Retrograde resonances at high mass ratio in the circular restricted 3-body problem

Studies involving retrograde orbits have been an emerging field in recent years, particularly in the case where there are resonances between objects orbiting in opposite directions. The high amount of data from space exploration missions increases the possibility of observing binary stellar systems...

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Bibliographic Details
Published in:Nonlinear dynamics 2023-09, Vol.111 (18), p.17021-17035
Main Authors: Caritá, G. A., Signor, A. C., Morais, M. H. M., de Carvalho, R. Egydio, Prado, A. F. B. A.
Format: Article
Language:English
Subjects:
Asteroid missions
Asteroids
Astrodynamics
Automotive Engineering
Bifurcations
Binary stars
Classical Mechanics
Control
Dynamical Systems
Engineering
Extrasolar planets
Mechanical Engineering
Mission planning
Numerical analysis
Orbital resonances (celestial mechanics)
Orbits
Original Paper
Period doubling
Planetary systems
Resonance
Retrograde orbits
Space exploration
Stellar systems
Three body problem
Vibration
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Summary:Studies involving retrograde orbits have been an emerging field in recent years, particularly in the case where there are resonances between objects orbiting in opposite directions. The high amount of data from space exploration missions increases the possibility of observing binary stellar systems which may have additional bodies with retrograde orbits. Furthermore, such orbits are relevant to understanding the dynamics of spacecrafts around binary asteroids, being essential to planning exploratory missions. In this work, we survey retrograde orbits around binary systems with mass ratio between 0.01 (hierarchical) and 0.5 (equal masses) in the framework of the planar circular restricted three-body problem (PCR3BP). We build surfaces of section and identify retrograde resonances up to fifth order, namely the 2/−1, 3/−2, 1/−1, 2/−3, 1/−2, 1/−3 and 1/−4 resonances. We conclude that retrograde resonances occur in binary systems at high mass ratio, including the co-orbital (1/−1) resonance. Period doubling bifurcations occur for the 1/−1 resonance, and period doubling and period tripling bifurcations are observed for the 1/−2 resonance. Asymmetric retrograde resonances of the type 1/−n occur for almost equal masses of the binary system. This study may be used for identifying retrograde planets in extrasolar systems and may possibly have applications to astrodynamics mission planning.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-023-08779-y