Global search for periodic orbits in the irregular gravity field of a binary asteroid system

Shi, Yu; Xu, Shijie

doi:10.1016/j.actaastro.2018.10.014

Cited by 19 publications

(5 citation statements)

References 33 publications

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“…Using the method of successive approximations up to the second-order terms, the periodic solutions of system (14) are in the following form (see [17])…”

Section: Periodic Orbits In the Spatial Spacementioning

confidence: 99%

“…When two asteroids were approximated as triaxial ellipsoids, Hou et al [13] studied the forced periodic orbits around the triangular libration points in a binary asteroid system influenced by the solar radiation pressure. Recently, a numerical method was proposed to search for three-dimensional periodic orbits by Shi et al [14]. After applying this method to binary asteroid 1999 KW4, they found five kinds of periodic orbits of the binary system.…”

Section: Introductionmentioning

confidence: 99%

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Bifurcation Analysis and Periodic Solutions of the HD 191408 System with Triaxial and Radiative Perturbations

Gao

Wang

2020

Universe

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The nonlinear orbital dynamics of a class of the perturbed restricted three-body problem is studied. The two primaries considered here refer to the binary system HD 191408. The third particle moves under the gravity of the binary system, whose triaxial rate and radiation factor are also considered. Based on the dynamic governing equation of the third particle in the binary HD 191408 system, the motion state manifold is given. By plotting bifurcation diagrams of the system, the effects of various perturbation factors on the dynamic behavior of the third particle are discussed in detail. In addition, the relationship between the geometric configuration and the Jacobian constant is discussed by analyzing the zero-velocity surface and zero-velocity curve of the system. Then, using the Poincaré–Lindsted method and numerical simulation, the second- and third-order periodic orbits of the third particle around the collinear libration point in two- and three-dimensional spaces are analytically and numerically presented. This paper complements the results by Singh et al. [Singh et al., AMC, 2018]. It contains not only higher-order analytical periodic solutions in the vicinity of the collinear equilibrium points but also conducts extensive numerical research on the bifurcation of the binary system.

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“…Using the method of successive approximations up to the second-order terms, the periodic solutions of system (14) are in the following form (see [17])…”

Section: Periodic Orbits In the Spatial Spacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis and Periodic Solutions of the HD 191408 System with Triaxial and Radiative Perturbations

Gao

Wang

2020

Universe

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“…About 16 per cent of near-Earth asteroids and main-belt asteroids with diameters below 10 km are binary systems. In recent years, many studies have been devoted to studying the orbital dynamics about these systems, including equilibrium and stability, as well as periodic orbits and invariant manifolds based on the restricted full three-body problem (Bellerose and Scheeres, 2008;Chappaz & Howell, 2015;Dell'Elce et al, 2017;Shi et al, 2019;Shi et al, 2020;Zhang et al, 2020;Li et al, 2021). Recently, Wang and Fu (2020) and Fu and Wang (2021) have extended the semianalytical orbital theory to an orbiter of a binary asteroid system, assuming a coplanar and circular configuration, by retaining the thirdbody gravity to the hexadecapole order and including the non-spherical third-body gravity.…”

Section: Introductionmentioning

confidence: 99%

Semi-analytical orbital model around an oblate body with an inclined eccentric perturber

Wang²,

Hu³

2023

Front. Astron. Space Sci.

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The semi-analytical model (based on the averaging technique) for long-term orbital evolution has proven to be useful in both astrophysical and astrodynamical contexts. In this secular approximation, orbits exhibit rich evolutionary behaviors under the effects of various perturbations. For example, in the hierarchical three-body systems, the Lidov-Kozai mechanism based on the quadrupole-level third-body perturbation model can produce large-amplitude oscillations of the eccentricity and inclination. In recent years, the octupole order has been found to induce dramatically new features when the perturbing body’s orbit is eccentric, including extremely high eccentricities and orbit flips between prograde and retrograde. Motivated by the striking effects of the octupole-order terms, we intend to derive a more general dynamical model by incorporating J2 of the central body and the inclined eccentric third-body perturbation to the hexadecapole order with its non-spherical gravity also included. This issue can be relevant for astrophysical and astrodynamical systems such as planets in stellar binaries, irregular satellites in planetary systems, and artificial probes about binary asteroid systems. Applications to the binary asteroid system 4951 Iwamoto and a fictitious exoplanetary system are illustrated as examples to validate our secular model. From these numerical results, we show the high accuracy of our secular model. Also, we show the important role of these high-order terms and the effects of the third-body’s inclination and eccentricity. Besides, we have found several different secular effects that could drive large eccentricities.

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“…Due to the non-spherical shape, the close distance, and the relative orbital and attitude motion of the asteroids, the dynamic environment in binary systems has the chaotic characteristic. A variety of researchers have dealt with the motion near binary asteroids in the past, including analogous equilibrium points [7,8], periodic orbits [9][10][11][12][13][14], resonant orbits [15] and lift-off motion on the surface [16]. Separate periodic orbits and bounded motions have been found based on a non-synchronized model [15,[17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Investigation of Stable Regions of Spacecraft Motion in Binary Asteroid Systems by Terminal Condition Maps

Dong

Jia

2021

J Astronaut Sci

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In this paper, the stable regions of spacecraft motion in binary asteroid systems are studied and applied to design trajectories for exploration missions. Due to the non-spherical shape and the relative motion of small bodies, the motion in a binary asteroid system exhibits chaotic characteristics, which bring difficulties to proximity operations. A terminal condition map is developed to analyze the motion stability, where the initial periapsides of trajectories are classified according to their terminal states, including orbiting the asteroids, impacting on the surface or escaping from the system. The binary asteroid system 66391 Moshup is chosen as the target. The geometry of terminal condition maps is first discussed based on a synchronized model. The stable regions around asteroids are found for both planar and spatial motions, and their evolutions with orbital energy are investigated. Then, a method to trajectory design in binary asteroid systems via terminal condition maps is proposed. Opportunities for ballistic capture and escape are found in the vicinity of the asteroids by matching backward and forward terminal condition maps. Meanwhile, V-assisted periodic orbits, as well as flyby trajectories, can be designed on the basis of the symmetry of maps. Finally, the terminal condition map is applied to discuss the effect of the primary and secondary's mutual motion on the spacecraft motion. This study provides a global picture of the motion stability and makes trajectory design flexible in binary asteroid systems, which can support future binary asteroid exploration missions.

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Global search for periodic orbits in the irregular gravity field of a binary asteroid system

Cited by 19 publications

References 33 publications

Bifurcation Analysis and Periodic Solutions of the HD 191408 System with Triaxial and Radiative Perturbations

Bifurcation Analysis and Periodic Solutions of the HD 191408 System with Triaxial and Radiative Perturbations

Semi-analytical orbital model around an oblate body with an inclined eccentric perturber

Investigation of Stable Regions of Spacecraft Motion in Binary Asteroid Systems by Terminal Condition Maps

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