%% increase =GMm6rGMm2r=GMm6rGMm2r×100×100

=33.3%=33.3%

Hence b is the correct answer