How do the moons of Jupiter behave when considered in terms of the relationship between the period P and radius a of their orbits around the planet? A) Jupiter's moons follow the Keplerian relationship P² = ka³, where k is a constant that is different from that in the relation governing planetary motion around the Sun. B) Jupiter's moons do not obey the Keplerian relationship P² = ka³ because their motion about Jupiter is affected by Jupiter's motion about the Sun. C) Jupiter's moons obey the Keplerian relationship P² = ka³ where k is the same as that for planetary motion around the Sun because it is a universal constant. D) Jupiter's moons do not obey the Keplerian relationship P² = ka³ because they orbit Jupiter, not the Sun.

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Quizplus · Accepted Answer

Jupiter's moons follow the Keplerian relationship $P^2 = ka^3$, where $P$ is the orbital period and $a$ is the radius of the orbit, similar to the planets orbiting the Sun. However, the constant $k$ is different because it depends on the mass of the central body, which in this case is Jupiter, not the Sun.

How Do the Moons of Jupiter Behave When Considered in Terms