Finding an Invariant

To understand an analyze these odd results, we see an invariant of the motion. That is, a quanitity that won't change as the planet migrates.

Starting with the Hill Hamiltonian and jumping over a lot of gorey details, under the assumption of an elliptical orbit we get

J = r2(± w - n)
is an invariant.

rOrbital radius of the moon
wOrbital frequency of moon
nOrbital frequency of the planet

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By John Weiss
Rendered Sunday 30 March 2003