GATE_AE_2027_MOCK_03_Q51 GATE 2027 Aerospace Engineering All-India Master Mock 03 (Flight Dynamics, Controls & Space Trajectories) NAT · 2 Marks
Flight Mechanics & Space Dynamics • Space Dynamics & Orbital Mechanics • Kepler's Laws & Orbital Period

A satellite is in a circular orbit around a planet of mass M with orbital radius r_1 = 10000 km, having orbital period T_1 = 4 hours. What is the orbital period T_2 (in hours) of another satellite in a circular orbit of radius r_2 = 40000 km around the same planet?

Answer Key:
32

Step-by-Step Verified Solution

### Solution: By Kepler's Third Law, T^2 \propto r^3 ==> (T_2 / T_1) = (r_2 / r_1)^{3/2} = (40000 / 10000)^{3/2} = 4^{3/2} = 8. T_2 = 8 * T_1 = 8 * 4 = 32 hours. Correct: 32.
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