Question

Two satellites are in circular orbits around the earth. The orbit for satellite A is at a height of 406 km above the earth's surface, while that for satellite B is at a height of 904 km. Find the orbital speed for satellite A and satellite B.

Answer 1

Given:

A = 406,000 m
B = 904,000 m
G = 6.67428E-11 m^3/kg-s^2
Mass of earth = 5.9736E+24 kg
radius of earth = 6,371,000 m

Recall that you need the actual orbital distance from the *center* of the Earth, giving radius plus altitude:

rA = 6.777*10⁶ m
rB = 7.275*10⁶ m

Equation:

V = sqrt (GM / r )

Solve for A

Va = sqrt { [ (6.67428E-11 m^3/kg-s^2) * (5.9736E+24 kg) ] / (6.777*10⁶ m) }
Va = sqrt (5.87*10⁷)
Va = 7.665*10³ m/s

Solve for B

Vb = SQRT { [ (6.67428E-11 m^3/kg-s^2) * (5.9736E+24 kg) ] / (7.275*10⁶ m) }
Vb = SQRT { [ 3.9869 m^3/s^2 ] / (7,272,000 m) }
Vb = SQRT { 54,826,016 m^2/s^2 }
Vb = 7.398*10³ m/s