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.

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.

基于遗传算法的极短弧定轨(续)

采用遗传算法解决极短弧定轨问题时,由于遗传算法不同于经典方法的计算过程,野值剔除方法不再适用.在遗传算法中通过在适值函数中采用不同损失函数实现了稳健估计,解决了极短弧定轨中的野值处理问题.在遗传算法中不同损失函数的引入较经典方法大大简化.通过对多种损失函数的计算比较,表明采用最小中值二乘(LMS,Least Median Square)和截尾最小二乘(LTS,Least Trimmed Square)估计可大幅度提高极短弧定轨的稳健性,具有极高的崩溃点.

初轨计算精度的bootstrap估计

从非参数统计角度,在仅有观测资料而没有其它信息的情况下,分别给出了初轨计算的精度和置信区间的估计方法.该方法基于bootstrap方法,仅依赖于观测资料,不需要精密定轨结果作为参考,也无需假设观测资料误差呈正态分布,并且对各种初轨计算方法均适用.数值计算结果表明该方法应用简便,可作为初轨的评估和后续应用的重要参考.

一种初轨计算的稳健方法

光学测角资料的初轨计算在空间目标搜索发现中具有重要作用,当观测资料存在野值时,基于最小二乘的经典初轨计算方法不够稳健.采用最小一乘方法建立了一种初轨计算的稳健方法,方法将初轨计算问题转换为线性规划问题求解,并通过bootstrap方法给出估计精度.数值计算结果表明方法稳健有效,并具有较高的崩溃点.

Orbital correlation of space objects based on orbital elements

Orbital correlation of space objects is one of the most important elements in space object iden- tification. Using the orbital elements, we provide correlation criteria to determine if objects are coplanar, co-orbital or the same. We analyze the prediction error of the correlation parameters for different orbital types and propose an orbital correlation method for space objects. The method is validated using two line elements and multisatellite launching data. The experimental results show that the proposed method is ef- fective, especially for space objects in near-circular orbits.

基于核密度估计的极短弧定轨的分布估计方法

采用分布估计算法,通过建立解空间的概率模型,实现了一种测角资料的极短弧初轨计算方法.在概率模型建立中,采用非参数核密度估计,无需对分布进行任何假设.不同于遗传算法、粒子群算法等进化算法,方法不仅考虑解的适值优劣,同时考虑了解的整体特性.根据基于实测数据的数值计算表明:方法在没有任何约束条件情况下对于一般观测精度仍可获得有效解.

多星混合资料的定轨

在空间目标光学观测资料定轨中常常会遇到多个目标的观测被标记为同一个目标的情况,由于包含了多个目标的数据,定轨过程无法收敛或者完全错误.从极大似然估计角度,采用EM(Expectation Maximum)方法提出一种将轨道改进和识别过程相互融合的处理方法,并在具体实现过程中给出一种稳健估计方法.数值模拟表明方法简便、有效、可行.采用站间差历元差的手段,对当前电离层变化值进行求解与预测,可以将电离层延时误差的变化控制在一定范围,满足频率传递的要求.

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.

Centaurs颜色及其与轨道参数的统计分析

为了探究太阳系小天体Centaurs色指数和轨道参数的统计特征及其物理学意义,根据现今已知的39个Centaurs的色指数和轨道参数值,利用统计学方法,分析了Centaurs各色指数之间、色指数与轨道参数之间的统计特征.结果显示B-V与V-R、V-R与R-I、B-V与R-I、B-R与R-I之间均呈现强相关性;Centaurs表现出明显的红蓝双色性,分界点在B-R=1.4左右;Centaurs各色指数值均呈现正态分布特征;除B-V与轨道倾角i、V-R与轨道半长轴a存在弱关联性外,其它Centaurs色指数与轨道参数之间均未表现出相关性.

Feasible region and stability analysis for hovering around elongated asteroids with low thrust

This paper investigates properties of low-thrust hovering, including the feasible region and stability, in terms of the dynamical parameters for elongated asteroids. An approximate rotating mass dipole model, by which the description of the rotational gravitational field is reduced to two independent parameters, is employed to construct normalized dynamical equations. The boundaries of the feasible region are determined by contours representing the magnitude of the active control. The effects of a rotating gravitational field and maximal magnitude of the low thrust on the feasible hovering regions are analyzed with numerical results. The stability conditions are derived according to the forms of the eigenvalues of the linearized equation near the hovering position. The stable regions are then determined by a grid search and the effects of the relevant parameters are analyzed in a parametric way. The results show that a close hovering can be easier to realize near the middle of the asteroid than near the two ends in the sense of both required control magnitude and stability.

Capturing near earth objects

Recently, Near Earth Objects （NEOs） have been attracting great attention, and thousands of NEOs have been found to date. This paper examines the NEOs＇ orbital dynamics using the framework of an accurate solar system model and a Sun- Earth-NEO three-body system when the NEOs are close to Earth to search for NEOs with low-energy orbits. It is possible for such an NEO to be temporarily captured by Earth; its orbit would thereby be changed and it would become an Earth-orbiting object after a small increase in its velocity. From the point of view of the Sun-Earth- NEO restricted three-body system, it is possible for an NEO whose Jacobian constant is slightly lower than C1 but higher than C3 to be temporarily captured by Earth. When such an NEO approaches Earth, it is possible to change its orbital energy to nearly the zero velocity surface of the three-body system at point L1 and make the NEO become a small satellite of the Earth. Some such NEOs were found; the best example only required a 410 m s^-1 increase in velocity.

Application of two special orbits in the orbit determination of lunar satellites

Using inter-satellite range data, the combined autonomous orbit determina- tion problem of a lunar satellite and a probe on some special orbits is studied in this paper. The problem is firstly studied in the circular restricted three-body problem, and then generalized to the real force model of the Earth-Moon system. Two kinds of spe- cial orbits are discussed： collinear libration point orbits and distant retrograde orbits. Studies show that the orbit determination accuracy in both cases can reach that of the observations. Some important properties of the system are carefully studied. These findings should be useful in the future engineering implementation of this conceptual study.

Several fourth-order force gradient symplectic algorithms

By adding force gradient operators to symmetric compositions, we build a set of explicit fourth-order force gradient symplectic algorithms, including those of Chin and coworkers, for a separable Hamiltonian system with quadratic kinetic en- ergy T and potential energy V. They are extended to solve a gravitational n-body Hamiltonian system that can be split into a Keplerian part H0 and a perturbation part H1 in Jacobi coordinates. It is found that the accuracy of each gradient scheme is greatly superior to that of the standard fourth-order Forest-Ruth symplectic integra- tor in T ＋ V-type Hamiltonian decomposition, but they are both almost equivalent in the mean longitude and the relative position for H0 ＋//1-type decomposition. At the same time, there are no typical differences between the numerical performances of these gradient algorithms, either in the splitting of T ＋ V or in the splitting of H0 ＋//1. In particular, compared with the former decomposition, the latter can dra- matically improve the numerical accuracy. Because this extension provides a fast and high-precision method to simulate various orbital motions of n-body problems, it is worth recommending for practical computation.

New adaptive time step symplectic integrator:an application to the elliptic restricted three-body problem

The time-transformed leapfrog scheme of Mikkola ＆ Aarseth was specifi- cally designed for a second-order differential equation with two individually separable forms of positions and velocities. It can have good numerical accuracy for extremely close two-body encounters in gravitating few-body systems with large mass ratios, but the non-time-transformed one does not work well. Following this idea, we develop a new explicit symplectic integrator with an adaptive time step that can be applied to a time-dependent Hamiltonian. Our method relies on a time step function having two distinct but equivalent forms and on the inclusion of two pairs of new canonical con- jugate variables in the extended phase space. In addition, the Hamiltonian must be modified to be a new time-transformed Hamiltonian with three integrable parts. When this method is applied to the elliptic restricted three-body problem, its numerical pre- cision is explicitly higher by several orders of magnitude than the nonadaptive one＇s, and its numerical stability is also better. In particular, it can eliminate the overestima- tion of Lyapunov exponents and suppress the spurious rapid growth of fast Lyapunov indicators for high-eccentricity orbits of a massless third body. The present technique will be useful for conservative systems including N-body problems in the Jacobian coordinates in the the field of solar system dynamics, and nonconservative systems such as a time-dependent barred galaxy model in a rotating coordinate system.

A method for calculating probability of collision between space objects

A method is developed to calculate probability of collision. Based on geometric features of space objects during the encounter, it is reasonable to separate the radial orbital motions from those in the cross section for most encounter events that occur in a near-circular orbit. Therefore, the probability of collision caused by differences in both altitude of the orbit in the radial direction and the probability of collision caused by differences in arrival time in the cross section are calculated. The net probability of collision is expressed as an explicit expression by multiplying the above two components. Numerical cases are applied to test this method by comparing the results with the general method. The results indicate that this method is valid for most encounter events that occur in near-circular orbits.

Recursive harmonic analysis for computing Hansen coefficients

We report on a simple pure numerical method developed for computing Hansen coefficients by using a recursive harmonic analysis technique. The precision criteria of the computations are very satisfactory and provide materials for computing Hansen＇s and Hansen＇s like expansions, and also to check the accuracy of some existing algorithms.

An object correlation and maneuver detection approach for space surveillance

Object correlation and maneuver detection are persistent problems in space surveillance and maintenance of a space object catalog. We integrate these two prob- lems into one interrelated problem, and consider them simultaneously under a sce- nario where space objects only perform a single in-track orbital maneuver during the time intervals between observations. We mathematically formulate this integrated sce- nario as a maximum a posteriori （MAP） estimation. In this work, we propose a novel approach to solve the MAP estimation. More precisely, the corresponding posterior probability of an orbital maneuver and a joint association event can be approximated by the Joint Probabilistic Data Association （JPDA） algorithm. Subsequently, the ma- neuvering parameters are estimated by optimally solving the constrained non-linear least squares iterative process based on the second-order cone programming （SOCP） algorithm. The desired solution is derived according to the MAP criterions. The per- formance and advantages of the proposed approach have been shown by both theoret- ical analysis and simulation results. We hope that our work will stimulate future work on space surveillance and maintenance of a space object catalog.

The dynamical architecture and habitable zones of the quintuplet planetary system 55 Cancri

We perform numerical simulations to study the secular orbital evolution and dynamical structure of the quintuplet planetary system 55 Cancri with the self-consistent orbital solutions by Fischer and coworkers. In the simulations, we show that this system can be stable for at least 108 yr. In addition, we extensively investigate the planetary configuration of four outer companions with one terrestrial planet in the wide region of 0.790AU 〈 a 〈 5.900AU to examine the existence of potential asteroid structure and Habitable Zones （HZs）. We show that there are unstable regions for orbits about 4：1, 3：1 and 5：2 mean motion resonances （MMRs） of the outermost planet in the system, and several stable orbits can remain at 3：2 and 1：1 MMRs, which resembles the asteroid belt in the solar system. From a dynamical viewpoint, proper HZ candidates for the existence of more potential terrestrial planets reside in the wide area between 1.0 AU and 2.3 AU with relatively low eccentricities.

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

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’oalewa.This 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 spacecraft.Different 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 comet.Compared to exclusive two-way range-rate,the introduction of local ranging observables improves the final GM uncertainties by up to one order of magnitude.An 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.