Review Article: Resonant Families of Periodic Orbits in the Restricted Three-body Problem*

Pan, Shanshan; Hou, Xiyun

doi:10.1088/1674-4527/ac6aaa

Cited by 5 publications

(8 citation statements)

References 102 publications

(172 reference statements)

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“…When the bin resolution is enhanced to Δa = 0.0005 au, Δe = 0.0005 (see the right frame of Figure 9), we can observe some fine structures at specific positions. We believe that these structures are closely related to orbital resonances with P2, which are very close to the 1: 1 one (Pan & Hou 2022;Tan et al 2023).…”

Section: Steady-state Distributionmentioning

confidence: 61%

Capture Efficiency Analysis in the Circular Restricted Three-body Problem

Miao,

Hou

2024

Res. Astron. Astrophys.

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The temporary capture problem of massless particles around the secondary is studied in the circular restricted three-body problem. The gravitational influence of the secondary on the orbit distribution of the particles is taken into account by means of a numerical iterative process. A relatively steady state of the orbital element distribution of the particles is used to compute the capture efficiency. Our study finds that the final computed result is influenced by the circumsphere around the secondary, and a way is proposed to determine the size of the circumsphere. Two methods of computing the capture efficiency are used and compared, and consistent results are obtained. When the mass ratio μ is 3.0035 × 10-6 (which is the same as in the Sun-Earth system), a recommended value of the circumsphere size is 6 Hill Radii of the secondary, and the computed capture efficiency is ∼ 1.54 × 10-4. The influence of the mass parameter of the secondary on the capture efficiency is also investigated and a power-law relationship between the capture efficiency p and the mass ratio μ holds as p ≈ 0.14 × μ0.52, when 3.0035 × 10−6 ≤ μ ≤ 3.0034 × 10−5. The current study can be extended to more realistic force models and may help us understand the temporary capture of natural bodies by the major celestial bodies in our solar system (e.g. the Sun-Earth system).

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Section: Steady-state Distributionmentioning

confidence: 61%

Capture Efficiency Analysis in the Circular Restricted Three-body Problem

Miao,

Hou

2024

Res. Astron. Astrophys.

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“…In the unperturbed two-body model, two different kinds of symmetric periodic orbits exist in the synodic frame [4,13,29,30]. The periodic orbits related to the circular orbits of the small body are called periodic orbits of the first kind, which belong to the circular family.…”

Section: The First-order Resonant Periodic Familiesmentioning

confidence: 99%

“…Example orbits in "Branch-I" (Type-I ) and "Branch-II" (Type-II ) of the interior 3:2, 4:3, and 5:4 resonances and the exterior 2:3, 3:4, and 4:5 resonances in the Sun-Earth system are presented in Figure 2. Recently, Pan and Hou [4] presented the genealogy of the first-order interior as well as exterior resonant periodic families in the T − C plane for the Sun-Earth, Sun-Jupiter, and Earth-Moon systems. Studies indicate that the two branches of each first-order resonant periodic family split and combine with the near-circular branch to form a new family in the T − C plane (see Figure 4a,b).…”

Section: The Crtbp Model: µ >mentioning

confidence: 99%

“…The resonant motions in the restricted three-body problem have been studied many times in the past years. The resonant periodic families and their stability corresponding to first-, second-, and other higher-order resonances in the CRTBP and the ERTBP model are reviewed by [3,4]. The transition between different resonances is also an interesting problem and has been investigated by many researchers.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Resonance Transition Periodic Orbits in the Circular Restricted Three-Body Problem

Pan

Hou

2022

Applied Sciences

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Resonance transition periodic orbits exist in the chaotic regions where the 1:1 resonance overlaps with nearby interior or exterior resonances in the circular restricted three-body problem (CRTBP). The resonance transition periodic orbits have important applications for tour missions between the interior and the exterior regions of the system. In this work, following the increase of the mass parameter μ in the CRTBP model, we investigate the breakup of the first-order resonant periodic families and their recombination with the resonance transition periodic families. In this process, we can describe in detail how the 1:1 resonance gradually overlaps with nearby first-order resonances with increasing strength of the secondary’s perturbation. Utilizing the continuation method, features of the resonance transition periodic families are discussed and characterized. Finally, an efficient approach to finding these orbits is proposed and some example resonance transition periodic orbits in the Sun–Jupiter system are presented.

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“…Celestial mechanics plays an important role in understanding the dynamics of solar system bodies (see, e.g., Murray & Dermott 1999;Souchay & Dvorak 2010;Lei 2021;Pan & Hou 2022). One of the problems in celestial mechanics is the Circular Restricted Three-Body Problem (CRTBP).…”

Section: Introductionmentioning

confidence: 99%

Studying the Equilibrium Points of the Modified Circular Restricted Three-body Problem: The Case of Sun–Haumea System

Nurul Huda,

Dermawan,

Saputra

et al. 2023

Res. Astron. Astrophys.

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We intend to study a modified version of the planar Circular Restricted Three-Body Problem (CRTBP) by incorporating several perturbing parameters. We consider the bigger primary as an oblate spheroid and emitting radiation while the small primary has an elongated body. We also consider the perturbation from a disk-like structure encompassing this three-body system. First, we develop a mathematical model of this modified CRTBP. We have found there exist five equilibrium points in this modified CRTBP model, where three of them are collinear and the other two are non-collinear. Second, we apply our modified CRTBP model to the Sun–Haumea system by considering several values of each perturbing parameter. Through our numerical investigation, we have discovered that the incorporation of perturbing parameters has resulted in a shift in the equilibrium point positions of the Sun–Haumea system compared to their positions in the classical CRTBP. The stability of equilibrium points is investigated. We have shown that the collinear equilibrium points are unstable and the stability of non-collinear equilibrium points depends on the mass parameter μ of the system. Unlike the classical case, non-collinear equilibrium points have both a maximum and minimum limit of μ for achieving stability. We remark that the stability range of μ in non-collinear equilibrium points depends on the perturbing parameters. In the context of the Sun–Haumea system, we have found that the non-collinear equilibrium points are stable.

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Review Article: Resonant Families of Periodic Orbits in the Restricted Three-body Problem*

Cited by 5 publications

References 102 publications

Capture Efficiency Analysis in the Circular Restricted Three-body Problem

Capture Efficiency Analysis in the Circular Restricted Three-body Problem

Analysis of Resonance Transition Periodic Orbits in the Circular Restricted Three-Body Problem

Studying the Equilibrium Points of the Modified Circular Restricted Three-body Problem: The Case of Sun–Haumea System

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