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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 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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A simulation experiment on the GM estimation for Comet 133P/Elst-Pizarro

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Research in Astronomy and Astrophysics 2021年第1期21卷 158-164页

作者： Wu-Tong Gao Jian-Guo Yan Wei-Tong Jin Xuan Yang Chen Yang Mao Ye Fei Li Jean-Pierre Barriot l State Key Laboratory of Information Engineering in Surveying Mapping and Remote SensingWuhan UniversityWuhan 430079China China Academy of Space Technology Beijing 100094China Geodesy Observatory of Tahiti University of French PolynesiaBP 657098702 FaaaTahitiFrench Polynesia

In China’s asteroid mission to be launched around 2025,(7968)133 P/Elst-Pizarro(hereafter 133 P)will be the second target,after a visit to asteroid(469219)Kamo’*** paper describes a simulation of precise orbit determination for the spacecraft around comet 133 P,as well as estimation of its gravitational parameter(GM)value and the solar radiation pressure coefficient Cr for the *** cometocentric distances of 200,150 and 100 km orbits are considered,as well as two tracking modes:exclusive two-way range-rate mode(Earth station to spacecraft)and combinations of two-way range-rate and local spacecraft onboard ranging to the *** to exclusive two-way range-rate,the introduction of local ranging observables improves the final GM uncertainties by up to one order of *** ephemeris error in the orbit of 133 P is also considered,and we show that,to obtain a reliable estimate of the GM for 133 P,this error cannot exceed a one km range.

关键词： celestial mechanics space vehicles comets:individual(133P/Elst-Pizarro) methods:statistical

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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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A survey of weak stability boundaries in the Sun-Mars system

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Research in Astronomy and Astrophysics 2015年第3期15卷 376-392页

作者： Jian Li Yi-Sui Sun School of Astronomy and Space Science & Key Laboratory of Modern Astronomy and Astrophysics in Ministry of Education Nanjing University

We investigate the weak stability boundary （WSB） for a new primary, Mars, in the framework of the planar circular restricted 3-body problem, and also in the pla- nar bicircular restricted 4-body problem by including a perturbation due to Jupiter. For the sake of a simple stability/instability criterion, our computations have been done us- ing the equations of motion in polar coordinates. It is found that the relative size of the weakly stable sets around Mars is much larger than that of the Earth-Moon and the Sun-Jupiter systems, as the mass ratio of the Sun-Mars system is significantly smaller. We propose that this difference could be scaled by the Hill radius. In an enlarged view of the domain close to Mars, the geometry of the WSB has been presented for various parameters and compared to previous works. Our results also show that Jupiter＇s grav- itational force would strongly affect the Martian stable regions and should be taken into account to design a ballistic capture trajectory.

关键词： celestial mechanics

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On some applications of invariant manifolds

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Research in Astronomy and Astrophysics 2011年第1期11卷 103-118页

作者： Xi-Yun Hou Lin Liu Yu-Hui Zhao Astronomy Department Nanjing University Nanjing 210093 China Institute of Space Environment and Astrodynamics Nanjing University Nanjing 210093 China

Taking transfer orbits of a collinear libration point probe, a lunar probe and an interplanetary probe as examples, some applications of stable and unstable invariant manifolds of the restricted three-body problem are discussed. Research shows that transfer energy is not necessarily conserved when invariant manifolds are used. For the cases in which the transfer energy is conserved, the cost is a much longer transfer time.

关键词： celestial mechanics

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