A particle of mass m orbits in a central potential U(r). Take U(∞) = 0. a) Determine the period of a circular orbit of radius r0, in terms of the potential and its derivatives. b) Suppose that the orbit is slightly noncircular, with r(t) = r0 + ̵(t). Find the general solution for ̵(t) in the limit ̵^2 ≪ r0^2. Determine the period of small oscillations. c) Now consider the Yukawa potential U(r) = -k e^(-̱r) / r. What is the condition for the existence of stable circular orbits? Find the period of small oscillations about the circular orbits. d) Show that it is possible to have bound orbits with positive energy for the Yukawa potential. (Note that U=0 at infinity.)