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

0.63

Step-by-step 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=-(GM)/(R_A)=-(GM)/(13960)`

Potential energy of orbit B=
`U_B=-(GM)/(R_B)=-(GM)/(22170)`

`(U_B)/(U_A)=(13960)/(22170)=0.63`

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