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First-order
Epicyclic theory (yes, epicycles!)
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Just
an overview here for context
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Work
with nearly circular orbits in a flattened
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axisymmetric
gravitational potential. Write down
the
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equations
of motion in polar coordinates, using a
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Taylor
series.
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Basically
just looking at the linear deviation from
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circular
orbits. You wind up with equations
that
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solve
for the radial excursions and the precession of
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the
orbit in terms of “epicycles” of frequency κ.
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