A hypothetical moon orbits a planet which in turn orbitsa star. Suppose that the orbits
Chapter 4, Problem 61(choose chapter or problem)
A hypothetical moon orbits a planet which in turn orbitsa star. Suppose that the orbits are circular and thatthe moon orbits the planet 12 times in the time it takesfor the planet to orbit the star once. In this problem wewill investigate whether the moon could come to a stopat some instant. (See Figure 4.112.)(a) Suppose the radius of the moons orbit around theplanet is 1 unit and the radius of the planets orbitaround the star is R units. Explain why the motionof the moon relative to the star can be described bythe parametric equationsx = R cos t + cos(12t), y = R sin t + sin(12t).(b) Find values for R and t such that the moon stopsrelative to the star at time t.(c) On a graphing calculator, plot the path of the moonfor the value of R you obtained in part (b). Experimentwith other values for R
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