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Quaternion methods and models of regular celestial mechanics and astrodynamics

Applied Mathematics and mechanics(English Edition) 2022年第1期43卷 21-80页

作者： Y.N.CHELNOKOV Institute of Precision mechanics and Control Russian Academy of SciencesSaratov410031Russia

This paper is a review,which focuses on our work,while including an analysis of many works of other researchers in the field of quaternionic *** regular quaternion models of celestial mechanics and astrodynamics in the Kustaanheimo-Stiefel(KS)variables and Euler(Rodrigues-Hamilton)parameters are *** models are derived by the quaternion methods of mechanics and are based on the differential equations of the perturbed spatial two-body problem and the perturbed spatial central motion of a point *** paper also covers some applications of these *** and Scheifele are known to have doubted that quaternions and quaternion matrices can be used efficiently to regularize the equations of celestial ***,the author of this paper and other researchers refuted this point of view and showed that the quaternion approach actually leads to efficient solutions for regularizing the equations of celestial mechanics and *** paper presents convenient geometric and kinematic interpretations of the KS transformation and the KS bilinear relation proposed by the present *** general(compared with the KS equations)quaternion regular equations of the perturbed spatial two-body problem in the KS variables are *** equations are derived with the assumption that the KS bilinear relation was not *** main stages of the quaternion theory of regularizing the vector differential equation of the perturbed central motion of a point particle are presented,together with regular equations in the KS variables and Euler parameters,derived by the aforementioned *** also present the derivation of regular quaternion equations of the perturbed spatial two-body problem in the Levi-Civita variables and the Euler parameters,developed by the ideal rectangular Hansen coordinates and the orientation quaternion of the ideal coordinate *** paper also gives new results using quaternionic methods in the pertur

关键词： celestial mechanics astrodynamics perturbed spatial two-body problem central motion regularization Levi-Civita and Kustaanheimo-Stiefel(KS)variables Euler parameter quaternion

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A Rendezvous Mission to the Second Earth Trojan Asteroid 2020 XL_5 with Low-Thrust Multi-Gravity Assist Techniques

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Research in Astronomy and Astrophysics 2024年第1期24卷 245-264页

作者： Shi-Hai Yang Bo Xu Xin Li School of Aeronautics and Astronautics Sun Yat-sen UniversityShenzhen 518107China

As the second of Earth's Trojan asteroids, 2020 XL_(5) is worthy of rendezvous and even sample return missions in many aspects. In this paper, a rendezvous mission to Earth's second Trojan asteroid 2020 XL_(5) is ***, due to its high inclination and large eccentricity, direct impulsive transfer requires large amounts of fuel consumption. To address this challenge, we explore the benefits of electric propulsion and multi-gravity assist techniques for interplanetary missions. These two techniques are integrated in this mission design. The design of a low-thrust gravity-assist(LTGA) trajectory in multi-body dynamics is thoroughly investigated,which is a complex process. A comprehensive framework including three steps is presented here for optimization of LTGA trajectories in multi-body dynamics. The rendezvous mission to 2020 XL_(5) is designed with this three-step approach. The most effective transfer sequence among the outcomes involves Earth–Venus–Earth–Venus-2020 XL_(5). Numerical results indicate that the combination of electric propulsion and multi-gravity assists can greatly reduce the fuel consumption, with fuel consumption of 9.03%, making it a highly favorable choice for this rendezvous mission.

关键词： minor planets asteroids:general celestial mechanics Planetary Systems

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Time Dilation Cosmology 2

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Journal of Modern Physics 2024年第4期15卷 448-461页

作者： Joseph H. (Cass) Forrington Managing Editor Journal of Cosmology California USA

This paper is a further elaboration of the author’s Time Dilation Cosmology (TDC) holographic model that ties gravitation and celestial mechanics and kinematics directly to time dilation, resolving all the major conundrums in astrophysics, and ties astrophysics directly to quantum physics. It begins with a brief summary of the TDC model and contains the new derivation for the time dilation version of the formula for summing relativistic velocities, Einstein’s gravitational constant and the time dilation versions for the Lorentz factor and the Euclidean norm of the 3d velocity vector, the two of which can then be used in the Four-velocity formula. It is demonstrated how orbital curvature is manifested as the resultant of two time dilation-manifested velocities. It also explains why an interferometer cannot distinguish free fall from zero gravity and further elaborates on the author’s previous explanations of how spiral galaxies are formed, and contains mathematical proof that Black Holes are actually Magnetospheric Eternally Collapsing Objects (MECOs) that are massless spacetime vortices.

关键词： Gravitation Time Time Dilation celestial mechanics ISM: Kinematics and Dynamics Cosmology: Theory Galaxies: Evolution

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The Investigation of the Dynamical Evolution of Extrasolar Three-planetary System GJ 3138

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Research in Astronomy and Astrophysics 2022年第1期22卷 68-84页

作者： Alexander Perminov Eduard Kuznetsov Ural Federal University 51 Lenin AvenueYekaterinburgRussia

This article is devoted to studying the dynamical evolution and orbital stability of compact extrasolar threeplanetary system GJ 3138. In this system, all semimajor axes are less than 0.7 au. The modeling of planetary motion is performed using the averaged semi-analytical motion theory of the second order in planetary masses,which the authors construct. Unknown and known with errors orbital elements vary in allowable limits to obtain a set of initial conditions. Each of these initial conditions is applied for the modeling of planetary motion. The assumption about the stability of observed planetary systems allows to eliminate the initial conditions leading to excessive growth of the orbital eccentricities and inclinations and to identify those under which these orbital elements conserve moderate values over the whole modeling interval. Thus, it becomes possible to limit the range of possible values of unknown orbital elements and determine their most probable values in terms of stability.

关键词： Planetary Systems planets and satellites:dynamical evolution and stability planetstar interactions celestial mechanics

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Tracklet-to-object Matching for Climbing Starlink Satellites through Recursive Orbit Determination and Prediction

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Research in Astronomy and Astrophysics 2022年第11期22卷 107-119页

作者： Bin Li Lei Liu Ji-Zhang Sang School of Geodesy and Geomatics Wuhan UniversityWuhan 430079China Collaborative Innovation Center for Geospatial Technology Wuhan 430079China

Concerns for the collision risk involving Starlink satellites have motivated the interest in obtaining their accurate orbit ***,accurate orbit determination(OD)and prediction(OP)of Starlink satellites confront two main challenges:mismatching or missed matching of sparse tracklets to maneuvering satellites,and unknown or unmodeled orbit *** to exactly associate a tracklet to the right satellite is the primary issue,since a maneuvering satellite does not follow the naturally evolving orbit during the maneuvering,while more tracklets are needed for developing an accurate orbit maneuver *** these two challenges are not well addressed,it may lead to catalog maintenance failure or even loss of *** paper proposes a method to correctly match tracklets to the climbing Starlink *** is based on the recursive OD and OP,in which the orbit maneuver is modeled and the thrust is estimated,such that the subsequent OP accuracy guarantees the correct match of tracklets shortly after the OD *** with climbing Starlink satellites demonstrate that the tracklets within three days of the last TLE(two-line element)are all correctly matched to the right *** the matched tracklets,the thrust accelerations of climbing Starlink satellites can be precisely estimated through an orbit control approach,and the position prediction accuracy over 48 hours is at the level of a few kilometers,providing accurate orbit knowledge for reliable collision warning involving Starlink satellites.

关键词： celestial mechanics methods:analytical miscellaneous

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Tuning Symplectic Integrators is Easy and Worthwhile

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Communications in Computational Physics 2022年第3期31卷 987-996页

作者： Robert I.McLachlan School of Fundamental Sciences Massey UniversityNew Zealand

Many applications in computational physics that use numerical integrators based on splitting and composition can benefit from the development of optimized al-gorithms and from choosing the best ordering of *** cost in programming and execution time is minimal,while the performance improvements can be *** this note we report the influence of term ordering for random systems and for two systems from celestial mechanics that describe particle paths near black holes,quantifying its significance for both optimized and unoptimized *** also present a method for the computation of solutions of integrable monomial Hamiltonians that minimizes roundoff error and allows the effective use of compensation summation.

关键词： Symplectic integrators celestial mechanics splitting methods

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The Q Values of the Galilean Satellites and their Tidal Contributions to the Deceleration of Jupiter's Rotation

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Chinese Journal of Astronomy and Astrophysics 2004年第5期4卷 499-506页

作者： HongZhang Cheng-ZhiZhang DepartmentofAstronomy NanjingUniversityNanjing210093

The relationship between the k2/Q of the Galilean satellites and the k2J/QJ of Jupiter is derived from energy and momentum considerations. Calculations suggest that the Galilean satellites can be divided into two classes according to their Q values: Io and Ganymede have values between 10 and 50, while Europa and Callisto have values ranging from 200 to 700. The tidal contributions of the Galilean satellites to Jupiter's rotation are estimated. The main deceleration of Jupiter, which is about 99.04% of the total, comes from Io.

关键词： astrometry celestial mechanics planet and satellites: individual: (Io,Europa, Ganymede, Callisto)

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Optimized transfer trajectories in the earth-moon system

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Chinese Physics B 2008年第1期17卷 350-355页

作者：谢文贤徐伟蔡力 School of Science Northwestern Polytechnical University College of Astronautics Northwestern Polytechnical University

Investigations of low energy transfer trajectories are important for both celestial mechanics and astronautics. Methodologies using the theories from dynamical systems are developed in recent years. This paper investigates the dynamics of the earth-moon system. Low energy transfer trajectories are solved numerically by employing a hybrid strategy： first, a genetic hide and seek method performs a search in large domain to confine the global minimum f（η）（objective function） region; then, a deterministic Nelder-Mead method is utilized to refine the minimum quickly. Some transfer trajectories of the spacecraft in the earth-moon system are successfully simulated which verify the desired efficiency and robustness of the method of this paper.

关键词： celestial mechanics dynamical astronomy orbit

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Analysis of the wide area differential correction for BeiDou global satellite navigation system

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Research in Astronomy and Astrophysics 2018年第11期18卷 17-28页

作者： Ran Li Yue-Ling Cao Xiao-Gong Hu Cheng-Pan Tang Shan-Shi Zhou Xin Meng Li Liu Ran-Ran Su Zhi-Qiao Chang Shanghai Astronomical Observatory Chinese Academy of SciencesShanghai 200030China University of Chinese Academy of Sciences Beijing 100049China Shanghai Key Laboratory of Space Navigation and Position Techniques Shanghai 200030China College of Surveying and Geo-Informatics Tongji UniversityShanghai 200092China Beijing Global Information Application and Development Center Beijing 100094China

The regional BeiDou Satellite System, or BDS2, broadcasts a differential correction as Equivalent Satellite Clock Correction to correct both orbit and satellite clock errors. For the global BDS, or BDS3, satellite orbit and clock corrections conforming with RTCA standards will be broadcast to authorized users. The hybrid constellation and regional monitoring network pose challenges for the high precision separation of orbit and satellite clock corrections. Three correction models of kinematic,dynamic and Two-way Satellite Time Frequency Transfer(TWSTFT)-based dynamic were studied to estimate the satellite orbit and clock corrections. The correction accuracy of the three models is compared and analyzed based on the BDS observation data. Results show that the accuracies(root mean square, RMS) of dual-frequency real-time positioning for the three models are about 1.76 m, 1.78 m and 2.08 m respectively, which are comparable with the performance of WAAS and EGNOS. With dynamic corrections, the precision of Precise Point Positioning(PPP) experiments may reach about 23 cm after convergence.

关键词： celestial mechanics methods: data analysis space vehicles

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Stability of the coplanar planetary four-body system

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Research in Astronomy and Astrophysics 2020年第9期20卷 228-240页

作者： Chao Liu Sheng-Ping Gong Jun-Feng Li School of Aerospace Engineering Tsinghua UniversityBeijing 100084China

We consider the coplanar planetary four-body problem,where three planets orbit a large star without the cross of their *** system is stable if there is no exchange or cross of *** from the Sundman inequality,the equation of the kinematical boundaries is *** discuss a reasonable situation,where two planets with known orbits are more massive than the third *** boundaries of possible motions are controlled by the parameter c^*** the actual value of c^2E is less than or equal to a critical value(c^2 E)cr,then the regions of possible motions are bounded and therefore the system is *** criteria obtained in special cases are applied to the Solar System and the currently known extrasolar planetary *** results are checked using N-body integrator.

关键词： methods:analytical methods:numerical celestial mechanics planets and satellites:dynamical evolution and stability stars:kinematics and dynamics galaxies:kinematics and dynamics

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