Question

Two planets X and Y travel counterclockwise in circular orbits about a star, as seen in the figure. The radii of their orbits are in the ratio 2:1. At some time, they are aligned, as seen in (a), making a straight line with the star. Five years later, planet X has rotated through 90.9°, as seen in (b). By what angle has planet Y rotated through during this time?

Answer 1

By 272.7 degrees angle has planet Y rotated through during this time.

What is Kepler's 3rd law?

The cubes of the semi-major axes of the planets' orbits are precisely proportional to the squares of the planets' orbital periods. According to Kepler's Third Law, as an orbiting planet's radius rises, so does the time of its orbit around the Sun.

Using Kepler's 3rd law, which says that the period of any planet's orbit squared is proportional to the radius of the orbit cubes, we can establish that

(period X / period Y)^2 = (radius X / radius Y)^3

(period X / period Y)^2 = 2^3 = 8

take sq root

period X / period Y = √8 = 2.82≅ 3

this means it takes planet X 2.82≅ 3  times longer to go through one orbit... so planet Y travels 2.82≅ 3  times as far (in its orbit...) as planet X!

This means...

planet Y travels   3 * 90.9  =   272.7 degrees

to learn more about  Kepler's 3rd law go to - brainly.com/question/16705471

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