
The basis for discussion is the abstract of the paper below. Instead of their ‘high-integer near commensurabilities among lunar months’ we’ll just say ‘numbers’ and try to make everything as straightforward as possible. This will expand on a previous Talkshop post on much the same topic.
Hunting for Periodic Orbits Close to that of the Moon in the Restricted Circular Three-Body Problem (1995)
Authors: G. B. Valsecchi, E. PerozziA, E. Roy, A. Steves
Abstract
The role of high-integer near commensurabilities among lunar months — like the long known Saros cycle — in the dynamics of the Moon has been examined in previous papers (Perozzi et al., 1991; Roy et al., 1991; Steves et al., 1993). A by-product of this study has been the discovery that the lunar orbit is very close to a set of 8 long-period periodic orbits of the restricted circular 3-dimensional Sun-Earth-Moon problem in which also the secular motion of the argument of perigee ω is involved (Valsecchi et al., 1993a). In each of these periodic orbits 223 synodic months are equal to 239 anomalistic and 242 nodical ones, a relationship that approximately holds in the case of the observed Saros cycle, and the various orbits differ from each other for the initial phases. Note that these integer ratios imply that, in one cycle of the periodic orbit, the argument of perigee ω makes exactly 3 revolutions, i.e. the difference between the 242 nodical and the 239 anomalistic months (these two months differ from each other just for the prograde rotation of ω).
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To start with we can create a model that pretends the ‘high-integer near commensurabilities’ really are whole numbers, then break down the logic of the result to see what’s going in with the Moon at the period of one Saros cycle.
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