Two planets X and Y travel counterclockwise in circular orbits about a star as s
ID: 2241824 • Letter: T
Question
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 5:2. 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
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 5:2. 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 degree as shown in figure (b). What is the angular displacement of planet Y at this moment?Explanation / Answer
You can start this with one of Kepler's Laws. I, however, don't bother to remember Kepler's Law about periods and orbital radii, as it's fairly quick to derive from things that need to be remembered, anyway.
The force on a planet is the force of gravity from the star. The acceleration of the planet is toward the center, a centripetal acceleration. Using Newton's Second Law
? F_c = GMm/r
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