Orbit Determination Using Satellite-to-Satellite Tracking Data

Satellite-to-Satellite tricking (SST) data can be used to determine the orbits of spacecraft in two ways. One is combined orbit determination, which combines SST data with ground-based tracking data and exploits the enhanced tracking geometry. The other is the autonomous orbit determination, which uses only SST. The latter only fits some particular circumstances since it suffers the rank defect problem in other circumstances. The proof of this statement is presented. The nature of the problem is also investigated in order to find an effective solution. Several. methods of solution are discussed. The feasibility of the methods is demonstrated by their application to a simulation.

Solution set on the natural satellite formation orbits under first-order earth's non-spherical perturbation

Using the reference orbital element approach, the precise governing equations for the relative motion of formation flight are formulated. A number of ideal formations with respect to an elliptic orbit can be designed based on the relative motion analysis from the equations. The features of the oscillating reference orbital elements are studied by using the perturbation theory. The changes in the relative orbit under perturbation are divided into three categories, termed scale enlargement, drift and distortion respectively. By properly choosing the initial mean orbital elements for the leader and follower satellites, the deviations from originally regular formation orbit caused by the perturbation can be suppressed. Thereby the natural formation is set up. It behaves either like non-disturbed or need little control to maintain. The presented reference orbital element approach highlights the kinematics properties of the relative motion and is convenient to incorporate the results of perturbation analysis on orbital elements. This method of formation design has advantages over other methods in seeking natural formation and in initializing formation.

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 Study on the Relationship between the Orbital Lifetime and Inclination of Low Lunar Satellites

A detailed theoretical analysis on the orbital lifetime and orbital inclination of a Low Moon-Orbiting satellite （LMOs） and the ‘stable areas＇ of long orbital lifetime are given. Numerical simulations under the real force model were carried out, which not only validate the theoretical analysis and also give some valuable results for the orbit design of the LMOs.

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.

Long-term effects of main-body's obliquity on satellite formation perturbed by third-body gravity in elliptical and inclined orbit

A new non-simplified model of formation flying is derived in the presence of an oblate main- body and third-body perturbation. In the proposed model, considering the perturbation of the third- body in an inclined orbit, the effect of obliquity （axial tilt） of the main-body is becoming important and has been propounded in the absolute motion of a reference satellite and the relative motion of a follower satellite. From a new point of view, J2 perturbed relative motion equations and considering a disturbing body in an elliptic inclined three dimensional orbit, are derived using Lagrangian mechanics based on accurate introduced perturbed reference satellite motion. To validate the accuracy of the model presented in this study, an auxiliary model was constructed as the Main-body Center based Relative Motion （MCRM） model. Finally, the importance of the main-body＇s obliquity is demonstrated by several examples related to the Earth-Moon system in relative motion and lunar satellite formation keeping. The main-body＇s obliquity has a remarkable effect on formation keeping in the examined in-track and projected circular orbit （PCO） formations.

Everything Is a Circle: A New Universal Orbital Model

Based on measured astronomical position data of heavenly objects in the Solar System and other planetary systems, all bodies in space seem to move in some kind of elliptical motion with respect to each other. According to Kepler’s 1st Law, “orbit of a planet with respect to the Sun is an ellipse, with the Sun at one of the two foci.” Orbit of the Moon with respect to Earth is also distinctly elliptical, but this ellipse has a varying eccentricity as the Moon comes closer to and goes farther away from the Earth in a harmonic style along a full cycle of this ellipse. In this paper, our research results are summarized, where it is first mathematically shown that the “distance between points around any two different circles in three-dimensional space” is equivalent to the “distance of points around a vector ellipse to another fixed or moving point, as in two-dimensional space”. What is done is equivalent to showing that bodies moving on two different circular orbits in space vector-wise behave as if moving on an elliptical path with respect to each other, and virtually seeing each other as positioned at an instantaneously stationary point in space on their relative ecliptic plane, whether they are moving with the same angular velocity, or different but fixed angular velocities, or even with different and changing angular velocities with respect to their own centers of revolution. This mathematical revelation has the potential to lead to far reaching discoveries in physics, enabling more insight into forces of nature, with a formulation of a new fundamental model regarding the motions of bodies in the Universe, including the Sun, Planets, and Satellites in the Solar System and elsewhere, as well as at particle and subatomic level. Based on the demonstrated mathematical analysis, as they exhibit almost fixed elliptic orbits relative to one another over time, the assertion is made that the Sun, the Earth, and the Moon must each be revolving in their individual circular orbits of revolution in space. With this expectation, individual orbital parameters of the Sun, the Earth, and the Moon are calculated based on observed Earth to Sun and Earth to Moon distance data, also using analytical methods developed as part of this research to an approximation. This calculation and analysis process have revealed additional results aligned with observation, and this also supports our assertion that the Sun, the Earth, and the Moon must actually be revolving in individual circular orbits.

Periodic Orbits in Rotating Second Degree and Order Gravity Fields

Periodic orbits in an arbitrary 2nd degree and order uniformly rotating gravity field are studied. We investigate the four equilibrium points in this gravity field. We see that close relation exists between the stability of these equilibria and the existence and stability of their nearby periodic orbits. We check the periodic orbits with non-zero periods. In our searching procedure for these periodic orbits, we remove the two unity eigenvalues from the state transition matrix to find a robust, non-singular linear map to solve for the periodic orbits. The algorithm converges well, especially for stable periodic orbits. Using the searching procedure, which is relatively automatic, we find five basic families of periodic orbits in the rotating second degree and order gravity field for planar motion, and discuss their existence and stability at different central body rotation rates.

The principle of a navigation constellation composed of SIGSO communication satellites

The Chinese Area Positioning System （CAPS）, a navigation system based on geostafionary orbit （GEO） communication satellites, was developed in 2002 by astronomers at Chinese Academy of Sciences. Extensive positioning experiments of CAPS have been performed since 2005. On the basis of CAPS, this paper studies the principle of a navigation constellation composed of slightly inclined geostationary orbit （SIGSO） communication satellites. SIGSO satellites are derived from GEO satellites which are near the end of their operational life by inclined orbit operation. Considering the abundant frequency resources of SIGSO satellites, multi-frequency observations could be conducted to enhance the precision of pseudorange measurements and ameliorate the positioning performance. A constellation composed of two GEO satellites and four SIGSO satellites with an inclination of 5° can provide service to most of the territory of China with a maximum position dilution of precision （PDOP） over 24 h of less than 42. With synthetic utilization of the truncated precise code and a physical augmentation factor in four frequencies, the navigation system with this constellation is expected to obtain comparable positioning performance to that of the coarse acquisition code of the Global Positioning System （GPS）. When the new method of code-carrier phase combinations is adopted, the system has the potential to possess commensurate accuracy with the precise code in GPS. Additionally, the copious frequency resources can also be used to develop new anti-interference techniques and integrate navigation and communication.

Orbital evolution of a planet with tidal dissipation in a restricted three-body system

The angle between planetary spin and the normal direction of an orbital plane is supposed to reveal a range of information about the associated planetary formation and evolution. Since the orbit’s eccentricity and inclination oscillate periodically in a hierarchical triple body and tidal friction makes the spin parallel to the normal orientation of the orbital plane with a short timescale in an isolated binary system, we focus on the comprehensive effect of third body perturbation and tidal mechanism on the angle. Firstly, we extend the Hut tidal model(1981) to the general spatial case, adopting the equilibrium tide and weak friction hypothesis with constant delay time, which is suitable for arbitrary eccentricity and any angle ? between the planetary spin and normal orientation of the orbital plane. Furthermore, under the constraint of angular momentum conservation, the equations of orbital and ratational motion are given. Secondly, considering the coupled effects of tidal dissipation and third body perturbation, and adopting the quadrupole approximation as the third body perturbation effect, a comprehensive model is established by this work. Finally, we find that the ultimate evolution depends on the timescales of the third body and tidal friction. When the timescale of the third body is much shorter than that of tidal friction, the angle ? will oscillate for a long time,even over the whole evolution;when the timescale of the third body is observably larger than that of the tidal friction, the system may enter stable states, with the angle ? decaying to zero ultimately, and some cases may have a stable inclination beyond the critical value of Lidov-Kozai resonance. In addition, these dynamical evolutions depend on the initial values of the orbital elements and may aid in understanding the characteristics of the orbits of exoplanets.

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

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.

Nereid's orbit based on new precise observations

A new orbit of Triton was provided by our previous work, benefitted by new Gaia Data, both in a new precise reduction of charge-coupled device observations and in the planetary ephemeris INPOP19 a.In this paper, we provide a new ephemeris for another main Neptunian satellite, Nereid. The orbit is fitted for the newest observations, including 2 075 ground-based observations during the period 1949-2018 and 83 space observations acquired by the Voyager 2 spacecraft in 1989. The dynamical model used here is consistent with that of our previous work. For the ground-based absolute observations of Nereid, the rootmean-square deviations are 0.201′′in right ascension and 0.189′′in declination. Finally, a comparison with the HORIZONS ephemeris is made and discussed.

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.

Review Article: Resonant Families of Periodic Orbits in the Restricted Three-body Problem

The restricted three-body problem(RTBP) is a fundamental model in celestial mechanics.Periodic orbits in the synodic frame play a very important role in understanding the dynamics of the RTBP model.Most of these periodic orbits,when interpreted in the sidereal frame,are actually resonant periodic orbits.As a result,numerical computation of the periodic orbits is also one approach for researchers to understand the orbital resonances of the three-body problem.Extensive studies have been carried out on this topic,concerning either the circular case or the elliptic case of this model.In this paper,we make a brief review of the history and current status of the studies on resonant periodic orbits in the RTBP model.Starting from the unperturbed two-body problem,we organize the review paper by the two cases of this model—the circular restricted three-body problem and the elliptic restricted three-body problem.

Solar Radiation Pressure and Gravitational Waves Effects on Sun-Synchronous Orbits

For certain values of semi-major axis and eccentricity, orbit plane precession caused by Earth oblate is synchronous with the mean orbital motion of the apparent Sun (a sun-synchronism). Many forces cause slow changes in the inclination and ascending node of sun-synchronous orbits. In this work, we investigate the analytical perturbations due to the direct solar radiation pressure and gravitational waves effects. A full analytical solution is obtained using technique of canonical Lie-transformation up to the order three in (the oblateness of the Earth). The solar radiation pressure and gravitational waves perturbations cause second order effects on all the elements of the elliptic orbit (the eccentricity, inclination, ascending node, argument of perigee, and semi-major axis) consequently these perturbations will cause disturbance in the sun-synchronism. Also we found that the perturbation or the behavior of gravitational waves almost the same as the perturbation or the behavior of solar radiation pressure and their coupling will incorporate the sun-synchronism through the secular rate of the ascending node precession.

Scaling and Orbits for an Isotropic Metric

Conventional interpretation of the Einstein Equation has inconsistencies and contradictions, such as gravitational fields without energy, objects crossing event-horizons, objects exceeding the speed of light, and inconsistency in scaling the speed of light and its factors. An isotropic metric resolves such problems by attributing energy to the gravitational field, in the Einstein Equation. This paper discusses symmetries of an isotropic metric, including scaling of physical quantities, the Lorentz transformation, covariant derivatives, and stress-energy tensors, and transitivity of this scaling between inertial reference frames. Force, charge, Planck’s constant, and the fine structure constant remain invariant under isotropic gravitational scaling. Gravitational scattering, orbital period, and precession distinguish between isotropic and Schwarzschild metrics. An isotropic metric accommodates quantum mechanics and improves models of black-holes.

基于功能链的北斗三号卫星控制技术

为适应卫星研制技术和规模空前发展,在卫星高可靠的同时做到低成本,将传统的分系统设计方法按特点和学科进行了重新梳理,提出国内首创的功能链设计理念和方法,并成功应用于北斗三号首发试验星、组网星及备份星中,实现了北斗三号卫星的快速批产组网.阐述基于功能链的设计理念,重点介绍基于功能链的北斗三号卫星姿态及轨道等控制技术,在轨运行结果表明,卫星实现了连续可靠的工作,全面适应ka及激光星间链路的高控制精度要求以及导航卫星对高连续性的要求.

HY2D星载北斗数据质量评估及事后精密定轨精度分析

基于海洋二号D卫星(HY2D)2021年7月7-16日(年积日Day Of Year(DOY)188-197)的星载北斗观测数据,从测量数据有效性、可见卫星数量、位置精度因子及伪距多路径效应等角度分析了数据质量,并利用其进行事后精密定轨,从相位残差、重叠弧段、轨道互比和激光检核4种手段评估了定轨结果精度.结论如下:(1)HY2D卫星接收北斗三号卫星数在4颗及以上占比约为86.66%;B1C频点多路径误差RMS(Root mean square)约为0.37 m,B2a频点约为0.18 m.(2)载波相位拟合残差RMS在6-8 mm之间;相邻轨道重叠4 h的位置差异小于2 cm,与法国CNES(Centre National d‘Etudes Spatiales)DORIS(Doppler Orbitography and Radio-positioning Integrated by Satellite)轨道比较径向RMS优于1.9 cm.(3)用激光测距数据检核轨道精度,其星距残差的RMS约为3.24 cm.结果表明,国产星载双频北斗接收机可以完成海洋测高卫星的精密定轨指标.

卫星星座的结构演化

主要研究星座几何结构的演化问题,分析了在地球扁率摄动和卫星的入轨偏差影响下轨道的演化过程,以卫星的相位和升交点赤经为参数描述了星座结构演化的一般规律,又以星下点轨迹变化和星下点的相互位置关系的变化为参数描述了区域星座结构演化的地域特性。分析表明,地球扁率摄动将导致星座结构的整体漂移,而卫星的入轨偏差则会导致星座几何结构的紊乱,特别是轨道半长轴的偏差,将是影响星座几何结构稳定性的决定因素。

LAGEOS卫星精密定轨及残差分析

介绍LAGEOS卫星用卫星激光测距(SLR)资料精密定轨和在精密定轨基础上的残差分析处理。SLR资料的分析处理方法、采用的力学模型和解参数的多少根据目标的不同而不同。对不同的方案进行了详细分析、比较。其关键是对LAGEOS卫星进行精密定轨。得出了目前上海天文台在SLR资料的分析处理中已采用的解算模式。作为例证,该解算模式分析处理了1998年12月31日至1999年6月29日LAGEOS卫星的SLR资料,得到每3天一个弧段的精密轨道。结果显示每3天一个弧段的定轨残差rms都小于2厘米。上海天文台从1999年10月1日开始了全球LAGEOS-1和LAGEOS-2资料的快速分析服务,结果可从APSG的网址:http://center.shao.ac.cn/APSG/result获得。