If you quadruple the radius of the orbit of a moon around the planet Jupiter,the new time of revolution,T',of this moon is

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Quizplus · Accepted Answer

According to Kepler's third law, the square of the orbital period (T) of a planet (or moon in this case) is directly proportional to the cube of the semi-major axis of its orbit (r), which in this case is equivalent to the radius of the orbit for a circular orbit. Mathematically, this can be expressed as T^2 ∝ r^3. If the radius of the orbit is quadrupled (r' = 4r), then the new period (T') can be found by setting up the ratio (T'^2 / T^2) = (r'^3 / r^3) = (4r)^3 / r^3 = 64. Taking the square root of both sides gives T' / T = √64 = 8, meaning the new time of revolution is 8 times the original period, T.

If You Quadruple the Radius of the Orbit of a Moon