Question

How high above Earth is a satellite orbiting if its tangential velocity is 5000 m/s? Earth’s mass is kg and its radius is m.

1,500,000 m
2,240,000 m
9,608,000 m
16,008,000 m

Answer 1

Use v^2 = GM/r for a circular orbit → r = GM / v^2. With G = 6.67×10^-11 N·m^2/kg^2 and M = 5.97×10^24 kg,
r = (6.67×10^-11·5.97×10^24)/(5000^2) ≈ 1.594×10^7 m.
Altitude h = r − R_earth ≈ 1.594×10^7 − 6.37×10^6 ≈ 9.58×10^6 m.

Closest choice: 9,608,000 m.