Hamilton Jacobi and the Kepler Problem In this problem, we explore the Kepler problem; but this time 

Hamilton-Jacobi and the Kepler Problem In this problem, we explore the Kepler problem; but this time using the Hamilton-Jacobi equation. Consider two particles such that their total mass is M and their reduced mass is p in a potential V(r) where r is the distance between the particles. Show that the Hamilton-Jacobi equation for the Kepler system can be written as 2M ∇S - 4 (08 - 12 sin²θ) ∇t = E. (2) where we define S = Wt. Use separation of variables to guess a form for the solution S. Show that the Hamilton-Jacobi equation can be written in the form ∇S - 2M ∇t + [(esc²θ) - 4 (95509)² sin²θ] ∇φ = E. where S = Sn (R) + Sc(r) + So(θ) + So(φ) Et Show that the solution for SR can be written as SR (R) = const - X R. What does the constant correspond to here Next, show that the solution for So can be written as So = const X φ What does the constant correspond to here
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