A satellite moves in a circular orbit of radius 2.0 × 10^7 m around a planet. The mass of the planet is 8.0 × 10^24 kg. What is the orbital speed of the satellite? (G = 6.67 × 10^-11 N·m^2/kg^2)
Show the answer and explanation
Correct answer
A. 5.2 × 10^3 m/s
Principle or equation
For circular orbit, gravitational force provides centripetal force: GMm/r^2 = mv^2/r, so v = sqrt(GM/r).
Why this answer is correct
v = sqrt( (6.67 × 10^-11 × 8.0 × 10^24) / (2.0 × 10^7) ) = sqrt( (5.336 × 10^14) / (2.0 × 10^7) ) = sqrt(2.668 × 10^7) ≈ 5.16 × 10^3 m/s, which rounds to 5.2 × 10^3 m/s.
Example
For Earth, M = 6 × 10^24 kg, r = 6.4 × 10^6 m, v ≈ sqrt(6.67e-11 × 6e24 / 6.4e6) ≈ 7.9 × 10^3 m/s.
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