Problem 2. A planet of mass m moves around a star of mass M. The planet orbit is assumed to be a circle, the star being at its center. (a) Suppose the orbit radius is R. Find the period of the planet (the duration of its "year\"). . . o 2 RI'F,'Z Answer: The period T' = =75 77. (b) Suppose the speed of the planet is v. Find the radius R of the orbit. Answer: R = C:f (Hint: The force acting on the planet F = GmM W where r is the vector connecting the star and the planet, and G is the gravity constant; the planet acceleration is defined by the 2-d Newton's Law F =mr".)