Retrograde resonance in the planar three-body problem

Abstract

We continue the investigation of the dynamics of retrograde resonances initiated in Morais & Giuppone (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.

Celestial Mechanics and Dynamical Astronomy, in press

References in corpus (3)

• Asteroids in retrograde resonance with Jupiter and Saturn
• Dynamics of planets in retrograde mean motion resonance
• Are retrograde resonances possible in multi-planet systems?

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