The arrangement in mean elements space of the periodic orbits close to that of the Moon
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In a simplified model of the Earth-Moon-Sun system based on the restricted circular 3-dimensional 3-body problem, it is possible to find numerically a set of 8 periodic orbits whose time evolutions closely resemble that of the Moon's orbit. These orbits have a period of 223 synodic months (i.e. the period of the Saros cycle known for more than two millennia as a means of predicting eclipses), and are characterized by a secular rotation of the argument of perigee ω. Periodic orbits of longer durations exhibiting this last feature are very abundant in Earth-Moon-Sun dynamical models. Their arrangement in the space of the mean orbital elementsē-ī for various values of the lunar mean motion is presented.
Key wordsPeriodic orbits motion of the Moon Saros cycle
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