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Astrodynamics and Celestial Mechanics
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Astrodynamics and Celestial Mechanics

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Aerospace Science and Engineering".

Deadline for manuscript submissions: closed (20 April 2023) | Viewed by 14805

Special Issue Editors

Prof. Dr. Shengping Gong

E-Mail Website
Guest Editor
School of Astronautics, Beihang University, Beijing 100191, China
Interests: solar sailing; interplanetary optimization; many-body dynamics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Dong Qiao

E-Mail Website
Guest Editor
School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
Interests: multibody orbital dynamics; interplanetary trajectory transfer; asteroid orbital dynamics
Prof. Dr. Yazhong Luo

E-Mail Website
Guest Editor
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
Interests: spacecraft rendezvous; trajectory optimization; mission planning

Special Issue Information

Dear Colleagues,

Celestial mechanics is a classical and old discipline. The research on celestial mechanics, such as the three body problem, has attracted a number of famous scientists including Newton, Euler, Lagrange, Poincaré, Hill, Laplace, Cauchy, and Poisson. The research has generated many new theories in mathematics, dynamics, and physics. The origin of astrodynamics is celestial mechanics. Many classical methods in celestial mechanics, such as perturbation theory and the average method, are still used to design spacecraft orbits today in engineering practice. Several new methods such as invariant manifolds and weekly stable boundary theory have also been developed to handle the orbit or trajectory design in the restricted three body problem. As many new natural celestial bodies are observed and more complex spacecraft missions are proposed, models and methods should be developed to explain the new observed phenomena and design missions. This Special Issue will focus on new methods and results in celestial mechanics and astrodynamics.      

Prof. Dr. Shengping Gong
Prof. Dr. Dong Qiao
Prof. Dr. Yazhong Luo
Guest Editors

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Keywords

  • three body problem
  • four body problem
  • stability
  • retrograde orbit
  • orbital resonance
  • dynamical lifetime
  • capture
  • escape
  • evolution
  • asteroid
  • spacecraft dynamics
  • trajectory design
  • optimization

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Published Papers (6 papers)

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Research

17 pages, 1191 KiB  
Article
A Single-Launch Deployment Strategy for Lunar Constellations
by Stefano Carletta
Appl. Sci. 2023, 13(8), 5104; https://doi.org/10.3390/app13085104 - 19 Apr 2023
Cited by 5 | Viewed by 2019
Abstract
Satellite constellations can provide communication and navigation services to support future lunar missions, and are attracting growing interest from both the scientific community and industry. The deployment of satellites in orbital planes that can have significantly different inclinations and right ascension of the [...] Read more.
Satellite constellations can provide communication and navigation services to support future lunar missions, and are attracting growing interest from both the scientific community and industry. The deployment of satellites in orbital planes that can have significantly different inclinations and right ascension of the ascending node requires dedicated launches and represents a non-trivial issue for lunar constellations, due to the complexity and low accessibility of launches to the Moon. In this work, a strategy to deploy multiple satellites in different orbital planes around the Moon in a single launch is examined. The launch vehicle moves along a conventional lunar escape trajectory, with parameters selected to take advantage of gravity-braking upon encountering the Moon. A maneuver at the periselenium allows the transfer of the spacecraft along a trajectory converging to the equilibrium region about the Earth–Moon libration point L1, where the satellites are deployed. Providing a small ΔV, each satellite is transferred into a low-energy trajectory with the desired inclination, right ascension of the ascending node, and periselenium radius. A final maneuver, if required, allows the adjustment of the semimajor axis and the eccentricity. The method is verified using numerical integration using high-fidelity orbit propagators. The results indicate that the deployment could be accomplished within one sidereal month with a modest ΔV budget. Full article
(This article belongs to the Special Issue Astrodynamics and Celestial Mechanics)
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18 pages, 3399 KiB  
Article
Adaptive Gaussian Mixture Model for Uncertainty Propagation Using Virtual Sample Generation
by Tianlai Xu, Zhe Zhang and Hongwei Han
Appl. Sci. 2023, 13(5), 3069; https://doi.org/10.3390/app13053069 - 27 Feb 2023
Cited by 2 | Viewed by 2410
Abstract
Orbit uncertainty propagation plays an important role in the analysis of a space mission. The accuracy and computation expense are two critical essences of uncertainty propagation. Repeated evaluations of the objective model are required to improve the preciseness of prediction, especially for long-term [...] Read more.
Orbit uncertainty propagation plays an important role in the analysis of a space mission. The accuracy and computation expense are two critical essences of uncertainty propagation. Repeated evaluations of the objective model are required to improve the preciseness of prediction, especially for long-term propagation. To balance the computational complexity and accuracy, an adaptive Gaussian mixture model using virtual sample generation (AGMM-VSG) is proposed. First, an unscented transformation and Cubature rule (UT-CR) based splitting method is employed to adaptive update the weights of Gaussian components for nonlinear dynamics. The Gaussian mixture model (GMM) approximation is applied to better approximate the original probability density function. Second, instead of the pure expensive evaluations by conventional GMM methods, virtual samples are generated using a new active-sampling-based Kriging (AS-KRG) method to improve the propagation efficiency. Three cases of uncertain orbital dynamical systems are used to verify the accuracy and efficiency of the proposed manuscript. The likelihood agreement measure (LAM) criterion and the number of expense evaluations prove the performance. Full article
(This article belongs to the Special Issue Astrodynamics and Celestial Mechanics)
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18 pages, 5189 KiB  
Article
Analysis of Resonance Transition Periodic Orbits in the Circular Restricted Three-Body Problem
by Shanshan Pan and Xiyun Hou
Appl. Sci. 2022, 12(18), 8952; https://doi.org/10.3390/app12188952 - 6 Sep 2022
Cited by 3 | Viewed by 2526
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Astrodynamics and Celestial Mechanics)
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17 pages, 7403 KiB  
Article
Integrated Design of Moon-to-Earth Transfer Trajectory Considering Re-Entry Constraints
by Feida Jia, Qibo Peng, Wanmeng Zhou and Xiangyu Li
Appl. Sci. 2022, 12(17), 8716; https://doi.org/10.3390/app12178716 - 30 Aug 2022
Cited by 4 | Viewed by 2418
Abstract
The exploration of the Moon has always been a hot topic. The determination of the Moon-to-Earth transfer opportunity and the design of the precise transfer trajectory play important roles in manned Moon exploration missions. It is still a difficult problem to determine the [...] Read more.
The exploration of the Moon has always been a hot topic. The determination of the Moon-to-Earth transfer opportunity and the design of the precise transfer trajectory play important roles in manned Moon exploration missions. It is still a difficult problem to determine the Moon-to-Earth return opportunity for accurate atmospheric re-entry and landing, through which the actual return trajectory can be easily obtained later. This paper proposes an efficient integrated design method for Moon-to-Earth window searching and precise trajectory optimization considering the constraints of Earth re-entry and landing. First, an analytical geometry-based method is proposed to determine the state of the re-entry point according to the landing field and re-entry constraints to ensure accurate landing. Next, the transfer window is determined with the perilune heights, which are acquired by inversely integrating the re-entry state under the simplified dynamics as criterion. Then, the precise Moon-to-Earth trajectory is quickly obtained by a three-impulse correction. Simulations show the accuracy and efficiency of the proposed method compared with methods such as the patched-conic method and provide an explicit reference for future Moon exploration missions. Full article
(This article belongs to the Special Issue Astrodynamics and Celestial Mechanics)
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14 pages, 1634 KiB  
Article
Dynamics of Polar Resonances and Their Effects on Kozai–Lidov Mechanism
by Miao Li and Shengping Gong
Appl. Sci. 2022, 12(13), 6530; https://doi.org/10.3390/app12136530 - 28 Jun 2022
Viewed by 1855
Abstract
The research on highly inclined mean motion resonances (MMRs), even retrograde resonances, has drawn more attention in recent years. However, the dynamics of polar resonance with inclination i≈90∘ have received much less attention. This paper systematically studies the dynamics of [...] Read more.
The research on highly inclined mean motion resonances (MMRs), even retrograde resonances, has drawn more attention in recent years. However, the dynamics of polar resonance with inclination i≈90∘ have received much less attention. This paper systematically studies the dynamics of polar resonance and their effects on the Kozai–Lidov mechanism in the circular restricted three-body problem (CRTBP). The maps of dynamics are obtained through the numerical method and semi-analytical method, by mutual authenticating. We investigate the secular dynamics inside polar resonance. The phase-space portraits on the e−ω plane are plotted under exact polar resonance and considering libration amplitude of critical angle σ. Simultaneously, we investigate the evolution of 5000 particles in polar resonance by numerical integrations. We confirm that the e−ω portraits can entirely explain the results of numerical experiments, which demonstrate that the phase-space portraits on the e−ω plane obtained through the semi-analytical method can represent the real Kozai–Lidov dynamics inside polar resonance. The resonant secular dynamical maps can provide meaningful guidance for predicting the long-term evolution of polar resonant particles. As a supplement, in the polar 2/1 case, we analyze the pure secular dynamics outside resonance, and confirm that the effect of polar resonance on secular dynamics is pronounced and cannot be ignored. Our work is a meaningful supplement to the general inclined cases and can help us understand the evolution of asteroids in polar resonance with the planet. Full article
(This article belongs to the Special Issue Astrodynamics and Celestial Mechanics)
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11 pages, 1725 KiB  
Article
Vibration Prediction of Space Large-Scale Membranes Using Energy Flow Analysis
by Kun Wang, Qi Zhang and Jiafu Liu
Appl. Sci. 2022, 12(12), 6238; https://doi.org/10.3390/app12126238 - 19 Jun 2022
Cited by 2 | Viewed by 1858
Abstract
In this work, vibration prediction of space large-scale membranes from the energy point of view is investigated. Based on the Green kernel of vibrating membranes, a new analytical representation of energy response of infinite membranes is derived. Averaged energy is used as the [...] Read more.
In this work, vibration prediction of space large-scale membranes from the energy point of view is investigated. Based on the Green kernel of vibrating membranes, a new analytical representation of energy response of infinite membranes is derived. Averaged energy is used as the main variable so that the response fluctuation can be smoothed. Then membranes of various shapes can be taken into account by introducing the mean free path into the formulation to describe travel distances of energy waves. The energy response of finite membranes is obtained with the superposition of energy waves subsequently. Considering uncertainties usually becomes significant in large-scale structures, the formulation expressed with random variables is obtained for membranes with uncertain properties. The mathematical expectation and variance of energy response are derived subsequently. And the confidence interval of random response is obtained. Finally, numerical simulations are performed to validate the proposed formulations and characteristics of the random energy responses are analyzed by taking a space large-scale membrane structure as a model. The developed formulations make the analysis of membranes with uncertainties more convenient than Finite Element Method (FEM) since they are expressed in analytical forms. Compared with existing formulations of energy flow derived from deterministic travel distances of waves that only apply to regular shapes of structures, the proposed formulations are suitable for membranes of various shapes. This work provides an alternative analytical approach to vibration prediction for space large-scale membranes with uncertainties. And the approach is thought helpful for the vibration analysis of other two-dimensional structures. Full article
(This article belongs to the Special Issue Astrodynamics and Celestial Mechanics)
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