Retrograde resonance in the planar three-body problem

ISSN： 0923-2958

Source： Celestial Mechanics and Dynamical Astronomy, Vol.117, Iss.4, 2013-12, pp. : 405-421

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Abstract

We continue the investigation of the dynamics of retrograde resonances initiated in Morais and Giuppone (Mon Notices R Astron Soc 424:52–64, doi: 10.1111/j.1365-2966.2012.21151.x , 2012). After deriving a procedure to deduce the retrograde resonance terms from the standard expansion of the three-dimensional disturbing function, we concentrate on the planar problem and construct surfaces of section that explore phase-space in the vicinity of the main retrograde resonances (2/ $$-$$ $-$ 1, 1/ $$-$$ $-$ 1 and 1/ $$-$$ $-$ 2). In the case of the 1/ $$-$$ $-$ 1 resonance for which the standard expansion is not adequate to describe the dynamics, we develop a semi-analytic model based on numerical averaging of the unexpanded disturbing function, and show that the predicted libration modes are in agreement with the behavior seen in the surfaces of section.