The force of attraction between a star of mass M and a planet of mass m (where т «М) is: ЗЫ? a F where is the angular momentum of the planet and a,b are both positive constants. [Note: black hole, in the non- this does approximate the force of attraction between a planet and a relativistic limit, with a = GMm. (a) 15 points Under what conditions is a stable circular orbit possible? Give the radius of the stable circular orbit in terms of the given parameters (M, m,a, b, l). function of a (b) 15 pointsWhat is the smallest radius possible for any circular orbit as a and b, allowing for arbitrary l? (Hint: this occurs in the limit of very large .) Is this circular orbit stable or unstable? (c) [10 points] If the planet travels in a slightly non-circular orbit about a stable radius, find expression for the angular frequency of small radial oscillations