关于X射线脉冲星自主导航的位置观测方程

在X射线脉冲星自主导航(XNAV)中,位置观测方程表达了X光子到达航天器的时刻(TOA)和航天器位置的关系.具体讨论时,一般用TOA和"时间基准"的差值代替TOA,用太阳系质心系中的位置矢量表示航天器的位置."时间基准"可以取X光子到达太阳系质心(SSB)的真实时间,也可以取X光子到达SSB的"等效时间".讨论了基于这两种时间基准的位置观测方程,给出了时间精度为0.1 ns的位置观测方程,分析了其中各项的物理意义.     

The Time Equation of Light Propagation in XNAV

We discuss in detail the general relativistic effect in the X-ray sourcebased navigation for autonomous position determination program (XNAV). By using the post-Newtonian approximate method of the DSX scheme, we calculate the bending of light and the gravitational time delay under the 1PN metric, as well as the gravitational time delay under the 2PN metric, and finally obtain the high-accuracy time equation of light propagation in XNAV.     

Orbit of Comet C/1845 D1 (de Vico) and the utility of Bulirsch-Stoer integration

Comet C/1845 D1 (de Vico) is one of a large number of comets with parabolic orbits. Given that there are sufficient observations of the comet, 291 in right ascension and 269 in declination, it proves possible to calculate a better orbit. The calculations are based on a 12th order predictor-corrector method. The comet's orbit is hyperbolic and, from calculated mean errors, statistically different from a parabola. Bulirsch-Stoer integration, although more flexible and of comparable precision, proves considerably more laborious.     

Optimization of Low-Thrust Trajectories Using an Indirect Shooting Method without Guesses of Initial Costates

According to the optimal control theory, the optimal control problem of the low-thrust tra jectory can be converted into a solution of nonlinear two- point boundary-value problem (TPBVP). To solve the TPBVP, the repeated random guesses for the initial costate variables and iterative computations are needed. In order to enhance the convergence of the iterations, we select an appropriate performance index, and then linearize the equations of the TPBVP around a Keplerian orbit. For multi-revolution transfers, instead of the multi- revolution Lambert tra jectory, multiple segmented Keplerian arcs are used to ensure the effectiveness of the linearization. The method is totally automatic with multiple iterations. With this method, we can get the results within 3 ∼ 5 iterations, and the random guess of the initial costates is unnecessary. Finally by the iterative optimization of the performance index, a better control strategy approaching to the bang-bang control is obtained.     

Orbit Determination Using Satellite—to—Satellite Tracking Data

1 INTRODUCTIONThe tracking arc-length should be increased in order to approve the accuracy in orbitdetermination of LEO (Low Earth Orbit) satellites. The local ground-based tracking networkdoes not provide sufficient orbit coverage for the user satellites. The most promising methodis to use high orbiting satellites, such as GPS and TDRS, as trackers to observe the usersatellites. For examPle, tWO geosynclironous satellites could cover more than 85% of the orbitof any given user sate…     

Simulations for the Original Distribution of KBOs

Using the N-body dynamical model that includes the sun, the 8 planets, Pluto, UB313 and massless particles, we simulate the orbital evolution of 551 Kuiper Belt Objects (KBOs) with known parameters. The initial conditions of the simulations are the currently observed orbital parameters. The integration backtracks from now to -10×10⁸ yr. The results show that about 10×10⁸ years ago, more than 1/3 of the presently observed KBOs resided in the region of the present Kuiper main belt, a few were located inside the Neptune orbit, and the rest were beyond 50AU; and that about 4.5×10⁸ years ago, all the objects in the Kuiper main belt exhibited a rather good normal distribution, without so many objects concentrated in the Neptune's 3:2 resonance region, as at present time.     

Dynamics and gravitational waveforms in spinning compact eccentric binaries

The effects of eccentricity on the Hamiltonian dynamics of post-Newtonian spinning compact binaries and gravitational radiation from eccentric orbits are discussed. The simulation results of scans for chaos show that the eccentricity has a great effect on the dynamics without considering dissipation due to gravitational radiation. Moreover, both the dynamics behavior and the orbital eccentricity jointly modulate the gravitational waveforms, and the spin–spin coupling effect play an important role during the gravitational radiation of inspiral and coalescence. Moreover, the imprint of characteristic of the original system can be deduced from the time-domain and frequency-domain waveforms.     

基于单站短弧段光学观测的低轨卫星轨道预报算法

基于单站短弧段的目标跟踪预报技术是保证高精度光电经纬仪在非常规环境下正常跟踪捕获目标的重要途径.构建了基于非线性滤波器的跟踪预报算法,能够在正常情况下为闭环跟踪提供引导数据,同时构建了基于非线性变换的目标预报算法,可以在无有效观测数据情况下为经纬仪提供轨迹引导,保证目标不丢失.证明了非线性滤波在单站短弧段跟踪预报算法中比常规扩展卡尔曼滤波(Extended Kalman Filter,EKF)更有效.计算表明,本文设计的非线性滤波器可以作为光学跟踪设备的引导算法,引导精度同经纬仪的随机测量精度等量级,在设备系统误差达到50"时,预报60 s的精度可达到20",仍然满足跟踪设备的视场要求.     

Normal forms for the epicyclic approximations of the perturbed Kepler problem

We compute the normal forms for the Hamiltonian leading to the epicyclic approximations of the (perturbed) Kepler problem in the plane. The Hamiltonian setting corresponds to the dynamics in the Hill synodic system where, by means of the tidal expansion of the potential, the equations of motion take the form of perturbed harmonic oscillators in a rotating frame. In the unperturbed, purely Keplerian case, the post-epicyclic solutions produced with the normal form coincide with those obtained from the expansion of the solution of the Kepler equation. In all cases where the perturbed problem can be cast in autonomous form, the solution is easily obtained as a perturbation series. The generalization to the spatial problem and/or the non-autonomous case is straightforward.     

A Three Body Solution for the DI Her System

The DI Herculis system has been extensively studied over the past few decades because its observed rate of apsidal advance is less than a quarter of that which is expected from its physical and orbital properties. Work by Khaliullin et al. (1991) proposed that this slow rate of apsidal advance is a result of the presence of a third (stellar mass) body orbiting the system, however, observations by Guinan et al. (1994) severely restrict the orbital properties of such a solution. We show that a planetary mass object in a highly inclined orbit relative to the binary is capable of producing the observed apsidal motion, while remaining within the bounds of the most recent set of observations. A wide range of stable solutions are possible.     

制约卫星轨道寿命的另一种机制

近点共振会导致太阳系小天体(小行星,自然卫星以及大行星和月球的人造卫星)的轨道偏心率出现变幅较大的长周期变化,特别是以月球和大行星为中心天体的大倾角轨道(确切地说是倾角接近90°的极轨道)卫星,由于类似的原因,偏心率的增大而导致近星距rp=a(1-e)≤ae(ae是中心天体的赤道半径),使其落到中心天体上,结束轨道寿命,这与耗散机制大不相同,因此将对其作理论分析,并以计算实例加以证实.     

The influence of shapes of the bodies on the dynamics of planetary and star systems

The dynamics of planetary and star systems including perturbing forces due to the flattering and quadrupole distortion of the bodies is studied. The analytical model describing the perturbations which influence on the orbital motion of extrasolar planetary systems is presented. The calculations of the secular evolution of the mean orbital elements have shown that the effects related to the shape of the body are more important than the ones due to the quadrupole distortion.     

A Research on the Orbit Determination Method by Means of Sparse Data of Electronic Fences

Based on the Lambert equation and knowledge of space geometry a method of orbit determination is given using the sparse observational data provided by the space monitoring electronic fence device. Our simulated experiment of a large number of targets shows that the initial orbit determined by this method can be improved and can converge to a final accuracy better than 100 m, so proving that the method can be applied to the orbit determination of an overwhelming majority of space targets with the observed data of the electronic fence. Finally, the effect of the latitude of the observing station on the application of the method is discussed.     

The Effect of GPS Ephemeris on the Accuracy of Precise Orbit Determination of LEO Satellite-borne GPS

The satellite-borne GPS receivers dedicated to precise orbit determination are now being carried by more and more low earth orbit (LEO) satellites and the satellite-borne GPS has become one of the main means for the precise orbit determination of low earth orbit satellites. The accuracy of satellite-borne GPS precise orbit determination depends on the accuracies of the GPS ephemeris and the clock error. Based on the orbit determination function of SHORDEIII zero-difference dynamics and using the observational data obtained by the GRACE satellites for the week from 2005 August 1 to 7 as an example, three versions of GPS ephemerides (igs, igr and igu) are used to carry out orbit determination under the same conditions and to estimate the effect of the GPS ephemeris accuracy on the accuracy of orbit determination of low earth orbit satellites. Our calculated results show that the two ephemerides, igs and igr, are equivalent to each other in orbit determination accuracy (about 9.5 cm), while igu is slightly less accurate, at about 10.5 cm. The effect produced by the data of the high frequency GPS satellite clock error on the accuracy of orbit determination is 1–6 cm.     

Optical surveys for space debris

Space debris—man-made non-functional objects of all sizes in near-Earth space—has been recognized as an increasing threat for current and future space operations. The debris population in near-Earth space has therefore been extensively studied during the last decade. Information on objects at altitudes higher than about 2,000 km is, however, still comparatively sparse. Debris in this region is best detected by surveys utilizing optical telescopes. Moreover, the instruments and the applied observation techniques, as well as the processing methods, have many similarities with those used in optical surveys for ‘astronomical’ objects like near-Earth objects (NEOs). The present article gives a general introduction to the problem of space debris, presents the used observation and processing techniques emphasizing the similarities and differences compared to optical surveys for NEOs, and reviews the results from optical surveys for space debris in high-altitude Earth orbits. Predictions on the influence of space debris on the future of space research and space astronomy in particular are reported as well.     

An Analysis of the Lifetimes of Large Elliptical Orbits of Space Debris

The lunisolar perturbation is the principal factor that causes variation in the orbit of a GTO (geosychronous transfer orbit) space debris. In the present article the analytical expression of the long-periodic term of the altitude of the GTO orbital perigee caused by the lunisolar perturbation is derived, and the basic characteristics of the variation of the perigee caused by the lunisolar perturbation are analyzed. A method of selecting a launch window that will help to improve the space debris situation is given, and its correctness is tested and verified through simulation calculation.     

A Research on the Pulsar Timing Based on Kalman Filtering

The pulsar is a high-speed rotationing neutron star with a stable rotational period, being not disturbed and destroyed artificially, and can be taken as the reference quantity of the absolute time. In this article a kind of pulsar time service method based on the Kalman filtering algorithm is proposed, and the simulation analysis of the clock error control based on the Kalman filtering and of the effect of the pulsar catalogue error and the measuring accuracy of the pulsar time of arrival (TOA) on the accuracy of time service is made by taking a certain solar synchronous orbit as an example. The result shows that by utilizing this method the clock error of the satellite-borne clock can be effectively eliminated and its time-dependent increase is restrained, thereby solving the problem that the accuracy of the spacecraft-borne low cost clock can not meet the needs.     

Clues to the origin of jupiter’s trojans: the libration amplitude distribution

We model with numerical algorithms the dynamical processes that possibly lead to the trapping of Jupiter’s Trojans from a primordial population of planetesimals orbiting nearby a proto-Jupiter. The predictions of models based on mutual planetesimal collisions and on the mass growth of Jupiter are compared with observations. In particular, we concentrate on the distribution of the libration amplitude. The two mechanisms for trapping reproduce closely the libration amplitude distribution of the real Trojans only when the long-term dynamical diffusion described by Levison et al. (1997, Nature 385, 42-44) is taken into account.     

The Dynamics of Objects in the Inner Edgeworth–Kuiper Belt

Objects in 3:2 mean motion resonance with Neptune are protected from close encounters with Neptune by the resonance. Bodies in orbits with semi-major axis between 39.5 and about 42 AU are not protected by the resonance; indeed due to overlapping secular resonances, the eccentricities of orbits in this region are driven up so that a close encounter with Neptune becomes inevitable. It is thus expected that such orbits are unstable. The list of known Trans-Neptunian objects shows a deficiency in the number of objects in this gap compared to the 43–50 AU region, but the gap is not empty. We numerically integrate models for the initial population in the gap, and also all known objects over the age of the Solar System to determine what fraction can survive. We find that this fraction is significantly less than the ratio of the population in the gap to that in the main belt, suggesting that some mechanism must exist to introduce new members into the gap. By looking at the evolution of the test body orbits, we also determine the manner in which they are lost. Though all have close encounters with Neptune, in most cases this does not lead to ejection from the Solar System, but rather to a reduced perihelion distance causing close encounters with some or all of the other giant planets before being eventually lost from the system, with Saturn appearing to be the cause of the ejection of most of the objects.     

Study on the Orbit Prediction Errors of Space Objects Based on Historical TLE Data

Two line element (TLE) released by the North American Aerospace Defense Command (NORAD) is widely used by aerospace workers, and the matched SGP4/SDP4 (Simplified General Perturbation Version 4/Simplified Deep-space Perturbation Version 4) model is used to propagate it. Nevertheless, no corresponding information about its accuracy and covariance is clearly given, thus the application of the TLE data is greatly restricted. In this paper, the determined and predicted orbits are compared to generate the orbit error data, based on the historical TLE data obtained from the Space-Track website and the SGP4/SDP4 model. By dividing different time bins, the fitting coefficients of the variation of orbit prediction error with time are given for each space object, and the characteristics of the error evolution are further discussed for the different types of orbits. The mean analytic model of the orbit prediction error evolution with time is given respectively for the four orbit types of space objects, which provides a valuable reference for extending the application of the TLE data.