A satellite is in a circular orbit around a planet. The planet has mass 6.0 × 10^24 kg and the satellite orbits at a radius of 1.5 × 10^7 m from the planet's center. 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 a satellite in circular orbit, the gravitational force provides the centripetal force: GMm/r^2 = mv^2/r, so v = sqrt(GM/r).
Why this answer is correct
v = sqrt((6.67 × 10^-11)(6.0 × 10^24)/(1.5 × 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 = 6.0 × 10^24 kg, r = 6.4 × 10^6 m gives v ≈ 7.9 × 10^3 m/s.
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