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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.
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