Two planets each of mass m are in counter-clockwise circular orbits around a star of mass M (see the figure below). The inner planet P is in an orbit of radius R, while the outer planet P is in an orbit of radius 2R. Express your answer to all parts of this problem in terms of R, M, m and G, Newton's gravitational constant. Assume m < < M. P P a) (2 points) What is the ratio T/T of the orbital period of planet P to that of P? What is the value of T? b) (2 points) What is the ratio of E/E of the total energies of the orbits? What is the value of E? c) (2 points) What is the ratio L/L of the orbital angular momenta of the orbits? What is the value of L? Now suppose that we send a spacecraft of mass m, from P to P along the elliptical transfer orbit shown below. The orbit has a "periastron" (the distance of closest approach to the star about which the planets are orbiting) of R and an "apastron" (the greatest distance to the star) of 2R. d) (4 points) What are the semi-major axis a, the energy E, the angular momentum L and the eccentricity e of the transfer orbit? Transfer Orbit