The Main Problem of Lunar Orbit Revisited

Li, Bosheng; Hou, Xiyun

doi:10.3847/1538-3881/acbafa

Cited by 2 publications

(1 citation statement)

References 22 publications

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“…In this paper, we analytically deal with planar sphere-ellipsoid model and carry out the solution of the quasi-periodic motion to high orders by the LP method. As far as the author knows, the LP method is valid for many celestial mechanics problems (Jorba and Masdemont, 1999;Li and Hou, 2023), but it is seldom applied to the spin-orbit coupling study in the complete sphere-ellipsoid model of the binary asteroid system. In contrast to previous studies, where numerical approaches are usually used, or the high-order Hamiltonian normal form is obtained by the canonical transformations (Gkolias et al, 2016), the advantage of the LP method is to directly obtain the explicit quasi-periodic solution.…”

Section: Introductionmentioning

confidence: 99%

Spin-orbit coupling dynamics in a planar synchronous binary asteroid

Li,

Tan,

Hou

2024

Astrophys Space Sci

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Purpose: The 1:1 spin-orbit resonance phenomenon is widely observed in binary asteroid systems. We aim to investigate the intrinsic dynamic mechanism behind the phenomenon under the coupled influence of the secondary's rotation and orbital motion. Methods: The planar sphereellipsoid model is used to approximate the synchronous binary asteroid. To solve this strongly nonlinear problem, a novel algorithm based on the Lindstedt-Poincaré (LP) method is proposed to find the explicit solution of the quasi-periodic motion. Results: Numerical simulations for the Didymos system show that the high-order solution is accurate enough to provide the initial orbital conditions for further dynamic study. With the help of the solution, we compute the stable region for the synchronous state, the contour maps of the Lyapunov characteristic exponent, and the resonance curves of the basic frequencies in the parameter space. Conclusion: The stable synchronous state requires a small eccentricity e of the mutual orbit but permits a large libration angle θ of the secondary. The anti-correlation of θ and e is confirmed. The sable region for a very elongated secondary is small, which explains the lack of such secondaries in observations (see table 1 in Pravec et al ( 2016)). In addition, the findings of this research Article Title provide insights into chaos and the resonances of basic frequencies, which may play an important role in the evolution of a binary asteroid.

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Section: Introductionmentioning

confidence: 99%

Spin-orbit coupling dynamics in a planar synchronous binary asteroid

Li,

Tan,

Hou

2024

Astrophys Space Sci

Self Cite

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Spin-Orbit Coupling Dynamics in a Planar Synchronous Binary Asteroid

Tan

Hou

2023

Preprint

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Purpose: The 1:1 spin-orbit resonance phenomenon is widely observed in binary asteroid systems. We aim to investigate the intrinsic dynamic mechanism behind the phenomenon under the coupled influence of the secondary’s rotation and orbital motion. Methods: The planar sphere--ellipsoid model is used to approximate the synchronous binary asteroid. To solve this strongly nonlinear problem, a novel algorithm based on the Lindstedt--Poincaré (LP) method is proposed to find the explicit solution of the quasi-periodic motion. Results: Numerical simulations for the Didymos system show that the high-order solution is accurate enough to provide the initial orbital conditions for further dynamic study. With the help of the solution, we compute the stable region for the synchronous state, the contour maps of the Lyapunov characteristic exponent, and the resonance curves of the basic frequencies in the parameter space. Conclusion: The stable synchronous state requires a small eccentricity e of the mutual orbit but permits a large libration angle θ of the secondary. The anti-correlation of θ and e is confirmed. The sable region for a very elongated secondary is small, which explains the lack of such secondaries in observations (see table 1 in Pravec et al (2016)). In addition, the findings of this research provide insights into chaos and the resonances of basic frequencies, which may play an important role in the evolution of a binary asteroid.

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The Main Problem of Lunar Orbit Revisited

Cited by 2 publications

References 22 publications

Spin-orbit coupling dynamics in a planar synchronous binary asteroid

Spin-orbit coupling dynamics in a planar synchronous binary asteroid

Spin-Orbit Coupling Dynamics in a Planar Synchronous Binary Asteroid

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