Question: A hypothetical moon orbits a planet which in turn orbits a star. Suppose that the orbits are circular and that the moon orbits the planet 12 times in the time it takes for the planet to orbit the star once. In this problem we will investigate whether the moon could come to a stop at some instant. (See Figure)
(a) Suppose the radius of the moon's orbit around the planet is 1 unit and the radius of the planet's orbit around the star is R units. Explain why the motion of the moon relative to the star can be described by the parametric equations
x = R cos t + cos(12t), y = R sin t + sin (12t)
(b) Find values for R and t such that the moon stops relative to the star at time t.
(c) On a graphing calculator, plot the path of the moon for the value of R you obtained in part (b). Experiment with other values for R.
