Physics
Physics
Problem
Planet X moves in a nearly circular orbit of radius around a star. Its orbital period is observed to be . Planet Y revolves around the same star in a circular orbit of radius . (a) Calculate the orbital period of Planet Y in days. (b) By what factor is the length of a year on Planet Y greater than that on Planet X?Intuitive explanation
This problem hinges on Kepler's Third Law, which relates orbital period to orbital radius. The key insight is that the period squared is proportional to the radius cubed—so planets farther out take much longer to orbit, even though they move more slowly. Once you set up the ratio of periods for two planets around the same star, the star's mass cancels out, letting you find Planet Y's period directly from the given data.
Intuitive explanation
This problem hinges on Kepler's Third Law, which relates orbital period to orbital radius. The key insight is that the period squared is proportional to the radius cubed—so planets farther out take much longer to orbit, even though they move more slowly. Once you set up the ratio of periods for two planets around the same star, the star's mass cancels out, letting you find Planet Y's period directly from the given data.