GATE_AE_2027_MOCK_02_Q25 GATE 2027 Aerospace Engineering All-India Master Mock 02 (Compressible Aerodynamics & High-Speed Propulsion) NAT · 1 Mark
Flight Mechanics & Space Dynamics • Space Dynamics & Orbital Mechanics • Keplerian Orbits & Escape Velocity

A satellite is in a circular low Earth orbit at radius $r = 6700\text{ km}$. The standard gravitational parameter of Earth is $\mu = 3.986 \times 10^5\text{ km}^3/\text{s}^2$. What is the satellite's orbital speed in km/s? (Round to two decimal places).

Answer Key:
7.71

Step-by-Step Verified Solution

### Solution: $v_c = \sqrt{\frac{\mu}{r}} = \sqrt{\frac{398600}{6700}} = \sqrt{59.4925} \approx 7.713 \approx 7.71\text{ km/s}$. Correct: 7.71 (range 7.68 to 7.74).
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