Phase-Space Orbits for the Kepler Problem on Constant Energy Surfaces

Trajectories for the Kepler two-body problem are plotted on a constant-energy surface in reduced phase space. The variables are the coordinates , and the velocity components , . The four initial values are selected by sliders. This Demonstration helps in understanding the relationship between energy and stable orbits. The contour plots take a few seconds to load for some sets of initial conditions.