Sarah B.

asked • 12/01/19

Satellite A of mass m orbits a planet of mass M at a distance of R from the center of the planet. The speed of the satellite is v. Answer in terms of m, M, R and v.

Satellite B has mass m and orbits a planet of mass M. What should satellite B's orbital radius be so that its period is 8 times that of satellite A?

(The answer is 4 R I just don't know how to get there)

1 Expert Answer

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Arturo O. answered • 12/02/19

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Use Kepler's 3rd law.


T = period

R = orbital radius


R3/T2 = constant


RA3 / TA2 = RB3 / TB2


TB = 8TA ⇒


RB3 = (TB / TA)2 RA3 = 82 RA3


RB = (64)1/3 RA = 4RA = 4R

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Arturo O.

I want to add that Kepler's 3rd law applies here, since both A and B are orbiting a body of the same mass.
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12/02/19

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