Question

Two satellites A and B each of- Mass -50 kg are in circular orbits at altitudes of $1\times {10}^6$ m and $35\times {10}^6$ respectively. what is the difference in the gravitational potential energies of the two satellites in their respective orbits ? given mass of earth $=M=6\times {10}^{3x}kg$ . Radius of earth $=R=6.4\times {10}^{6}m$ and G=$6.67\times {10}^{-11}{Nm}^2{Kg}^{-2}$

Answer 1

We know, gravitational potential energy

$U_g=\frac{-G{m}_1{m}_2}{r}$

According to the question

$U_1=\frac{-6.67\times {10}^{-11}\times 6\times {10}^{24}\times 50}{(6.4+1)\times {10}^6}=2.7\times {10}^9$

$U_2=\frac{-6.67\times {10}^{-11}\times 6\times {10}^{24}\times 50}{(6.4+35)\times {10}^6}=4.8\times {10}^8$

Finding difference in their potential energy

$U_2-U_1=△U$

$△U-4.8\times {10}^8-27\times {10}^8$

$△U=-22.2\times {10}^8$

Thus, the difference is $22.2\times {10}^{8}J$