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?

Respuesta :

Answer:

0.63

Explanation:

We are given that

Radius of earth,[tex]R_E=6370 km[/tex]

Radius of orbit A,[tex]R_A=7590+6370=13960 km[/tex]

Radius of orbit B,[tex]R_B=6370+15800=22170 km[/tex]

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=[tex]U_A=-\frac{GM}{R_A}=-\frac{GM}{13960}[/tex]

Potential energy of orbit  B=[tex]U_B=-\frac{GM}{R_B}=-\frac{GM}{22170}[/tex]

[tex]\frac{U_B}{U_A}=\frac{13960}{22170}=0.63[/tex]

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