Abstract
A modified periodic orbit of the third kind is introduced that is closely related to periodic orbits of the third kind as defined by Poincaré. It is shown that Pluto librates about the periodic orbit with apparent stability. This further explains the librational motion of the resonant argument of Pluto and the avoidance of a Pluto-Neptune close approach as found by Cohen and Hubbard and the long-term motion of Pluto and the librational motion of the perihelion as found by Williams and Benson. With libration about a periodic orbit, the numerical solution of Williams and Benson can be extrapolated to longer times in the past and future.
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Nacozy, P.E., Diehl, R.E. On the long-term motion of Pluto. Celestial Mechanics 8, 445–454 (1974). https://doi.org/10.1007/BF01227797
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DOI: https://doi.org/10.1007/BF01227797