Halo orbits around $L_{1}$, $L_{2}$, and $L_{3}$ in the photogravitational Sun–Mars elliptical restricted three-body problem

Sheth, Dhwani; Thomas, V. O.

doi:10.1007/s10509-022-04130-w

Cited by 6 publications

(3 citation statements)

References 48 publications

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“…Other studies have either focused on different three-body systems or solely analyzed the effects of noncircular orbits on the autonomous CR3BP dynamics. These studies determined the effects of eccentricity by analyzing the dynamical behavior in the Elliptic Restricted Three-Body Problem (ER3BP) [21][22][23][24][25][26]. It has been proved mathematically that the system dynamics become further chaotic and more unstable for any spacecraft in the ER3BP when compared to the original CR3BP [21].…”

Section: Introductionmentioning

confidence: 99%

“…The results are indicative of the fact that consideration of eccentricity leading to non-autonomous motion can have profound effects on the legacy dynamical structures from the more benign circular restricted case. Periodicity for halo orbit counterparts has been achieved via numerical continuation and shows significant dissimilarity from corresponding motions in the CR3BP family [22][23][24][25]. Therefore, the need to analyze systems of intermediate fidelity using advanced numerical methods to understand long-term dynamical behavior and motion structures has been established.…”

Section: Introductionmentioning

confidence: 99%

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Exploration and Maintenance of Homeomorphic Orbit Revs in the Elliptic Restricted Three-Body Problem

Alvarado,

Singh

2024

Aerospace

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A novel station-keeping strategy leveraging periodic revolutions of homeomorphic orbits in the Elliptic Restricted Three-Body Problem within the pulsating frame is presented. A systemic approach founded on arc-length continuation is presented for the discovery, computation, and classification of periodic revolutions that morph from their traditional circular restricted three-body counterparts to build an a priori dataset. The dataset is comprehensive in covering all possible geometric architectures of the restricted problem. Shape similarity is quantified using Hausdorff distance and works as a filter for the station-keeping algorithm in relation to appropriate target conditions. Finally, an efficient scheme to quantify impulsive orbit maintenance maneuvers that minimize the total fuel cost is presented. The proposed approach is salient in its generic applicability across any elliptic three-body system and any periodic orbit family. Finally, average annual station-keeping costs using the described methodology are quantified for selected “orbits of interest” in the cis-lunar and the Sun–Earth systems. The robustness and efficacy of the approach instill confidence in its applicability for realistic mission design scenarios.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exploration and Maintenance of Homeomorphic Orbit Revs in the Elliptic Restricted Three-Body Problem

Alvarado,

Singh

2024

Aerospace

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“…While in [22] the locations of collinear points in photogravitational ER3BP under the effect of the zonal harmonics of the smaller primary is studied with their linear stability. But the ER3BP is employed to study the halo orbits around Sun-Mars collinear points L 1 , L 2 , and L 3 when the bigger primary is a source of radiation [23]. Also in [24][25][26] the authors analysed the effects of the third body perturbation in the framework of elliptic restricted 4-body problem dynamics, where some interesting resonant periodic solutions were derived in this operative environment.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Resonant Periodic Orbits in the Framework of the Perturbed Restricted Three Bodies Problem

2023

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In this work, the perturbed equations of motion of the infinitesimal body are constructed in the framework of the circular restricted three-body problem when the main two bodies are oblate and radiating. Under the perturbations effects of the oblateness and the radiation pressure the positions of collinear Lagrange points are evaluated, the interior and exterior first-order resonant periodic orbits are also studied. In addition, the initial positions of the periodic orbits and the size of loops have been estimated under these effects. Thus, the characteristics of periodic orbits have been studied under the combine effects of two, three and four perturbations for all the possible combinations of the perturbed parameters. The different order of resonant periodic orbits have been also analysed under the effects of Jacobi constant, mass factor, order of resonance and number of loops.

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Analysis of exterior resonant periodic orbits in the photogravitational ERTBP

et al. 2023

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Halo orbits around $L_{1}$, $L_{2}$, and $L_{3}$ in the photogravitational Sun–Mars elliptical restricted three-body problem

Cited by 6 publications

References 48 publications

Exploration and Maintenance of Homeomorphic Orbit Revs in the Elliptic Restricted Three-Body Problem

Exploration and Maintenance of Homeomorphic Orbit Revs in the Elliptic Restricted Three-Body Problem

Analysis of Resonant Periodic Orbits in the Framework of the Perturbed Restricted Three Bodies Problem

Analysis of exterior resonant periodic orbits in the photogravitational ERTBP

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