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