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?

1 Answer
Oct 26, 2016

Answer:

#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#