Time Scales and Tidal Effects in Minor Mergers

We use controlled N-body simulation to investigate the dynamical processes (dynamical friction, tidal truncation, etc.) involved in the merging of small satellites into bigger halos. We confirm the validity of some analytic formulae proposed earlier based on simple arguments. For rigid satellites represented by softened point masses, the merging time scale depends on both the orbital shape and concentration of the satellite. The dependence on orbital ellipticity is roughly a power law, as suggested by Lacey & Cole, and the dependence on satellite concentration is similar to that proposed by White. When merging satellites are represented by non-rigid objects, Tidal effects must be considered. We found that material beyond the tidal radius are stripped off. The decrease in the satellite mass might mean an increase in the merging time scale, but in fact, the merging time is decreased, because the stripped-off material carries away a proportionately larger amount of of orbital energy and angular momentum.     

Influence of Solar Activity on Precise Orbit Prediction of LEO Satellites

The perturbations of low earth orbit(LEO) satellites operating in the orbit of 300～2000 km are complicated.In particular,the atmospheric drag force and solar radiation pressure force change rapidly over a short period of time due to solar activities.Using spaceborne global positioning system(GPS) data of the CHAMP,GRACE and SWARM satellites from 2002 to 2020,this paper studies in depth the influence of solar activity on LEO satellites’ precise orbit prediction by performing a series of orbit pre...     

Electromagnetic effects on the orbital motion of a charged spacecraft

This paper deals with the effects of electromagnetic forces on the orbital motion of a spacecraft.The electrostatic charge which a spacecraft generates on its surface in the Earth’s magnetic field will be subject to a perturbative Lorentz force.A model incorporating all Lorentz forces as a function of orbital elements has been developed on the basis of magnetic and electric fields.This Lorentz force can be used to modify or perturb the spacecraft’s orbits.Lagrange’s planetary equations in the Gauss variational form are derived using the Lorentz force as a perturbation to a Keplerian orbit.Our approach incorporates orbital inclination and the true anomaly.The numerical results of Lagrange’s planetary equations for some operational satellites show that the perturbation in the orbital elements of the spacecraft is a second order perturbation for a certain value of charge.The effect of the Lorentz force due to its magnetic component is three times that of the Lorentz force due to its electric component.In addition,the numerical results confirm that the strong effects are due to the Lorentz force in a polar orbit,which is consistent with realistic physical phenomena that occur in polar orbits.The results confirm that the magnitude of the Lorentz force depends on the amount of charge.This means that we can use artificial charging to create a force to control the attitude and orbital motion of a spacecraft.     

The New Doppler Shift-and-Range Positioning Algorithm for the Global Navigation Satellite System

Under some circumstances in using the Global Navigation Satellite System （GNSS）, since navigation signals from the satellites are blocked a receiver cannot simultaneously track four or more satellites to estimate its 3-dimensional （3D） coordinates and clock bias. This paper proposes a Doppler Shift-and-Range （DS-R） positioning algorithm with which pseudoranges and Doppler shifts are simultaneously measured. The measurement results are used as inputs to four equations in the algorithm, and the 3D position can be estimated from the equations. Through this approach the algorithm can achieve real-time 3D positioning. By synthesizing multi-frequency observational results and adopting a new method of jointly using code-carrier phases, this algorithm expectably has accuracies similar to those of the standard approach of point positioning.     

Azimuth Control for Large Aperture Telescope Based on Segmented Arc Permanent Magnet Synchronous Motors

A tracking control algorithm based on active disturbance rejection controller(ADRC) is proposed to overcome the telescope's mount fluctuation. The fluctuations are caused by internal and external disturbance when the large aperture telescope runs at ultra-low speed with direct drive. According to the high-precision and high-stability requirements of a large aperture telescope, the ADRC position controller is designed based on segmented arc Permanent Magnet Synchronous Motors(arc PMSMs). The tracking differentiator of ADRC is designed to undergo a transition process to avoid overshoot in the position loop.The speed of target tracking process is observed by the extended state observer and the position information in the system is estimated in real time. The current control variable of the segmented arc PMSM is generated by implementing a non-linear state error feedback control law. The simulation results demonstrate that the proposed control strategy can not only accurately estimate the position and speed of the tracking target, but also estimate the disturbance to compensate the control variables. Experiments showed that the speed error is less than 0.05′′s~(-1) when using the ADRC, and it can realize high tracking performance when compared with PID controller, which improves the robustness of a large aperture telescope control system.     

A new method to determine the gravity field of small bodies from line-of-sight acceleration data

We present a new method to derive line-of-sight acceleration observables from spacecraft radio tracking data. The observables can be used to estimate the mass and gravity of a natural satellite as a spacecraft flyby. The corresponding observation model adapts to one-way and two/three-way tracking modes. As a test case for method validation and application, we estimated the mass and degree two gravity field for the Martian moon Phobos using simulated tracking data when the spacecraft Mars Express flew by Phobos on 2013 December 29. We have a few real tracking data during flyby and they will be used to confirm raw data simulation. The main purpose of this paper is to demonstrate the method of line-of-sight acceleration reduction from raw tracking data and the feasibility to estimate mass and gravity of a natural satellite using this type of observable. This novel method is potentially applicable to planet and asteroid gravity field studies combined with Doppler tracking data.     

What is the right way to quench star formation in semi-analytic models of galaxy formation?

Semi-analytic models of galaxy formation are powerful tools to study the evolution of a galaxy population in a cosmological context. However, most models overpredict the number of lowmass galaxies at high redshifts and the colors of model galaxies are not right in the sense that low-mass satellite galaxies are too red and centrals are too blue. The recent version of the L-Galaxies model by Henriques et al.(H15) is a step forward to solve these problems by reproducing the evolution of stellar mass function and the overall fraction of red galaxies. In this paper we compare the two model predictions of L-Galaxies(the other is Guo et al., G13) to SDSS data in detail. We find that in the H15 model the red fraction of central galaxies now agrees with the data due to their implementation of strong AGN feedback, but the stellar mass of centrals in massive halos is now slightly lower than what is indicated by the data. For satellite galaxies, the red fraction of low-mass galaxies(log M*/M⊙ 10)also agrees with the data, but the color of massive satellites(10 log M*/M⊙ 11) is slightly bluer.The correct color of centrals and the bluer color of massive satellites indicate that quenching in massive satellites is not strong enough. We also find that there are too many red spirals and less bulge-dominated galaxies in both H15 and G13 models. Our results suggest that additional mechanisms, such as more minor mergers or disk instability, are needed to slightly increase the stellar mass of the central galaxy in massive galaxies, mainly in the bulge component, and bulge dominated galaxies will be quenched not only by minor mergers, but also by some other mechanisms.     

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.     

A Positioning System based on Communication Satellites and the Chinese Area Positioning System （CAPS）

The Chinese Area Positioning System (CAPS) is a positioning system based on satellite communication that is fundamentally different from the 3"G" (GPS, GLONASS and GALILEO) systems. The latter use special-purpose navigation satellites to broadcast navi-gation information generated on-board to users, while the CAPS transfers ground-generated navigation information to users via the communication satellite. In order to achieve accurate Positioning, Velocity and Time (PVT), the CAPS employs the following strategies to over-come the three main obstacles caused by using the communication satellite: (a) by real-time following-up frequency stabilization to achieve stable frequency; (b) by using a single carrier in the transponder with 36 MHz band-width to gain sufficient power; (c) by incorporating Decommissioned Geostationary Orbit communication satellite (DGEO), barometric pressure and Inclined Geostationary Orbit communication satellite (IGSO) to achieve the 3-D posi-tioning. Furthermore, the abundant transponders available on DGEO can be used to realize the large capacity of communication as well as the integrated navigation and communication. With the communication functions incorporated, five new functions appear in the CAPS: (1) combination of navigation and communication; (2) combination of navigation and high accu-racy orbit measurement; (3) combination of navigation message and wide/local area differen-tial processing; (4) combination of the switching of satellites, frequencies and codes; and (5) combination of the navigation message and the barometric altimetry. The CAPS is thereby labelled a PVT5C system of high accuracy. In order to validate the working principle and the performance of the CAPS, a trial system was established in the course of two years at a cost of about 20 million dollars. The trial constellation consists of two GEO satellites located at E87.5°and E110.5°, two DGEOs located at E130° and E142°, as well as barometric altimetry as a virtual satellite. Static and dynamic performance tests were completed for the Eastern, the Western, the Northern, the Southern and the Middle regions of China. The evaluation results are as follows: (1) land static test, plane accuracy range: C/A code, 15～25 m; P code, 5～10 meters; altitude accuracy range, 1～3 m; (2) land dynamic test, plane accuracy range, C/A code, 15～25 m; P code, 8～10m; (3) velocity accuracy, C/A code, 0.13～0.3 ms-1, P code, 0.15～0.17m s-1; (4) timing accuracy, C/A code, 160ns, P code, 13 ns; (5) timing compared accuracy of Two Way Satellite Time and Frequency Transfer (TWSTFT), average accuracy, 0.068 ns; (6) random error of the satellite ranging, 10.7 mm; (7) orbit determination accuracy, better than 2 m. The above stated random error is 1σ error. At present, this system is used as a preliminary operational system and a complete system with 3 GEO, 3 DGEO and 3 IGSO is being established.     

The influence of ionospheric thin shell height on TEC retrieval from GPS observation

We investigate the influence of assumed height for the thin shell ionosphere model on the Total Electron Content(TEC) derived from a small scale Global Positioning System(GPS) network. TEC and instrumental bias are determined by applying a grid-based algorithm to the data on several geomagnetically quiet days covering a 10 month period in 2006. Comparisons of TEC and instrumental bias are made among assumed heights from 250 km to 700 km with an interval of 10 km. While the TEC variations with time follow the same trend, TEC tends to increase with the height of the thin shell. The difference in TEC between heights 250 km and 700 km can be as large as～8 TECU in both daytime and nighttime. The times at which the TEC reaches its peak or valley do not vary much with the assumed heights. The instrumental biases, especially bias from the satellite, can vary irregularly with assumed height. Several satellites show a large deviation of～3 ns for heights larger than 550 km. The goodness of fit for different assumed heights is also examined. The data can be generally well-fitted for heights from 350 km to 700 km. A large deviation happens at heights lower than 350 km. Using the grid-based algorithm, there is no consensus on assumed height as related to data fitting. A thin shell height in the range 350-500 km can be a reasonable compromise between data fitting and peak height of the ionosphere.     

两种观测技术综合精密定轨的探讨

利用T／P卫星的SLR和DORIS实测资料,对两种观测技术综合精密定轨中的加权及其对定轨影响的问题作了初步的探讨。根据所提出的一种经验性的加权方法进行了综合定轨计算,结果表明：对于两种不同技术的观测,相对权选取的恰当与否将影响综合定轨的精度;综合定轨的最优加权不仅依赖于观测资料的精度,还与观测资料的多少和几何分布有关;通过选用最优加权,可使得综合轨的精度优于仅用其中一种技术的定轨精度,综合定轨能有效地提高定轨精度。     

月球探测器过渡轨道的短弧定轨方法

论述的短弧定轨,是指在无先验信息情况下又避开多变元迭代的初轨计算方法,它需要相应的动力学问题有一能反映短弧内达到一定精度的近似分析解．探测器进入月球引力作用范围后接近月球时可以处理成相对月球的受摄二体问题,而在地球附近,则可处理成相对地球的受摄二体问题,但在整个过渡段的力模型只能处理成一个受摄的限制性三体问题．而限制性三体问题无分析解,即使在月球引力作用范围外,对于大推力脉冲式的过渡方式,相对地球的变化椭圆轨道的偏心率很大(超过Laplace极限),在考虑月球引力摄动时亦无法构造摄动分析解．就此问题,考虑在地球非球形引力(只包含J2项)和月球引力共同作用下,构造了探测器飞抵月球过渡轨道段的时间幂级数解,在此基础上给出一种受摄二体问题意义下的初轨计算方法,经数值验证,定轨方法有效,可供地面测控系统参考．     

基于智能优化算法的小天体初轨确定

经典的初轨确定方法包括Laplace方法和Gauss方法以及它们的各种变化形式. 除这些经典方法之外, 基于当今光学观测数据的特点, 学者们也陆续提出了一些其他的初轨确定方法, 包括双r (目标距离观测者的距离)方法和可行域方法. 双r方法的一种实现方式是通过猜测某两个时刻(通常是定轨弧段的首、末时刻)目标离观测者的距离, 结合观测者在空间中的位置矢量, 即可求解相应的Lambert弧段作为目标轨道的初始猜测. 进一步, 以其他观测时刻的RMS (Root Mean Square)为优化变量可以改进初始猜测从而确定初轨. 可行域方法则是针对一组初始观测参数(包括赤经、赤纬及其变率), 根据一些初始假设将目标(离观测者的)距离及其变率约束在可行域内, 并通过三角划分逐步逼近的方式寻找到使观测RMS最小的猜测解. 针对一系列模拟观测数据以及实测数据, 将智能优化算法(粒子群算法)应用于这两种初轨方法, 并将结果与改进的Laplace算法的结果进行比较. 由于双r方法不仅可以用于短弧定轨还可用于长弧关联, 所以进一步给出了针对长弧段数据的关联结果.     

同步卫星短弧定轨

同步卫星受到摄动力的影响,它的实际轨道有一点漂移．卫星需要不断的调轨调姿,以保证其正常运行．为了研究卫星在几小时,甚至更短的时间内的轨迹情况,采用短弧段定轨法．用动力学方法进行短弧定轨,分别研究1小时和15分钟定轨并进行比较,目的是为了在同步轨道卫星变轨后,能尽快地为卫星提供精密的预报轨道．此外,在系列短弧定轨后,得到精密轨道系列,为研究轨道变化的力学因素及研究短弧中卫星转发器时延变化规律等提供依据．     

Spacecraft Orbit Determination with The B-spline Approximation Method

It is known that the dynamical orbit determination is the most common way to get the precise orbits of spacecraft. However, it is hard to build up the precise dynamical model of spacecraft sometimes. In order to solve this problem, the technique of the orbit determination with the B-spline approximation method based on the theory of function approximation is presented in this article. In order to verify the effectiveness of this method, simulative orbit determinations in the cases of LEO (Low Earth Orbit), MEO (Medium Earth Orbit), and HEO (Highly Eccentric Orbit) satellites are performed, and it is shown that this method has a reliable accuracy and stable solution. The approach can be performed in both the conventional celestial coordinate system and the conventional terrestrial coordinate system. The spacecraft's position and velocity can be calculated directly with the B-spline approximation method, it needs not to integrate the dynamical equations, nor to calculate the state transfer matrix, thus the burden of calculations in the orbit determination is reduced substantially relative to the dynamical orbit determination method. The technique not only has a certain theoretical significance, but also can serve as a conventional algorithm in the spacecraft orbit determination.     

地月DRO星载光学测量近地小行星轨道确定

针对地基光学监测系统对近地小行星在近太阳方向的监测存在盲区的问题,提出了远距离逆行轨道(Distant Retrograde Orbit,DRO)天基光学平台对近地小行星进行跟踪定轨的方法.通过可视性分析,筛选仿真观测数据,利用美国宇航局喷气推进实验室(Jet Propulsion Laboratory,JPL)公布的小行星初始轨道信息对不同轨道类型的目标天体进行轨道确定,将计算结果与参考轨道对比分析.仿真结果表明:在测量精度2角秒,定轨弧长3年的情况下,DRO平台对仿真算例中所选择的近地小行星的定轨精度可以达到几十公里量级,其中Atira型轨道精度可达10公里以内.由此可见,DRO天基平台对近地小行星具有较好的监测能力,定轨精度能实现对目标小行星的精确跟踪,并对其进行轨道预报.     

Orbit determination of satellite “Tance 1” with VLBI data

The satellite “Tance 1” of the “Double-Star Program” is the first truly scientific experimentation satellite of China. Its orbit is the farthest so far launched in China, with a geocentric apogee reaching 78 thousand kilometers. The tracking of “Tance 1” and of more distant space targets, such as the lunar exploration craft, can be realized with the VLBI technique of radio astronomy. In order to test and verify the role which the VLBI technique plays in the lunar exploration program of China, Shanghai Astronomical Observatory organized the only 3 tracking stations in China (located at Shanghai, Urumqi and Kunming), to carry out test tracking of “Tance 1,” and used the time delay data obtained to determine the orbit of “Tance 1” over a two-day period, so providing a preliminary assessment of the possibility of VLBI orbit determination. The fitting error of the orbit so obtained is about 5.5 m in the time delay and about 2 cm/s in the delay rate (this for checking only), much better than is provided by the preliminary orbit (used merely for ensuring tracking) in which the corresponding figures are around 2 km and 15 cm/s. Further, if the orbit is determined by using both the time delay and time delay rate data (with weights according to their internal accuracies), then the residuals are 5.5 m in the time delay and 2 cm/s in the delay rate. For an appreciation of the true accuracy of the VLBI orbit determination, we used simulation data (of the observed two-day VLBI data) and found the results depended greatly on the error in the dynamic model of the satellite which, however, is difficult to assess, while the formal residuals are of the order of 1 kin in the delay and of cm/s in the delay rate. The simulation computation also indicates that a joint determination using both VLBI and USB data will have an improved accuracy.     

两行根数辅助的SLR单站定轨

单站测距资料定轨的困难限制了漫反射SLR(Satellite Laser Ranging)测距资料的应用.为此,提出利用两行根数模拟多站SLR测距资料作为辅助,实现单站SLR测距资料定轨的方法.该方法对卫星Ajisai单站SLR测距资料定轨并生成5 d预报轨道,误差小于40 m,实现利用单站测距资料的轨道改进,验证了方法的可行性.     

Homogeneous and Heterogeneous Observational Data Weighting Method of Combined Orbit Determination of Near-earth Satellites of Bi-satellite Positioning System and its Applications

In the light of the problem of amalgamation and processing of multisource observational data in the combined orbit determination of near-earth satellites of the bi-satellite positioning system, the optimal weighting method of the improved variance component estimation of the two-step systematic error correction of homogeneous observational data is proposed. Analyses show that the multi-source amalgamation measurement model of the heterogeneous observational data essentially is a multi-structure, multi-parameter non-linear regression model, and the optimal weighting method of the combination of model structure characteristic analysis and variance component estimation of the heterogeneous observational data is established. The realization algorithms of the optimal weighting and the combined orbit determination parameter estimation of the two sorts of observational data are designed, and the simulation experiments of the combined orbit determination are carried out by taking the distances among the two satellites and the backup satellite and the homogeneous observational data and the distance between the two satellites and the heterogeneous observational data of satellite sensor angle measurements as the examples. The results of theoretical analysis and simulation calculation show that for the combined orbit determination of homogeneous observational data, the accuracy of orbit determination obtained by adopting the variance component estimation method of the two-step systematic error correction can be more superior than that obtained by means of the traditional empirical weighting method. For the combined orbit determination of heterogeneous observational data, through the introduction of the weighting factor by which the model structure is characterized the accuracies of the combined orbit determination of the near-earth satellite and geostationary satellite are both improved to a certain extent in comparison with the mean weighting mode.     

海上移动站精密测轨方法

将人造卫星精密定轨理论应用于海上移动站精密定轨，根据移动站的特点，建立了相应的定轨条件方程，并在此基础上利用海上移动站某次飞船发射任务跟踪数据进行了实算，给出了定轨结果和讨论。