Question

Two satellites are in circular orbits around the earth. The orbit for satellite A is at a height of 539 km above the earth's surface, while that for satellite B is at a height of 876 km. How do you find the orbital speed for satellite A and satellite B?

Answer 1

`V_B=7408m/s`

Explanation:

To do this problem, you need the Earth's radius `R = 6371 km`

For the satellite to be in a stable orbit at a height, h, its centripetal acceleration `V^2/(R + h)` must equal the acceleration due to gravity at that distance from the center of the earth `g(R^2/(R + h)^2)`

`V^2/(R + h) = g(R^2/(R + h)^2)`

`V = sqrt(g(R^2/(R + h)))`

For satellite A:

`V_A = sqrt(g(R^2/(R + h_A)))`

`V_A = sqrt(9.8 m/s^2((6371000 m)^2)/(6371000 m + 539000 m))`

`V_A = 18131 m/s`

For satellite B:

`V_B = sqrt(g(R^2/(R + h_B)))`

`V_B = sqrt(9.8 m/s^2((6371000 m)^2)/(6371000 m + 876000 m))`

`V_B = 7408 m/s`