碰撞风险评估标准适用性分析

随着空间碎片数量的不断增加,空间目标碰撞预警技术已经受到人们越来越多的关注.早期普遍使用几何区域(BOX)判定法对空间目标的碰撞风险进行评估,但它是一种比较保守的方法,工程实用性低;90年代后开始广泛地研究和采用碰撞概率判定法,这种方法综合考虑空间目标交会时刻的多个参数,但是由于其数学模型对轨道误差数据的依赖程度很高,所以在某些情况下会导致预警结果不准确.通过仿真的方法,模拟两条确定交会的标准精密轨道,由程序生成随机误差加入到标准轨道生成有误差的轨道,计算最接近距离和碰撞概率,并分析二者之间的关系.结果表明,当轨道预报精度较差时,碰撞概率判定法可能会失效,需要结合几何区域判定法进行综合判定,以避免碰撞预警过程中的"误判"和"漏判".     

基于先验信息的空间碎片探测方法

提出了一种基于先验信息的空间碎片图像探测方法.该方法通过先验信息,在图像中碎片星像的邻域设置波门,计算波门内的局部背景阈值,辅以相关的判据识别目标.随后使用矩方法计算碎片质心相对波门中心的偏离值,通过线性平移计算碎片质心在整幅图像中的位置.实验表明:该方法复杂度低、便于实现、实时性好,可以高效、准确地探测空间碎片,比较精确地确定碎片的质心位置.     

卫星与空间碎片碰撞预警的快速算法

提出了一种空间目标与空间碎片碰撞预警的快速计算方法，该算法不仅计算速度快，而且减缓了沿迹误差的影响，延长了预警的有效期，利用该方法，检测一个卫星与5800个空间碎片在一天内是否碰撞，计算时间小于3秒；用2天前的资料，预报计算法国CERISE卫星和空间碎片的碰撞时间误差约为0．02秒，空间位置误差约为500—600米．     

近地小行星(10302) 1989 ML和(4660) Nereus的轨道特征及演化分析

近地小行星(10302) 1989 ML和(4660) Nereus作为下一代深空探测的候选目标一直备受关注. 在考虑太阳系主要天体的动力学背景下, 通过计算最大Lyapunov指数(MLE)及MEGNO (Mean Exponential Growth factor of Nearby Orbits)指数讨论它们的稳定性. 同时, 对每个小行星, 在其观测误差范围内按多元正态分布各选取1000个克隆粒子, 通过统计分析显示这两个小行星在10万年内可能的运动范围, 给出半长径-偏心率空间中的出现次数分布图, 并统计小行星与地球或其他大行星之间的密近交汇及碰撞的概率. 此外还对这两个小行星的标称轨道进行长期共振、Kozai共振及平运动共振的动力学分析. 综上得出结论, 1989 ML处在平运动共振主导的区域, 发生密近交汇的概率较小, 从而其轨道相对较稳定; 而Nereus处在地球的密近交汇区域, 轨道极不稳定.     

旋涡星系密度波理论中Poisson积分的简化及应用

本文给出了旋涡星系密度波理论中Poisson积分的一种简化方法。这一简化的最重要应用在于利用它计算旋涡模式时可节省大量计算机时。此外本文还利用这种简化方法对一系列密度——引力势渐近关系进行了系统的数值检验。 用这一简化方法计算核函数比用未简化的核函数形式直接计算节省机时八十四倍。当在数值模式理论研究中大量计算Poisson积分时,应用本文提出的简化将有效地提高计算效率并保证足够高的精度。     

综合评价线性多步积分公式轨道积分性能的两项新指标

概述了制约线性多步积分公式轨道积分状态的多种因素 ;提出了综合评价线性多步积分公式积分性能的两项新指标。建议在对数值计算有较高精度要求的科研项目中 ,应将构造并选择适合研究项目的线性多步积分公式以及高效的积分方式列为课题前期工作的重要部分     

综合评价线性多步积分公式轨道积分性能的两项新指标

概述了制约线性多步积分公式轨道积分状态的多种因素。提出了综合评价线性多步积分公式积分性能的两项新指标。建议在对数值计算有较高精度要求的科研项目中，应将构造并选择适合研究项目的线性多步积分公式以及高效的积分方式列为课题前期工作的重要部分。     

空间目标跟踪的概率数据关联方法

在空间目标的光学观测中,由于跟踪波门内多个量测事件频发,导致跟踪量测的不确定,降低自动跟踪精度引起跟踪不稳.结合Kalman滤波和概率数据关联算法,实现了空间目标自适应跟踪.方法通过Kalman滤波预测确定关联区域,采用概率数据关联技术获得等效量测作为Kalman滤波的有效馈源.实验表明:方法可以有效地提高自动跟踪精度,改善空间目标自动跟踪鲁棒性.     

一种适用于大偏心率轨道密集星历精密计算的快速处理方法

空间目标探测和编目是航天器安全的重要课题, 空间目标数量巨大, 造成轨道计算的工作量十分繁重. 分析方法虽然计算速度快, 却不能适应高精度观测资料的处理工作, 因而数值方法将成为目标轨道计算的重要方法. 空间目标编目工作普遍涉及密集星历的产生和计算问题, 针对这一问题的大偏心率轨道数值计算目前尚未形成兼具计算精度和计算效率的有效技术手段, 难以满足编目工作的处理要求. 在此背景下, 提出一种适用于大偏心率轨道密集星历精密计算的快速处理方法, 并通过数值实验对模型参数进行优选, 最后通过计算实例证实了该计算方案的优越性.     

GEO暗弱空间碎片目标搜索策略分析

在地球同步轨道特征的基础上,介绍了地球同步轨道空间碎片的运动特征。针对地球同步轨道暗弱空间碎片进行观测的搜索方案,考虑目标的预报误差以及视场的大小,用数学方法分别计算了同心圆搜索与爬楼梯搜索的成功概率,并由计算结果分析了两者的特征,认为在一般情况下,同心圆搜索方案具有更高的搜索效率。     

A Research on the Collision Probability Calculation of Space Debris for Nonlinear Relative Motions†

The calculation of collision probability is the foundation of collision detection and avoidance maneuver for space objects. Now an assumption of linear relative motion is usually applied in the calculation of collision probability and then the complex 3-dimensional problem can be reduced to a 2-dimensional integral of probability density function over the area of circle. However, if the relative velocity value is very small, the term of linear relative motion is not valid. So it is necessary to consider the calculation of collision probability for nonlinear relative motions. The method used to calculate collision probability for nonlinear relative motion is studied, and test cases are designed to justify the validity of this method. It is applicable to collision probability problems involving relative velocity and error covariance varying with time. The results indicate that it is necessary to calculate collision probability with this nonlinear method under certain circumstances. For example, for elliptical relative motions in Satellite Formation Flying, when the relative velocity is below 100 m/s, the relative error between the linear method and the nonlinear method exceeds 5%; for the problem of conjunction analysis of two satellites with circular orbits, when the relative velocity is below 10 m/s, the relative error is also larger than 1%. Some significant conclusions are obtained for the collision detection system of our country.     

Collision Probability for Earth-Crossing Asteroids Using Orbital Ranging

We introduce new techniques for the computation of the collision probability for Earth-crossing asteroids in the case of short observational arcs and/or small numbers of observations. The techniques rely on the orbital element probability density computed using statistical orbital ranging. We apply the techniques to the Earth-crossing asteroid 1998 OX₄with non-vanishing collision probability in numerous close approaches after the year 2012 (inclusive). We study the invariance of the collision probability in transformations between different orbital element sets, and develop a Spearman rank correlation measure for the validity of the linear approximation. We introduce an optimized, fast version of the statistical ranging method.     

The influence of the correlations between an asteroid’s orbital parameters on the estimation of the probability of planetary collision by the Monte Carlo method

The probability of an asteroid colliding with a planet can be estimated by the Monte Carlo method, in particular, through the statistical simulation of the possible initial conditions for the motion of an asteroid based on the probability density distribution set by the respective covariance matrix to be further projected with the orbital model onto the supposed time point of the collision. Hence, the collision probability is calculated as the ratio between the number of projected (virtual) asteroids striking the planet and their total number. The main problem is that different elements of the initial conditions (orbit or state vector) are correlated and, therefore, cannot be simulated independently. These correlations are reflected in the nondiagonal covariance matrix of the solution. The matrix is diagonalized by an orthogonal transformation. In the uncertainty domain constructed from the diagonal matrix elements, the initial values for each of the six orbital elements are simulated independently from the other elements, but with the accounting for their normal distribution. The program for calculating the normal distribution is based on the central limit theorem. Each sample of the initial values for the six orbital elements is transferred to the initial reference frame using an inverse transformation. Then, numerical integration is used to track the asteroid’s motion along the respective orbit to predict a possible impact event. Asteroids 99942 Apophis and 2007 WD5 are used as examples to show that disregarding the correlations when diagonalizing the covariance matrix to set the initial conditions may seriously distort the collision probability estimates. The paper gives the probabilities of the collisions of Apophis with the Earth and asteroid 2007 WD5 with Mars calculated by the author from observation sets showing nonzero collision probabilities. The author’s estimates are compared to those calculated by NASA.     

The electric charge distribution on interstellar grains

The results of the preceding paper are applied to a consideration of the motion of grains in a magnetic field, the calculation of particle collision cross-sections and charge effects in molecular synthesis.     

An extended canonical perturbation method

In this investigation, a procedure is described for extending the application of canonical perturbation theories, which have been applied previously to the study of conservative systems only, to the study of non-conservative dynamical systems. The extension is obtained by imbedding then-dimensional non-conservative motion in a 2n-dimensional space can always be specified in canonical form, and, consequently, the motion can be studied by direct application of any canonical perturbation method. The disadvantage of determining a solution to the 2n-dimensional problem instead of the originaln-dimensional problem is minimized if the canonical transformation theory is used to develop the perturbation solution. As examples to illustrate the application of the method, Duffing's equation, the equation for a linear oscillator with cubic damping and the van der Pol equation are solved using the Lie-Hori perturbation algorithm.This research was supported by the Office of Naval Research under Contract N00014-67-a-0126-0013.     

Energy exchange during collision of a pair of disc-sphere galaxies

We have considered the collision of a pair of disc-sphere galaxies under the impulsive approximation to study the variation of the energy change of the disc due to the passage of a spherical galaxy. Various collision parameters like the impact parameter the orientation of the disc galaxy and the relative velocity of the perturber were considered. It is shown that for small impact parameters and high relative velocities, a slightly inclined position of the disc galaxy produces maximum energy exchange. The energy exchange is observed to be asymmetric with respect to the direction of motion of the perturber.     

The Value of Ωo in a Colliding Bubble Universe

We present a calculation of the probability distribution of the invariant separation between the nucleation centers of colliding bubbles resulting from the decay of a false de Sitter space vacuum. We also discuss the probability of a collision with a `third' bubble. This study is motivated by the proposed `colliding bubble braneworld' scenario in which the value of Ω₀ today is a function of this invariant. This revised version was published online in July 2006 with corrections to the Cover Date.     

N-Body Simulation of a Deeply Penetrating Collision Between Unequal Galaxies

We study the tidal effects of a deeply penetrating collision between two spherical galaxies, one twice massive but less dense than the other, by numerical simulations. We consider the relative motion of the galaxies to be initially in a hyperbolic orbit. The collision parameters are so chosen that the primary (bigger) galaxy is just below the limit of disruption and the relative velocity of the pair is slightly in excess of the escape limit and the primary suffer greater tidal damage than the secondary. The primary develops a core halo structure and shows over all expansion while the secondary while the secondary shows contraction in the inner region and less significant expansion in the outer parts. The initially hyperbolic orbit is transformed into a parabolic orbit as a result of the collision. The result also indicate that the tidal interaction does not induce appreciable rotation in hyperbolic collision. We calculate the angle of deflection of the orbit and compare it with that computed using analytical work. The numerical work shows larger angle of deflection which is attributed to the large tidal effects of the bigger galaxy in the interpenetrating collision. This revised version was published online in July 2006 with corrections to the Cover Date.     

On Integrable Hamiltonians with Velocity Dependent Potentials

We study strongly and weakly integrable 2-dimensional Hamiltonian systems with velocity dependent potentials. We determine the set of conditions which must be satisfied in order to allow the existence of an independent second invariant polynomial in the momenta. We then investigate the linear case for which a complete solution of the problem can be obtained. We recover the classical set of linear strongly integrable systems and provide several new examples of weakly integrable systems whose equations of motion can be explicitly solved at a fixed value of the energy.     

Interaction of the lower thermosphere with the solid component of the interplanetary medium

We consider in this paper the motion of small meteoroids near to the Earth taking into account gravitation, acceleration and heating of particles in the upper atmosphere, and also the processes of thermal radiation, sputtering and evaporation.It is concluded that during an encounter of the Earth with a meteor stream a dust cloud can be formed only at very small geocentric velocities of the particles.We also carry out calculation of the ion-formation rate in the atmosphere due to the collision of ablated meteor atoms and air molecules reflected from a meteoroid with air molecules encountered. Meteor ionization makes the contribution necessary to the maintenance of the high E-region ionization. During annual meteor showers the rate of meteor ion-formation increases by not more than four times. Additional night sources of ionization of air molecules influence the relative number of atmospheric and meteor ions in the E-region. The contribution of the kinetic energy of meteor matter to the heating of the upper atmosphere is evaluated.