SP-345 Evolution of the Solar
System
Figure 3.3.1.- The guiding-center method of approximating
the Kepler motion. The guiding center moves with constant velocity
along the dashed circle of radius r0 in the center
of which the gravitating mass Mc is situated. The
body M moves in an "epicycle" around the guiding center. The
epicycle is an ellipse with the axis ratio 2/1 and semiminor axis of
er0. The epicycle motion is retrograde. The
resulting motion of M is an ellipse which almost coincides with the
undashed circle which has its center at O. The distance from O
to Mc is er0. The position of the
pericenter is given by 
. The difference between the undashed circle and the
exact Kepler ellipse is really less than the thickness of the
line.
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