Speaker
Description
I will show an elementary derivation of the bound orbits of an inverse-square force law. The approach uses the Hamilton equations of motion, which are just two coupled first-order differential equations for the time rate of change of the radial coordinate and of the radial momentum. By decoupling these equations, we simply have to integrate a first-order differential equation of a complex exponential function to find the orbit. This approach is much simpler than the standard approach, which requires one to solve a complicated integral for theta(r) and then invert it to find r(theta). This derivation is easily within reach of beginning physics students who are familiar with angular momentum and the fact that the derivative of an exponential is an exponential. Our approach has the added benefit of having a deep connection to the quantum solution of hydrogen as well. The original idea for this comes from the 1930 textbook Elementare Quantenmechanik by Born and Jordan.
