Two planets X and Y travel counterclockwise in circular orbits about a star as shown in the figure below. The radii of their orbits are in the ratio 4:3. At one moment, they are aligned as shown in figure (a), making a straight line with the star. During the next five years, the angular displacement of planet X is 90.0° as shown in figure (b). What is the angular displacement of planet Y at this moment?
Answer = ____ revolutions
The Attempt at a Solution
(GMplanetMstar)/r^2 = ma = Mplanet V^2 / r
GMstar = r^3ω^3=Rx^3ωx^3 = Ry^3ωy^3
ωy = (90 degrees/5 years)(4/3)^(3/2) = 16√3 degrees/year ≈ 27.712812921102 degrees/year
I think I have figured out most of this problem, but I can not figure out how to convert into revolutions. Can anyone help? Thanks.