New celestial assisted INS initial alignment method for lunar explorer

In the future lunar exploration programs of China, soft landing, sampling and returning will be realized. For lunar explorers such as Rovers, Landers and Ascenders, the inertial navigation system （INS） will be used to obtain high-precision navigation information. INS propagates position, velocity and attitude by integration of sensed accelerations, so initial alignment is needed before INS can work properly. However, traditional ground-based initial alignment methods cannot work well on the lunar surface because of its low rotation rate （0.55°/h）. For solving this problem, a new autonomous INS initial alignment method assisted by celestial observations is proposed, which uses star observations to help INS estimate its attitude, gyroscopes drifts and accelerometer biases. Simulations show that this new method can not only speed up alignment, but also improve the alignment accuracy. Furthermore, the impact factors such as initial conditions, accuracy of INS sensors, and accuracy of star sensor on alignment accuracy are analyzed in details, which provide guidance for the engineering applications of this method. This method could be a promising and attractive solution for lunar explorer＇s initial alignment.

Micro-arcsecond Celestial Reference Frames:definition and realization——Impact of the recent IAU Resolutions

The adoption of the International Celestial Reference System （ICRS）, based on Very Long Baseline Interferometry （VLBI） observations of extragalactic radiosources by the International Astronomical Union （IAU） since 1998 January 1, opened a new era for astronomy. The ICRS and the corresponding frame, the International Celestial Reference Frame （ICRF）, replaced the Fundamental Catalog （FK5） based on positions and proper motions of bright stars, with the Hipparcos cat- alog being adopted as the primary realization of the ICRS in optical wavelengths. According to its definition, the ICRS is such that the barycentric directions of distant extragalactic objects show no global rotation with respect to these objects; this pro- vides a quasi-inertial reference for measuring the positions and angular motions of the celestial objects. Other resolutions on reference systems were passed by the IAU in 2000 and 2006 and endorsed by the International Union of Geodesy and Geophysics （IUGG） in 2003 and 2007, respectively. These especially concern the definition and re- alization of the astronomical reference systems in the framework of general relativity and transformations between them. First, the IAU 2000 resolutions refined the con- cepts and definition of the astronomical reference systems and parameters for Earth＇s rotation, and adopted the IAU 2000 precession-nutation. Then, the IAU 2006 resolutions adopted a new precession model that is consistent with dynamical theories; they also addressed definition, terminology or orientation issues relative to reference systems and time scales that needed to be specified after the adoption of the IAU 2000 resolutions. An additional IUGG 2007 resolution defined the International Terrestrial Reference System （ITRS） so that it strictly complies with the IAU recommendations. Finally, the IAU 2009 resolutions adopted a new system of astronomical constants and an improved realization of the ICRF. These fundamental changes have led to significant improvements in the fields of astrometry, celestial mechanics, geodynam- ics, geodesy, etc. Of special interest are the improvements in the model for variations in Earth＇s rotation, which, in turn, can provide better knowledge of the dynamics of the Earth＇s interior. These have also contributed to a significant improvement in the accuracy of the ephemerides of the solar system bodies as determined from modern measurements, with a large number of scientific applications. This paper recalls the main aspects of the recent IAU resolutions on reference systems as well as their con- sequences on the concepts, definitions, nomenclature and models that are suitable for the definition, realization and transformation of reference frames at a microarcsecond level.

Electromagnetic Field Created by Rotation of Celestial Bodies

The observed correlation of the angular momenta Lik and magnetic moments μlm of celestial bodies (the Sun, planets and stars) was discussed by many authors but without any explanation. In this paper, a possible explanation of this phenomenon is suggested. It is shown that the function satisfies Maxwell equations and can be considered as a function which determines the electro-magnetic properties of rotating heavy bodies. The Riklm is the Riemann tensor, which determines the gravitational field of the body, rg is the gravitational radius of the body, and η is the constant which has to be determined by observations. The field Φlm describes the observed correlation. It explains the stability of magnetic field of white dwarfs and neutron stars despite the ohmic dissipation. The function Φl0 describes the electric field created by rotating heavy bodies. The presented theory does not contradict any existed experiments and observations.

Quaternion methods and models of regular celestial mechanics and astrodynamics

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 regularization.The regular quaternion models of celestial mechanics and astrodynamics in the Kustaanheimo-Stiefel(KS)variables and Euler(Rodrigues-Hamilton)parameters are analyzed.These 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 particle.This paper also covers some applications of these models.Stiefel and Scheifele are known to have doubted that quaternions and quaternion matrices can be used efficiently to regularize the equations of celestial mechanics.However,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 astrodynamics.This paper presents convenient geometric and kinematic interpretations of the KS transformation and the KS bilinear relation proposed by the present author.More general(compared with the KS equations)quaternion regular equations of the perturbed spatial two-body problem in the KS variables are presented.These equations are derived with the assumption that the KS bilinear relation was not satisfied.The 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 theory.We 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 frame.This paper also gives new results using quaternionic methods in the perturbed spatial restricted three-body problem.

The present status and prospects in the research of orbital dynamics and control near small celestial bodies

Small celestial body exploration is of great significance to deep space activities. The dynamics and control of orbits around small celestial bodies is of top priority in the exploration research. It includes the modeling of dynamics environment and the orbital dynamics mechanism. This paper introduced state-ofthe-art researches, major challenges, and future trends in this field. Three topics are mainly discussed： the gravitational field modeling of irregular-shaped small celestial bodies, natural orbital dynamics and control, and controlled orbital dynamics. Finally, constructive suggestions are made for China’s future space exploration missions.

Research career of an astronomer who has studied celestial mechanics

Celestial mechanics has been a classical field of astronomy. Only a few astronomers were in this field and not so many papers on this subject had been published during the first half of the 20th century. However, as the beauty of classical dynamics and celestial mechanics attracted me very much, I decided to take celestial mechanics as my research subject and entered university, where a very famous professor of celestial mechanics was a member of the faculty. Then as artificial satellites were launched starting from October 1958, new topics were investigated in the field of celestial mechanics. Moreover, planetary rings, asteroids with moderate values of eccentricity, inclination and so on have become new fields of celestial mechanics. In fact I have tried to solve such problems in an analytical way. Finally, to understand what gravitation is I joined the TAMA300 gravitational wave detector group.

A New Celestial Mechanics Dynamics of Accelerated Systems

We present in this text the research carried out on the dynamic behavior of non-inertial systems, proposing new keys to better understand the mechanics of the universe. Applying the field theory to the dynamic magnitudes circumscribed to a body, our research has achieved a new conception of the coupling of these magnitudes, to better understand the behavior of solid rigid bodies, when subjected to multiple simultaneous, non-coaxial rotations. The results of the research are consistent with Einstein’s theories on rotation;however, we propose a different mechanics and complementary to classical mechanics, specifically for systems accelerated by rotations. These new concepts define the Theory of Dynamic Interactions (TDI), a new dynamic model for non-inertial systems with axial symmetry, which is based on the principles of conservation of measurable quantities: the notion of quantity, total mass and total energy. This theory deduces a general equation of motion for bodies endowed with angular momentum, when they are subjected to successive non-coaxial torques.

Giorgio Vasari’s Celestial Utopia of Whimsy and Joy:Constellations,Zodiac Signs,and Grotesques

This study elaborates on the decoration of the ceiling in the refectory of the former Monteoliveto monastery in Naples,today part of the church of Sant’Anna dei Lombardi.It consists of three parts:an explanation of the ceiling design with its geometrical configurations of circles,octagons,hexagons,ovals,and squares;an iconographical analysis solely focusing on the ceiling decoration,which consists of grotesques,constellations,and zodiac signs;and a discussion of some of the literary and visual sources employed in the decoration.The Florentine Mannerist painter Giorgio Vasari,aided by several assistants,renovated and painted the ceilings between 1544 and 1545.Don Giammateo d’Anversa,the Abbot General of the Monteolivetan Order in Naples,composed the iconographical program with the assistance of insightful suggestions from the Florentine Monteolivetan prior Don Miniato Pitti,who was Vasari’s patron and friend as well.This oversight inspired Vasari to paint a celestial utopia of hilarity and whimsicality on the Neapolitan ceiling,thus leavening the other imagery,which combined both religious and secular representations of moral virtues and divine laws.

Notes on the Motion of Celestial Bodies

A novel method for the computation of the motion of multi-body systems is proposed against the traditional one, based on the dynamic exchange of attraction forces or using complex field equations, that hardly face two-body problems. The Newton gravitational model is interpreted as the emission of neutrino/gravitons from celestial bodies that combine to yield a cumulative flux that interacts with single bodies through a momentum balance. The neutrino was first found by Fermi to justify the energy conservation in β decay and, using his model;we found that the emission of neutrino from matter is almost constant independently from the nuclides involved. This flux can be correlated to Gauss constant G, allowing the rebuilding of Newton law on the basis of nuclear data, the neutrino weight and the speed of light. Similarly to nature, we can therefore separate in the calculations the neutrino flux, that represents the gravitational field, is dependent on masses and is not bound to the number of bodies involved, from the motion of each body that, given the field, is independent of the mass of bodies themselves. The conflict between exchanges of forces is avoided, the mathematics is simplified, the computational time is reduced to seconds and the stability of result is guaranteed. The example of computation of the solar system including the Sun and eight planets over a period of one to one hundred years is reported, together with the evolution of the shape of the orbits.

Proposal of New Criteria for Celestial Mechanics

Based on a new interpretation on the behavior of rigid bodies exposed to simultaneous non-coaxial rotations, we have developed a hypothesis: the Theory of Dynamics Interactions, which can be applied to understand celestial mechanics. We have analyzed the velocity and acceleration fields generated in a rigid body with intrinsic angular momentum, when exposed to successive torques, to assess new criteria for this speeds coupling. In this context, reactions and inertial fields take place, which cannot be justified by means of classical mechanics. We believe that the results obtained after the analysis of dynamics fields systems accelerated by rotation will allow us to conceive a new perspective in celestial dynamics, astrometry, stellar dynamics and galactic astronomy, unknown up to date. After carrying out ample research, we have come to the conclusion that there still exists an unstructured scientific area under the present general assumptions and, more specifically, in the area of dynamic systems submitted to rotational accelerations. The aim of this paper is to present information of the surprising results obtained, and to attract the interest towards the investigation of this new area of knowledge in rotational non-inertial dynamics, and its multiple and remarkable scientific applications.

A new method of single celestial-body sun positioning based on theory of mechanisms

Considering defects of current single celestial-body positioning methods such as discon- tinuity and long period, a new sun positioning algorithm is herein put forward. Instead of tradi- tional astronomical spherical trigonometry and celestial coordinate system, the proposed new positioning algorithm is built by theory of mechanisms. Based on previously derived solar vector equations （from a C1R2p2 series mechanism）, a further global positioning method is developed by inverse kinematics. The longitude and latitude coordinates expressed by Greenwich mean time （GMT） and solar vector in local coordinate system are formulated. Meanwhile, elimination method of multiple solutions, errors of longitude and latitude calculation are given. In addition, this algo- rithm has been integrated successfully into a mobile phone application to visualize sun positioning process. Results of theoretical verification and smart phone＇s test demonstrate the validity of pre- sented coordinate＇s expressions. Precision is shown as equivalent to current works and is acceptable to civil aviation requirement. This new method solves long-period problem in sun sight running fix- ing and improves applicability of sun positioning. Its methodology can inspire development of new sun positioning device. It would be more applicable to be combined with inertial navigation systems for overcoming discontinuity of celestial navigation systems and accumulative errors of inertial nav- igation systems.

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

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 proposed.However, 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.

Time Dilation Cosmology 2

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.

PyMsOfa:A Python Package for the Standards of Fundamental Astronomy(SOFA)Service

The Standards of Fundamental Astronomy(SOFA)is a service provided by the International Astronomical Union that offers algorithms and software for astronomical calculations,which was released in two versions for FORTRAN77 and ANSI C,respectively.In this work,we implement the Python package PyMsOfa for SOFA service by three ways:(1)a Python wrapper package based on a foreign function library for Python(ctypes),(2)a Python wrapper package with the foreign function interface for Python calling C code(cffi)and(3)a Python package directly written in pure Python codes from SOFA subroutines.The package PyMsOfa has fully implemented 247 functions of the original SOFA routines released on 2023 October 11.In addition,PyMsOfa is also extensively examined,which is exactly consistent with those test examples given by the original SOFA.This Python package can be suitable to not only the astrometric detection of habitable planets from the Closeby Habitable Exoplanet Survey mission,but also for the frontier themes of black holes and dark matter related to astrometric calculations and other fields.The source codes are available via http://pypi.org/project/PyMsOfa/and https://github.com/CHES2023/PyMsOfa.

Effect of Orbital Characteristic of Inclined Third-body on Motion of Secondary-body for a Hierarchical Triple Systems

The influence of a third-body's orbital elements on the second-body's motion in a hierarchical triple system is a crucial problem in astrophysics.Most prolonged evaluation studies have focused on a distant zero-inclined thirdbody.This study presents a new perspective on second-body motion equations that addresses a perturbing-body in an elliptic orbit derived with consideration of the axial-tilt(obliquity)of the primary.The proposed model is compared by the dual-averaged method and the N-body problem algorithm.After validation,a generalized threebody model is derived to investigate the effects of the third-body's orbital elements on secondary-body motion behavior.The proposed model considers short-time oscillations that affect secular evaluation and applies to exoplanets with all the primary and third body eccentricities,inclinations,and mass ratios.It is shown that the obliquity of the primary(or third-body's inclination)must be considered for precise long-term assessment,even in highly-hierarchical systems.

Analytical Study of the Co-orbital Motion in the Circular Restricted Three-body Problem

In the restricted three-body problem(RTBP), if a small body and a planet stably orbit around a central star with almost exactly the same semimajor axis, and thus almost the same mean motion, this phenomenon is called the coorbital motion, or equivalently, the 1:1 mean motion resonance. The classical expansion of the disturbing function is divergent when the semimajor axis ratio of the small body to the planet is close to unity. Thus, most of the previous studies on the co-orbital dynamics were carried out through numerical integrations or semi-analytical approaches. In this work, we construct an analytical averaged model for the co-orbital motion in the framework of the circular RTBP. This model is valid in the entire coorbital region except in the vicinity of the collision singularity. The results of the analytical averaged model are in good agreement with the numerical averaged model even for moderate eccentricities and inclinations. The analytical model can reproduce the tadpole, horseshoe and quasi-satellite orbits common in the planar problem. Furthermore, the asymmetry of 1:1 resonance and the compound orbits(Icarus 137:293–314) in the general spatial problem can also be obtained from the analytical model.

Studying the Equilibrium Points of the Modified Circular Restricted Three-body Problem: The Case of Sun–Haumea System

We intend to study a modified version of the planar Circular Restricted Three-Body Problem(CRTBP) by incorporating several perturbing parameters. We consider the bigger primary as an oblate spheroid and emitting radiation while the small primary has an elongated body. We also consider the perturbation from a disk-like structure encompassing this three-body system. First, we develop a mathematical model of this modified CRTBP.We have found there exist five equilibrium points in this modified CRTBP model, where three of them are collinear and the other two are non-collinear. Second, we apply our modified CRTBP model to the Sun–Haumea system by considering several values of each perturbing parameter. Through our numerical investigation, we have discovered that the incorporation of perturbing parameters has resulted in a shift in the equilibrium point positions of the Sun–Haumea system compared to their positions in the classical CRTBP. The stability of equilibrium points is investigated. We have shown that the collinear equilibrium points are unstable and the stability of non-collinear equilibrium points depends on the mass parameter μ of the system. Unlike the classical case, non-collinear equilibrium points have both a maximum and minimum limit of μ for achieving stability. We remark that the stability range of μ in non-collinear equilibrium points depends on the perturbing parameters. In the context of the Sun–Haumea system, we have found that the non-collinear equilibrium points are stable.

A Data-driven Method for Realistic Covariance Prediction of Space Object with Sparse Tracking Data

Covariance of the orbital state of a resident space object(RSO)is a necessary requirement for various space situational awareness tasks,like the space collision warning.It describes an accuracy envelope of the RSO's location.However,in current space surveillance,the tracking data of an individual RSO is often found insufficiently accurate and sparsely distributed,making the predicted covariance(PC)derived from the tracking data and classical orbit dynamic system usually unrealistic in describing the error characterization of orbit predictions.Given the fact that the tracking data of an RSO from a single station or a fixed network share a similar temporal and spatial distribution,the evolution of PC could share a hidden relationship with that data distribution.This study proposes a novel method to generate accurate PC by combining the classical covariance propagation method and the data-driven approach.Two popular machine learning algorithms are applied to model the inconsistency between the orbit prediction error and the PC from historical observations,and then this inconsistency model is used for the future PC.Experimental results with the Swarm constellation satellites demonstrate that the trained Random Forest models can capture more than 95%of the underlying inconsistency in a tracking scenario of sparse observations.More importantly,the trained models show great generalization capability in correcting the PC of future epochs and other RSOs with similar orbit characteristics and observation conditions.Besides,a deep analysis of generalization performance is carried out to describe the temporal and spatial similarities of two data sets,in which the Jaccard similarity is used.It demonstrates that the higher the Jaccard similarity is,the better the generalization performance will be,which may be used as a guide to whether to apply the trained models of a satellite to other satellites.Further,the generalization performance is also evaluated by the classical Cramer von Misses test,which also shows that trained models have encouraging generalization performance.

Time Dilation Cosmology

This model ties gravitation and celestial mechanics and kinematics directly to time dilation. It is a new theory of cosmology and the evolution of galaxies. Space and time are not two separate things, but two aspects of a single thing, “spacetime”. Whatever affects space, affects time, and vice-versa. If time speeds up, space must contract to maintain the speed of light, c, and when space thickens into a mass, it is harder to evolve forward, and time appears to slow. If spatial events are spinning as time passes, then the forward direction of time is spinning. This is Einstein’s curvature in the forward direction of time. Herein, the basis is outlined for time dilation cosmology in a spacetime/quantum continuum, including the time dilation-based derivation of the mass of the Cosmic Microwave Background Radiation (CMBR), and time dilation formulas are derived for stellar system orbital, and galactic rotation, velocities, the force in time in Newtons, the Hamiltonian, the Hubble shift, the empirical gravitational constant, G, and other formulas, showing their direct relationship to the difference in the rate of time between the far distant observer’s invariant 1 s/s rate of time and the slower rate of time at the coordinate point, proving the universe is not composed of separate bodies moving through space, but is an evolving 3-dimensional holographic continuum containing varying densities evolving forward in the forward direction of time, the 4th dimension, at apparently different rates of time, the velocities merely being compensation for those slower rates of time in a continuum evolving forward overall at c, which is why light propagates at c, even from a moving source. As per General Relativity, if there is no rate of time difference between coordinate points, there is no gravitational attraction between those points, and no gravitationally induced velocity. This model resolves all the major conundrums in astrophysics, eliminating Dark Energy and Dark Matter, and ties astrophysics directly to quantum physics.

Modification of the Lagrange-Jacobi Equation and Its Application

The Lagrange-Jacobi equation is one of the significant tools for the qualitative analysis of the n-body problem. In this paper, we present the modified Lagrange-Jacobi equation by introducing a new formal parameter of n-body problem and propose its application to the dynamical study of clusters of galaxies which are large-scale structures of Universe. We put forward and study a new dynamical problem which is related to the stage of relaxation of observed stationary clusters of galaxies which are considered as a non-equilibrium systems of point masses. We also received the analytical form of the potential energy of such galaxy clusters. One of the applications of this analytical form is the analytical relation between the time of setting up the virial equilibrium in relaxing clusters of galaxies and the cosmological epoch T.