A satellite of mass ms is orbiting a planet at a speed vs. The planet has a mass Mp. Which of the following represents the radius of the satellite’s orbit measured from the center of the planet?
A) GMp / vs2
B) √(GMpms / vs)
C) ½ (msvs2)
D) Gms / vs2
Explanation
An object travelling in circular orbit is experiencing a centripetal force from the planet’s gravity. We may thus set up the following equation:
Fc = GMpms / r2 = msv2 / r
Cancelling the mass of the satellite we get:
GMp / r2 = v2 / r
Multiply both sides by the radius of the orbit:
GMp / r = v2
The question asked for the radius of the orbit, so isolate r:
GMp / v2 = r
Thus, choice (A) is the right answer.
If you’re not sure how to proceed, always try to eliminate one or two choices before you guess. If you couldn’t remember the equations for centripetal force or for gravity, you may still have been able to recognize choice (C) as the kinetic energy equation. The question asked you for radius, so an answer choice that would be in joules would have to be wrong. So eliminate (C) and guess.
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