Hmm...Latex doesn't seem to be working at the moment... How does one show the conservation of the Laplace-Runge-Lenz (LRL) vector using the Hamiltonian of the two-body system? Showing it's conserved otherwise it's not hard. You can take the time derivative of the LRL vector and show that it's zero or a couple other ways which I worked out before (I would type it out but Latex seemingly disabled makes it tedious and cumbersome). The one thing I can't figure out is how to get the conservation of the LRL vector from the Hamiltonian of the two-body system. What I did was take the square of the LRL vector and find the energy from that but then it becomes uncertain.