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

x

0

1.2

y

0

-0.75

v

x0

0.4

v

y0

0.44

time

50

Trajectories for the Kepler two-body problem are plotted on a constant-energy surface in reduced phase space. The variables are the coordinates

x

,

y

and the velocity components

v

x

,

v

y

. 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.