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.

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.

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.

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.

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.

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.

On the Azimuth Error of ESG Strapdown North-Seeking Instrument

Because the vector of angular momentum of ESG (electrostatically suspended gyroscope) maintains the fixed direction in inertial space, it may be regarded as a fixed star. The astronavigation aigorithm is used to estimate the azimuth angle and the gyro constant drift in the paper. The relative errors which affect the estimation accuracy of the azimuth angle are the analysed.

SINS/CNS/GPS integrated navigation algorithm based on UKF

A new nonlinear algorithm is proposed for strapdown inertial navigation system （SINS）/celestial navigation system （CNS）/global positioning system （GPS） integrated navigation systems. The algorithm employs a nonlinear system error model which can be modified by unscented Kalman filter （UKF） to give predictions of local filters. And these predictions can be fused by the federated Kalman filter. In the system error model, the rotation vector is introduced to denote vehicle＇s attitude and has less variables than the quaternion. Also, the UKF method is simplified to estimate the system error model, which can both lead to less calculation and reduce algorithm implement time. In the information fusion section, a modified federated Kalman filter is proposed to solve the singular covariance problem. Specifically, the new algorithm is applied to maneuvering vehicles, and simulation results show that this algorithm is more accurate than the linear integrated navigation algorithm.

UPF based autonomous navigation scheme for deep space probe

The autonomous "celestial navigation scheme" for deep space probe departing from the earth and the autonomous "optical navigation scheme" for encountering object celestial body are presented. Then, aiming at the conditions that large initial estimation errors and non-Gaussian distribution of state or measurement errors may exist in orbit determination process of the two phases, UPF (unscented particle filter) is introduced into the navigation schemes. By tackling nonlinear and non-Gaussian problems, UPF overcomes the accuracy influence brought by the traditional EKF (extended Kalman filter), UKF (unscented Kalman filter), and PF (particle filter) schemes in approximate treatment to nonlinear and non-Gaussian state model and measurement model. The numerical simulations demonstrate the feasibility and higher accuracy of the UPF navigation scheme.

A tightly coupled rotational SINS/CNS integrated navigation method for aircraft

Strapdown inertial navigation system(SINS)/celestial navigation system(CNS)integrated navigation is widely used to achieve long-time and high-precision autonomous navigation for aircraft.In general,SINS/CNS integrated navigation can be divided into two integrated modes:loosely coupled integrated navigation and tightly coupled integrated navigation.Because the loosely coupled SINS/CNS integrated system is only available in the condition of at least three stars,the latter one is becoming a research hotspot.One major challenge of SINS/CNS integrated navigation is obtaining a high-precision horizon reference.To solve this problem,an innovative tightly coupled rotational SINS/CNS integrated navigation method is proposed.In this method,the rotational SINS error equation in the navigation frame is used as the state model,and the starlight vector and star altitude are used as measurements.Semi-physical simulations are conducted to test the performance of this integrated method.Results show that this tightly coupled rotational SINS/CNS method has the best navigation accuracy compared with SINS,rotational SINS,and traditional tightly coupled SINS/CNS integrated navigation method.

Pulsar/CNS integrated navigation based on federated UKF

In order to improve the autonomous navigation capability of satellite,a pulsar/CNS（celestial navigation system） integrated navigation method based on federated unscented Kalman filter（UKF） is proposed.The celestial navigation is a mature and stable navigation method.However,its position determination performance is not satisfied due to the low accuracy of horizon sensor.Single pulsar navigation is a new navigation method,which can provide highly accurate range measurements.The major drawback of single pulsar navigation is that the system is completely unobservable.As two methods are complementary to each other,the federated UKF is used here for fusing the navigation data from single pulsar navigation and CNS.Compared to the traditional celestial navigation method and single pulsar navigation,the integrated navigation method can provide better navigation performance.The simulation results demonstrate the feasibility and effectiveness of the navigation method.

CHES: A Space-borne Astrometric Mission for the Detection of Habitable Planets of the Nearby Solar-type Stars

The Closeby Habitable Exoplanet Survey(CHES) mission is proposed to discover habitable-zone Earth-like planets of nearby solar-type stars(~10 pc away from our solar system) via microarcsecond relative astrometry.The major scientific objectives of CHES are:to search for Earth Twins or terrestrial planets in habitable zones orbiting100 FGK nearby stars;further to conduct a comprehensive survey and extensively characterize nearby planetary systems.The primary payload is a high-quality,low-distortion,high-stability telescope.The optical subsystem is a coaxial three-mirror anastigmat(TMA) with a 1.2 m-aperture,0°.44 × 0°.44 field of view and 500 nm-900 nm working wave band.The camera focal plane is composed of a mosaic of 81 scientific CMOS detectors each with4 k × 4 k pixels.The heterodyne laser interferometric calibration technology is employed to ensure microarcsecond level(1 μas) relative astrometry precision to meet the requirements for detection of Earth-like planets.The CHES satellite operates at the Sun-Earth L2 point and observes all the target stars for 5 yr.CHES will offer the first direct measurements of true masses and inclinations of Earth Twins and super-Earths orbiting our neighbor stars based on microarcsecond astrometry from space.This will definitely enhance our understanding of the formation of diverse nearby planetary systems and the emergence of other worlds for solar-type stars,and finally provide insights to the evolution of our own solar system.

A Filtering Approach Based on MMAE for a SINS/CNS Integrated Navigation System

This paper explores multiple model adaptive estimation(MMAE) method, and with it, proposes a novel filtering algorithm. The proposed algorithm is an improved Kalman filter— multiple model adaptive estimation unscented Kalman filter(MMAE-UKF) rather than conventional Kalman filter methods,like the extended Kalman filter(EKF) and the unscented Kalman filter(UKF). UKF is used as a subfilter to obtain the system state estimate in the MMAE method. Single model filter has poor adaptability with uncertain or unknown system parameters,which the improved filtering method can overcome. Meanwhile,this algorithm is used for integrated navigation system of strapdown inertial navigation system(SINS) and celestial navigation system(CNS) by a ballistic missile's motion. The simulation results indicate that the proposed filtering algorithm has better navigation precision, can achieve optimal estimation of system state, and can be more flexible at the cost of increased computational burden.

New autonomous celestial navigation method for lunar satellite

Celestial navigation system is an important autonomous navigation system widely used for deep space exploration missions, in which extended Kalman filter and the measurement of angle between celestial bodies are used to estimate the position and velocity of explorer. In a conventional cartesian coordinate, this navigation system can not be used to achieve accurate determination of position for linearization errors of nonlinear spacecraft motion equation. A new autonomous celestial navigation method has been proposed for lunar satellite using classical orbital parameters. The error of linearizafion is reduced because orbit parameters change much more slowly than the position and velocity used in the cartesian coordinate. Simulations were made with both the cartesiane system and a system based on classical orbital parameters using extended Kalman filter under the same conditions for comparison. The results of comparison demonstrated high precision position determination of lunar satellite using this new method.

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

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.

Experiment on diffuse reflection laser ranging to space debris and data analysis

Space debris poses a serious threat to human space activities and needs to be measured and cataloged. As a new technology for space target surveillance, the measurement accuracy of diffuse reflection laser ranging （DRLR） is much higher than that of microwave radar and optoelectronic measurement. Based on the laser ranging data of space debris from the DRLR system at Shanghai Astronomical Observatory acquired in March-April, 2013, the characteristics and precision of the laser ranging data are analyzed and their applications in orbit determination of space debris are discussed, which is implemented for the first time in China. The experiment indicates that the precision of laser ranging data can reach 39 cm-228 cm. When the data are sufficient enough （four arcs measured over three days）, the orbital accuracy of space debris can be up to 50 m.

Study of tide prediction method influenced by nonperiodic factors based on support vector machines

Harmonic analysis, the traditional tidal forecasting method, cannot take into account the impact of noncyclical factors, and is also based on the BP neural network tidal prediction model which is easily limited by the amount of data. According to the movement of celestial bodies, and considering the insufficient tidal characteristics of historical data which are impacted by the nonperiodic weather, a tidal prediction method is designed based on support vector machine （SVM） to carry out the simulation experiment by using tidal data from Xiamen Tide Gauge, Luchaogang Tide Gauge and Weifang Tide Gauge individually. And the results show that the model satisfactorily carries out the tide prediction which is influenced by noncyclical factors. At the same time, it also proves that the proposed prediction method, which when compared with harmonic analysis method and the BP neural network method, has faster modeling speed, higher prediction precision and stronger generalization ability.