A satellite orbits a planet in a circular orbit of radius 4.0 × 10^7 m. The planet's mass is 6.0 × 10^24 kg. What is the orbital speed of the satellite? (Use G = 6.67 × 10^-11 N·m^2/kg^2.)
Show the answer and explanation
Correct answer
A. 3.2 × 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(GM/r) = sqrt((6.67e-11 * 6.0e24) / 4.0e7) = sqrt(4.002e14 / 4.0e7) = sqrt(1.0005e7) ≈ 3.16e3 m/s, which rounds to 3.2 × 10^3 m/s.
Example
For Earth (M = 6.0e24 kg, r = 6.4e6 m), v ≈ 7.9 km/s.
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