Question

A 400 kg satellite is in a circular orbit of radius 2re about the earth. how much energy is required to transfer it to a circular orbit of radius 4re ? what are the changes in the kinetic and potential energies ?

Answer 1

SoluTion :-

$\sf {M _1 =6 \times 10^{24}\ kg}\\\\\sf {M_2 = 400 \ kg}\\\\\sf {R_e=6.4 \times 10{6} \ m}\\\\\sf {G=6.67 \times 10^{-4} N^{m} \ 2/kg}\\\\\\\sf {\frac{GM_1M_2}{2(2R_e)} = \frac{6.67 \times 10^{-11} \times 6 \times 10^{24 \times 400}}{2 \times 12.8 \times 10^{6}} = 6.25 \times 10^{9} \ J}\\\\\\\sf {\therefore K.E=6.25 \times 10^{9}\ J}\\\\\sf {P.E = -2 KE = -12.5 \times 10^{9}\ J}\\\\\sf {\therefore T.E = P.E + K.E = 6.25 + 10^{9}\ J}$