Question

Satellites, A and B, each of mass m, are to be launched into circular orbits about Earth's center. Satellite A is to orbit at an altitude of 7590 km. Satellite B is to orbit at an altitude of 15800 km. The radius of Earth REis 6370 km. (a) What is the ratio of the potential energy of satellite B to that of satellite A, in orbit?

Answer 1

Answer:

0.63

Explanation:

We are given that

Radius of earth,$R_E=6370 km$

Radius of orbit A,$R_A=7590+6370=13960 km$

Radius of orbit B,$R_B=6370+15800=22170 km$

We have to find the ratio of the potential energy of satellite B to that of satellite A in orbit.

Potential energy of orbit A=$U_A=-\frac{GM}{R_A}=-\frac{GM}{13960}$

Potential energy of orbit  B=$U_B=-\frac{GM}{R_B}=-\frac{GM}{22170}$

$\frac{U_B}{U_A}=\frac{13960}{22170}=0.63$

Hence,the ratio of the potential energy of satellite B to that of satellite A in orbit=0.63