How does the orbital period P of particles moving around in the rings of Saturn depend on the distance r of the particles from the center of the planet?
A) P² is proportional to r³.
B) P is constant for all r because the rings move as a solid disk.
C) P is proportional to 1/r²
D) P increases directly with r.

Question

Quizplus · Accepted Answer

Kepler's Third Law states that the square of the orbital period of a planet around a star is proportional to the cube of the semi-major axis of its elliptical orbit. This can be generalized for any orbit, including the rings of Saturn. The distance r from the center of the planet to the ring particle is equivalent to the semi-major axis of the particle's orbit. Therefore, the square of the orbital period P² should be proportional to the cube of the distance r³, leading to choice A as the correct answer.

How Does the Orbital Period P of Particles Moving Around