小行星的搜寻和定轨

本文简要介绍了与小行星有关的一些基本知识和在小行星搜寻方面的国际进展情况，侧重与ASTROD项目有关的内容。并介绍了与小行星定轨有关的网络资源。     

国际小行星搜寻最新成果

2010～2011年度第六期国际小行星搜寻活动于2010年12月13日～2011年1月22日举行,第七期活动于2011年4月5日～2011年5月22日举行。两期活动先后有十八个学校的一百多位学生参加,取得了丰硕的成果：发现主带小行星7个,证认近地天体4个,进行近地天体观测100多次。     

国际小行星搜寻活动

2008年2月1日至3月14日和3月17日至4月30日,历时三个月共两期国际小行星搜寻活动（International Asteroid Search Campaign,简称IASC）已经圆满结束。中国、德国、意大利、日本、摩洛哥、波兰、葡萄牙、美国、加拿大等9个国家的几十所学校参加了活动。到目前为止,两期活动共发现主带小行星6颗,证认了近地小行星34颗,获得虚拟撞击体观测结果6次。中国学生在此次活动中发现主带小行星1颗,证认了近地小行星4颗,获得虚拟撞击体观测结果1次。     

小行星初轨计算的Fortran程序设计

由改进的Laplace和Gauss方法分别给出小行星初轨计算的程序,通过两程序的比较测试得出结论——两方法适用于三次长时间间隔的角观测资料。为实现一天内角观测资料的小行星初轨计算与位置预报,对改进的Laplace方法流程进行了调整。通过增加迭代方程右矩阵的调整,预报结果可用于指导小行星的跟踪观测,文中给出调整后的流程图及预报效果数值验证。     

国际小行星搜寻活动——中国学生成绩卓著

2012年3月18日,中国“动手天文”教学组织（China Hands—On Universe,简称中国HOU）和北京远程教育专业委员会在北京101中学学术报告厅隆重举办2010—2012年度《国际小行星搜寻》中国学生颁奖大会。会议由101中学曾旭红老师主持,101中学书记兼科技副校长王涛、北京远程教育专业委员会覃祖军秘书长、史家小学教学鄣主任等分别在会上致辞,     

GPS数据定轨与外测数据定轨结果比较

本文使用卫星上搭载的ＧＰＳ接收机获得的数据进行最小二乘法定轨。将ＧＰＳ数据定轨结果外推的星历与外测数据定轨结果外星历比较,在国境内有外测数据的弧段,两种方法位置相差３０－４０米;在国境外没有外测数据覆盖的弧段,相差１００米左右。     

统计定轨中随机模型的验后估计

在卫星精密定轨中,对资料的加权一般是采用经验的方法,本文采用赫尔默特（Ｈｅｌｍｅｒｔ）方差分量估计方法,对Ｌａｇｅｏｓ２卫星６个月的ＳＬＲ资料进行试算,统计了各台站的验后方差,结果表明,用验后方差估计的方法可以得到各台站大致合理的权重,而且可以检验参数配置的合理性。     

星载GPS卡尔曼滤波定轨算法

利用卡尔曼滤波定轨算法，处理神舟4号星载GPS伪距实测资料，重点在于研究卡尔曼滤波中模型误差方差矩阵的选取准则，GPS信号中断或连续野值对递推滤波的影响，如何自主监控滤波的运行状态，即是正常还是趋于发散，目的在于评价该算法用于星上自主定轨长期平稳运行的可靠性．     

区域导航卫星精密定轨研究

区域卫星导航系统采用混合星座设计,GEO(地球同步轨道)卫星是系统的重要组成部分,其精密定轨技术也是导航系统的关键技术之一。GEO卫星的高轨特性致使地面跟踪基线长度有限,定轨几何条件不佳;其静地特性致使卫星轨道与钟差存在强相关特性,对于基于伪距的GEO卫星定轨模式,需要星地与站间时间同步技术的支持。因此,如何利用区域卫星导航系统的多种测量技术实现多模式、多层次的导航卫星精密定轨,是一项值得深入研究的课题。     

From Astrometry to Celestial Mechanics: Orbit Determination with Very Short Arcs

Contemporary surveys provide a huge number of detections of small solar system bodies, mostly asteroids. Typically, the reported astrometry is not enough to compute an orbit and/or perform an identification with an already discovered object. The classical methods for preliminary orbit determination fail in such cases: a new approach is necessary. When the observations are not enough to compute an orbit we represent the data with an attributable (two angles and their time derivatives). The undetermined variables range and range rate span an admissible region of solar system orbits, which can be sampled by a set of Virtual Asteroids (VAs) selected by an optimal triangulation. The attributable results from a fit and has an uncertainty represented by a covariance matrix, thus the predictions of future observations can be described by a quasi-product structure (admissible region times confidence ellipsoid), which can be approximated by a triangulation with each node surrounded by a confidence ellipsoid. The problem of identifying two independent short arcs of observations has been solved. For each VA in the admissible region of the first arc we consider prediction at the time of the second arc and the corresponding covariance matrix, and we compare them with the attributable of the second arc with its own covariance. By using the penalty (increase in the sum of squares, as in the algorithms for identification) we select the VAs which can fit together both arcs and compute a preliminary orbit. Even two attributables may not be enough to compute an orbit with a convergent differential corrections algorithm. The preliminary orbits are used as first guess for constrained differential corrections, providing solutions along the Line Of Variations (LOV) which can be used as second generation VAs to further predict the observations at the time of a third arc. In general the identification with a third arc will ensure a least squares orbit, with uncertainty described by the covariance matrix.     

Orbit of an Astrometric Binary System

We present a new method to solve the problem of initial orbit determination of any binary system. This method is mainly based on the material available for an observer, for example relative positions at a given time of the couple in the “plane of sky”, namely the tangent plane to the celestial sphere at the position of the primary component. The problem of orbit determination is solved by splitting in successive stages in order to decorrelate the parameters of each other as much as possible. On one hand, the geometric problem is solved using the first Kepler’s law from a single observing run and, on the other hand, dynamical parameters are then inferred from the fit of the Kepler’s equation. At last, the final stage consists in determining the main physical parameters involved in the secular evolution of the system, that is the spin axis and the J₂ parameter of the primary if we assume that it is a quasi-spherical body. As a matter of fact there is no need to make too restrictive initial assumptions (such as circular orbit or zero eccentricity) and initial guesses of parameters required by a non-linear least-squares Levenberg–Marquardt algorithm are finally obtained after each stage. Such a protocol is very useful to study systems like binary asteroids for which all of the parameters should be considered a priori as unknowns. As an example of application, we used our method to estimate the set of the Pluto–Charon system parameters from observations collected in the literature since 1980.     

NEAR Infrared Spectrometer Photometry of Asteroid 433 Eros

We present near-infrared spectrometer (NIS) observations (0.8 to 2.4 μm) of the S-type asteroid 433 Eros obtained by the NEAR Shoemaker spacecraft and report results of our Hapke photometric model analysis of data obtained at phase angles ranging from 1.2° to 111.0° and at spatial resolutions of 1.25×2.5 to 2.75×5.5 km/spectrum. Our Hapke model fits successfully to the NEAR spectroscopic data for systematic color variations that accompany changing viewing and illumination geometry. Model parameters imply a geometric albedo at 0.946 μm of 0.27±0.04, which corresponds to a geometric albedo at 0.550 μm of 0.25±0.05. We find that Eros exhibits phase reddening of up to 10% across the phase angle range of 0-100°. We observe a 10% increase in the 1-μm band depth at high phase angles. In contrast, we observe only a 5% increase in continuum slope from 1.486 to 2.363 μm and essentially no difference in the 2-μm band depth at higher phase angles. These contrasting phase effects imply that there are phase-dependent differences in the parametric measurements of 1- and 2-μm band areas, and in their ratio. The Hapke model fits suggest that Eros exhibits a weaker opposition surge than either 951 Gaspra or 243 Ida (the only other S-type asteroids for which we possess disk-resolved photometric observations). On average, we find that Eros at 0.946 μm has a higher geometric albedo and a higher single-scatter albedo than Gaspra or Ida at 0.56 μm; however, Eros's single-particle phase function asymmetry and average surface macroscopic roughness parameters are intermediate between Gaspra and Ida. Only two of the five Hapke model parameters exhibit a notable wavelength dependence: (1) The single-scatter albedo mimics the spectrum of Eros, and (2) there is a decrease in angular width of the opposition surge with increasing wavelength from 0.8 to 1.7 μm. Such opposition surge behavior is not adequately modeled with our shadow-hiding Hapke model, consistent with coherent backscattering phenomena near zero phase.     

短期威胁小行星

为更明确近地小行星撞击地球威胁的监测预警需求, 提出了"短期威胁小行星"的概念, 即未来100yr内可能对地球造成撞击威胁且等效直径大于10m的近地小行星. 以目前已发现的756颗短期威胁小行星为基础, 分析短期威胁小行星的轨道分布特点, 研究显示其与一般近地小行星的轨道分布存在差异, 短期威胁小行星的轨道半长轴更集中于1au, 轨道面更集中于黄道面. 基于近地小行星的数量模型, 初步建立了短期威胁小行星的数量估计模型, 并预估了未来100yr内存在撞击可能的短期威胁小行星的总体数量. 短期威胁小行星的特定研究对制定近地小行星搜巡监测策略有重要意义.     

一种解析定轨方法

本文给出了人造地球卫星轨道计算的一种解析方法,定轨方案中摄动计算考虑了地球引力场非球形摄动的J2,J3,J4的长期项,长周期项,J2短周期项,大气阻力,太阳光压及日月引力摄动的长期项。初始根数改正量估计采用微分轨道改进算法。在定轨迭代收敛后,残差的均方根误差在5″左右,资料使用率超过80%。     

Orbit Determination of Binary Asteroids

In addition to the detection of an asteroid moon or a binary asteroid, the knowledge of the satellite’s true orbit is of high importance to derive fundamental physical parameters of the binary system such as its mass and to shed light on its possible formation history and dynamical evolution (prograde/retrograde orbit, large/small eccentricity or inclination, etc.). A new methodology for preliminary orbit determination of binary asteroids – and visual binaries in general – is proposed. It is based on Thiele–Innes method combined with a ‘trial and error’ Monte-Carlo technique. This method provides the full set of solutions (bundle of orbits, with the 7 orbital elements) even for a reduced number of observations. The mass is a direct by-product of this orbit determination, from which one can next infer the bulk-density and porosity. In addition to the bundle of orbits, the method provides the marginal probability densities of the foreseen parameters. Such error analysis – since it avoids linear approximation – can be of importance for the prediction of the satellite’s position in the plane-of-sky during future stellar occultations or subsequent observations, but also for the analysis of the orbit’s secular evolution. After briefly describing the method, we present the algorithm and its application to some practical cases, with particular emphasis on asteroids binaries and applications on orbital evolution.     

The Near-Earth Asteroid Size-Frequency Distribution: A Snapshot of the Lunar Impactor Size-Frequency Distribution

It is shown that the size-frequency distribution (SFD) of a time-averaged projectile population derived from the lunar crater SFD of Neukum and Ivanov (in Hazards Due to Comets and Asteroids (T. Gehrels, Ed.), 1994, pp. 359-416, Univ. of Arizona Press, Tucson) provides a convincing fit to the SFD of the current near-Earth asteroid (NEA) population, as deduced from the results of asteroid search programs. Our results suggest that the shape of the SFD of the impactor flux has remained in a steady state since the late heavy bombardment, so that the current NEA population can be viewed as a snapshot of the flux of impactors on the Moon. The number of bodies in the projectile population with diameters of 1 km or more is 700±130, which is in good agreement with recent estimates of the total number of NEAs in this size range. Our results imply that the contribution to the projectile flux from comets is small for diameters below 10 km.     

Symmetries and Rank Deficiency in the Orbit Determination Around Another Planet

We study the possible degeneracies for the normal matrix of the observations from the Earth of the motion of a satellite around a planet, and give the possible solutions to the loss of precision in the orbit determination caused by the rank deficiency. Finally we discuss the methods available to control the instability in the orbit determination resulting from the degeneracy.     

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…