An astronomer discovered two planets, X and Y, orbiting a star. From the perspective of the astronomer, the planets orbit the star as depicted in the figures. Five years ago, the planets were in the position shown in figure (a), with X, Y, and the star in a straight line. Today, planet X is in the position shown in figure (b), having made an angular displacement of 90.0°. If the radii of their orbits are in the ratio 5:4, what is the angular displacement of Y? (Give your answer in revolutions.) a b 1/5 × Equate Newton's law of universal gravitation with his second law, noting that the force in this case is a centripetal force, and use the relationship among angular velocity, radius, and linear velocity. Solve for the angular velocity of planet Y, and calculate the angular displacement in revolutions. revolutions

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