空间物体解体碎片云的长期演化建模与分析

空间碎片云由空间物体解体产生的大量空间碎片组成,由于其相对集中地分布在有限的空间内,将会对临近航天器产生较大的碰撞威胁。为了分析解体碎片云长期分布特点,文章首先利用数值积分方法对空间碎片云短期分布规律进行了研究;在此基础上,针对处于环状分布的碎片云,根据碎片所在的轨道高度和具有的面质比值,将碎片划分到不同分组,以每个组作为研究对象,建立了描述碎片云在大气阻力作用下的解析演化模型。模型避免了对单个解体碎片的运动状态进行积分,可大大降低对计算资源和计算时间的需求。考虑在高度为1422km 圆轨道上运行的物体,解体产生了1780个碎片,利用解析演化模型得到碎片云未来50年内的演化分布状态。数值结果表明,碎片云的峰值密度在解体物体轨道高度附近,并在大气阻力作用下向更大高度区间内扩散;较低高度区间内碎片密度具有先增加,然后在大气阻力作用下不断减少的特点。     

Practical method to identify orbital anomaly as spacecraft breakup in the geostationary region

Identifying spacecraft breakup events is an essential issue for better understanding of the current orbital debris environment. This paper proposes an observation planning approach to identify an orbital anomaly, which appears as a significant discontinuity in archived orbital history, as a spacecraft breakup. The proposed approach is applicable to orbital anomalies in the geostationary region. The proposed approach selects a spacecraft that experienced an orbital anomaly, and then predicts trajectories of possible fragments of the spacecraft at an observation epoch. This paper theoretically demonstrates that observation planning for the possible fragments can be conducted. To do this, long-term behaviors of the possible fragments are evaluated. It is concluded that intersections of their trajectories will converge into several corresponding regions in the celestial sphere even if the breakup epoch is not specified and it has uncertainty of the order of several weeks.     

Observation campaign dedicated to 1968-081E fragments identification

This paper proposes a comprehensive approach to associate origins of space objects newly discovered during optical surveys in the geostationary region with spacecraft breakup events. A recent study has shown that twelve breakup events would be occurred in the geostationary region. The proposed approach utilizes orbital debris modeling techniques to effectively conduct prediction, detection, and classification of breakup fragments. Two techniques are applied to get probable results for origin identifications. First, we select an observation point where a high detection rate for one breakup event among others can be expected. Second, we associate detected tracklets, which denotes the signals associated with a physical object, with the prediction results according to their angular velocities. The second technique investigates which breakup event a tracklet would belong to, and its probability by using the k-nearest neighbor (k-NN) algorithm.     

Taurid complex meteoroids detected near aphelion with Ulysses

Between 3.4 and 4.0 AU the dust detection system aboard the Ulysses spacecraft showed an increase in detection rate for particles with masses greater than 5 × 10⁻¹³ g. The spacecraft meteoroid encounter geometry indicates highly eccentric orbits detected near aphelion. The outer limit of the enhanced flux is imposed as meteoroids on such orbits move outside the aperture of the dust detector. The inner edge of the enhanced flux would be consistent with the aphelion distance acquired by 50-200 μm particles evolving for 10-20 kyr under Poynting-Robertson drag from an Encke type orbit. We propose such meteoroids provide a source population from which collisional fragmentation produces particles in the mass range to which the Ulysses detector is sensitive. Daughter fragments produced away from the aphelia of the parent orbits, a 2.2 AU, e 0.85, enter hyperbolic orbits which are not evident in the Ulysses data. The spatial density of fragments from collisions very near aphelion drops off rapidly as they evolve inward under Poynting-Robertson drag while collisions closer to 3.4 AU leave the subsequent peak density outside that radius for a significant fraction of the fragment's subsequent lifetime. The rapid orbital evolution for these collision fragments implies a recent breakup and probably a large reservoir of parent meteoroids.     

Characterization of the cataloged Fengyun-1C fragments and their long-term effect on the LEO environment

The intentional breakup of Fengyun-1C on 11 January 2007 created the most severe orbital debris cloud in history. The altitude where the event occurred was probably the worst location for a major breakup in the low Earth orbit (LEO) region, since it was already highly populated with operational satellites and debris generated from previous breakups. The addition of so many fragments not only poses a realistic threat to operational satellites in the region, but also increases the instability (i.e., collision cascade effect) of the debris population there.     

Finite element reconstruction approach for on-orbit spacecraft breakup dynamics simulation and fragment analysis

Breakup model is the key area of space debris environment modeling. NASA standard breakup model is currently the most widely used for general-purpose. It is a statistical model found based on space surveillance data and a few ground-based test data. NASA model takes the mass, impact velocity magnitude for input and provides the fragment size, area-to-mass ratio, velocity magnitude distributions for output. A more precise approach for spacecraft disintegration fragment analysis is presented in this paper. This approach is based on hypervelocity impact dynamics and takes the shape, material, internal structure and impact location etc. of spacecraft and impactor, which might greatly affect the fragment distribution, into consideration. The approach is a combination of finite element and particle methods, entitled finite element reconstruction (FER). By reconstructing elements from the particle debris cloud, reliable individual fragments are identified. Fragment distribution is generated with undirected graph conversion and connected component analysis. Ground-based test from literature is introduced for verification. In the simulation satellite targets and impactors are modeled in detail including the shape, material, internal structure and so on. FER output includes the total number of fragments and the mass, size and velocity vector of each fragment. The reported fragment distribution of FER shows good agreement with the test, and has good accuracy for small fragments.     

基于航天器解体事件的空间碎片寿命算法

研究了针对航天器解体事件所生成的空间碎片的寿命计算方法.给出了基于NASA标准航天器解体模型的航天器解体算法.该算法生成的一系列碎片参数,将作为寿命计算的初始条件.总结了现有求解碎片寿命的算法,并提出了一种半分析算法.该算法运用平均根数法的思路,计算了在J2摄动项的影响下,碎片的半长轴和偏心率的变化率;并采用微分积分法预报半长轴和偏心率随时间的变化.为了适应时变大气模型,该算法限制了计算步长.通过与数值法的比较分析了算法的计算速度和精度.选用了3种大气模型:SA76、GOST和MSIS-00,分析了不同大气模型在计算碎片寿命之间的差异.通过与P-78卫星解体事件的实测数据对比验证了整个算法的正确性.      

Strategy to search fragments from breakups in GEO

This paper proposes a strategy to search fragments from breakups in the Geosynchronous Earth Orbit (GEO) region based upon population prediction and motion prediction by means of ground-based optical observations. Breakup fragments have uncertainties in the states such as their position and motion, or even in their existence. Population prediction and motion prediction resolve those uncertainties. Population prediction evaluates the time-averaged distribution of fragments, whose position at a given time is unknown, in the celestial sphere. Motion prediction evaluates the expected motion of fragments appeared in image series acquired by a telescope’s CCD camera. This paper logically describes procedures of the search strategy, and provides mathematical expressions of population prediction and motion prediction. This paper also validates the search strategy via actual observations, in which a confirmed breakup in the GEO region is selected as a target. It is concluded that the proposed strategy is valid even for searching uncataloged fragments from breakups in the GEO region.     

在轨航天器撞击解体特性分析与计算

对在轨航天器撞击解体问题进行了研究, 基于NASA 标准解体模型, 给出了在轨航天器撞击解体算法, 重点分析了解体计算时应该满足的几个约束条件. 编写了该算法的通用仿真计算程序, 并通过与P-78 卫星解体事件的实测数据比较验证了算法和程序的正确性. 研究结果对预测分析在轨撞击事件的毁伤特性具有重要的参考价值.      

The critical energy density and the inelasticity coefficient for asteroidal catastrophic collisions

The experimental results on high-velocity impacts reported in the literature are analyzed in detail, with the purpose: (a) to check the possibility of applying to asteroidal collisions, without a size-dependent scaling, the critical energy densities associated with various degrees of fragmentation; (b) to ascertain which fraction of the projectile's energy is converted into kinetic energy of fragments after a catastrophic breakup.

The results of our analysis on these two problems indicate that: (a) the critical energy density is independent on size only for super-catastrophic events, when no massive core survives, while it slowly decreases for larger targets when the fragmentation is only partial (barely-catastrophic collisions). Therefore the “energy gap” between cratering and complete distruction is probably wider for the asteroids than for the small experimental targets. (b) the inelasticity coefficient (i.e., the resulting fraction of kinetic energy) depends both on the impact velocity and on the projectile-to-target mass ratio; for asteroidal catastrophic collisions, it probably ranges from 10⁻² to 10⁻¹.     

High-velocity impact experiments needed to improve our understanding of the asteroids

The lifetime of almost all the asteroids against catastrophic impact events is less than the age of the solar system, implying that the asteroids can be considered as outcomes of catastrophic collisions. Therefore to understand their physical properties (structure, shape, rotation, regolith development) and their family memberships (since families are generated by the escape of breakup fragments), a systematic knowledge of the outcomes of catastrophic impacts under a variety of conditions seems needed. In particular, interesting fields to be explored by laboratory experiments are: the dependence of the critical energy densities associated with various degrees of fragmentation on the target's size and composition; the velocity distribution of the fragments and the inelasticity of the process in different cases; the shape of the fragments and its possible correlation with other quantities; the way a dust- or regolith-covered target affects the collisional outcomes; the angular momentum partitioning and the rotation of the fragments. On this latter problem very few experimental results are presently available; on the other hand, the rotation of small asteroids presents several intriguing “anomalies”.

A significant progress of our understanding of asteroid collisional evolution and related phenomena can be provided by new laboratory experiments of collisional breakup. The targets should have spherical and/or irregular shape (up to axial ratios of the order of 2), and should be made of (possibly different) geological materials. The interesting projectile velocities are of the order of the relative velocities commonly found among asteroids, i.e., in the range 1 to 10 Kms⁻¹. In order to get catastrophic collisions, the ratio of the projectile kinetic energy to the target mass (≡E/M) has to be chosen within a “critical” range (for basalt targets, from 10⁶ to 10⁸ erg/g). In some particular cases, this kind of experiments has been already performed in past (Gault and Wedekind [10]; Fujiwara et al. [7]; Fujiwara and Tsukamoto [9]); however the generalization of the results to a wide range of experimental conditions is lacking, and many problems of outstanding importance to model asteroid evolution are still completely open.     

解体速度增量计算方法研究

解体速度增量是解体事件强度的重要指征, 它决定了解体产生碎片的轨道分布. 通过分析解体速度增量可以推断解体强度, 确定解体形式. 解体速度增量有两种计算方法, 即轨道位置演化法和轨道面相交法. 轨道位置演化法是根据解体前后轨道速度的变化直接得到解体速度增量; 而轨道面相交法是利用母体以及解体碎片的球面三角几何关系, 根据解体碎片的倾角和升交点赤经变化, 以及母体轨道的倾角和近地点辐角, 计算解体时刻母体轨道的真近点角, 从而得到解体的时间和速度增量. 相比来说, 轨道位置演化法适用于数据精度高, 解体高度高情况下的解体事件分析, 而轨道面相交法适用于解体高度低, 碎片数据公布时间较为滞后的解体事件分析. 根据解体速度增量的计算方法及其原理, 对两种方法的适用性进行了比较和讨论, 并选取已经发生的三次解体事件, 利用美国公布的TLE数据, 针对具体情况选择计算方法, 给出了三次解体事件发生的时间和解体碎片在空间三个方向上的速度增量.      

Instability of the present LEO satellite populations

Several studies conducted during 1991–2001 demonstrated, with some assumed launch rates, the future unintended growth potential of the Earth satellite population, resulting from random, accidental collisions among resident space objects. In some low Earth orbit (LEO) altitude regimes where the number density of satellites is above a critical spatial density, the production rate of new breakup debris due to collisions would exceed the loss of objects due to orbital decay.     

Assessment of the consequences of the Fengyun-1C breakup in low Earth orbit

On 11 January 2007, the People’s Republic of China conducted a successful anti-satellite test against one of their defunct polar-orbiting weather satellites. The target satellite, called Fengyun-1C, had a mass of 880 kg and was orbiting at an altitude of about 863 km when the collision occurred. Struck by a direct-ascent interceptor at a speed of 9.36 km/s, the satellite disintegrated, spreading the cataloged fragments between 200 and 4000 km, with the highest concentration near the breakup height. By the end of April 2008, 2377 pieces of debris, including the original payload remnant, had officially been cataloged by the US Space Surveillance Network. Of these, nearly 1% had reentered the Earth’s atmosphere. This deliberate act is the largest debris-generating event on record, and its consequences will adversely affect circumterrestrial space for many years.     

一种基于TLE数据的轨道异常分析方法

空间在轨物体的轨道异常是航天工程及预警领域普遍关注的问题,及时发现轨道异常意义重大,通过分析空间物体的轨道异常,可以及时发现和识别规避事件或碰撞事件,还可以了解监测网的能力.本文提出一种基于TLE数据的简单的轨道异常分析方法——长半轴变化法.该方法快速有效,应用到低轨在用卫星和美俄解体碎片的异常分析中,异常物体正确识别率可达到100%;对美俄解体碎片进行轨道异常分析后得出,美国空间监视网可以稳定探测90%以上的解体碎片.      

小行星防御动能撞击效果评估

以动能撞击防御潜在威胁小行星概念为背景,采用物质点法(Material Point Method,MPM)模拟了铝弹高速撞击S型小行星的过程,将撞击结果导入引力N体–离散元动力学模型中,对其后续演化过程进行仿真,并分析了撞击后碎片对地球的威胁指数。结果显示小行星在高速撞击的作用下部分破碎,大量碎片以与撞击方向相反的速度向外喷射,从而提升了小行星的撞击偏移效果。研究采用了两种不同结构的小行星模型:完整结构(monolithic structure)的小行星在遭受撞击后会喷射出比原小行星小得多的碎片,而碎石堆结构(rubble-pile structure)的小行星在撞击作用下可分裂成大小和速度分布较为均匀的碎片。威胁指数的分析表明动能撞击方式确实有效减小了小行星的威胁程度,撞击后的最大剩余碎片可被成功偏移至安全轨道,但仍有部分碎片会与地球相撞。与完整结构相比,针对碎石堆结构小行星的撞击防御的总体效果更好,次生灾害主要为大质量碎片的撞击。研究方法可用于未来开展防御小行星的动能撞击任务的撞击条件选择和撞击结果预估。     

Faster algorithm of debris cloud orbital character from spacecraft collision breakup

Space debris is polluting the space environment. Collision fragment is its important source. NASA standard breakup model, including size distributions, area-to-mass distributions, and delta velocity distributions, is a statistic experimental model used widely. The general algorithm based on the model is introduced. But this algorithm is difficult when debris quantity is more than hundreds or thousands. So a new faster algorithm for calculating debris cloud orbital lifetime and character from spacecraft collision breakup is presented first. For validating the faster algorithm, USA 193 satellite breakup event is simulated and compared with general algorithm. Contrast result indicates that calculation speed and efficiency of faster algorithm is very good. When debris size is in 0.01–0.05 m, the faster algorithm is almost a hundred times faster than general algorithm. And at the same time, its calculation precision is held well. The difference between corresponding orbital debris ratios from two algorithms is less than 1% generally.     

A simple and valid analysis method for orbit anomaly detection

A simple analysis method for orbit anomaly detection, called semi-major axis change method (SACM) was presented by using a relationship between the change of orbit parameters and velocity increments. In this method, the mean value and standard deviation of the semi-major axis change in different time intervals were first calculated according to historical data. Then, these two parameters, the mean value and standard deviation of the semi-major axis change, are chosen as basis variables and combined as an anomalous criterion. For orbit objects with different characteristic, anomalous thresholds were given in different time intervals for identifying the anomalies of the orbital objects. Finally, this method is used for low earth orbit (LEO) satellites and American–Russian breakup debris. By adopting this method, the characteristics of the orbit change were given. The accuracy rate of anomaly analysis for LEO satellites and American–Russian breakup debris can reach to 100%, which demonstrates that the method was rapid and valid.     

Substorms in the inner plasma sheet

Thin Current Sheets (TCS) are regularly formed prior to substorm breakup, even in the near-Earth plasma sheet, as close as the geostationary orbit. A self-consistent kinetic theory describing the response of the plasma sheet to an electromagnetic perturbation is given. This perturbation corresponds to an external forcing, for instance caused by the solar wind (not an internal instability). The equilibrium of the configuration of this TCS in the presence of a time varying perturbation is shown to produce a strong parallel thermal anisotropy (T T) of energetic electrons and ions (E>50keV) as well as an enhanced diamagnetic current carried by low energy ions (E<50keV). Both currents tend to enhance the confinement of this current sheet near the magnetic equator. These results are compared with data gathered by GEOS-2 at the geostationary orbit, where the magnetic signatures of TCS, and parallel anisotropics are regularly observed prior to breakup. By ensuring quasi-neutrality everywhere we find, when low frequency electromagnetic perturbations are applied, that although the magnetic field line remains an equipotential to the lowest order in T_e/T_i, a field-aligned potential drop exists to the next order in (T_e/T_i). Thus the development of a TCS implies the formation of a field-aligned potential drop ( few hundred volts) to ensure the quasi-neutrality everywhere. For an earthward directed pressure gradient, a field-aligned electric field, directed towards the ionosphere, is obtained, on the western edge of the perturbation (i.e. western edge of the current sheet). Thus field aligned beams of electrons are expected to flow towards the equatorial region on the western edge of the current sheet. We study the stability of these electron beams and show that they are unstable to “High Frequency” (HF) waves. These “HF” waves are regularly observed at frequencies of the order of the proton gyrofrequency (f_H+) just before, or at breakup. The amplitude of these HF waves is so large that they can produce a strong pitch-angle diffusion of energetic ions and a spatial diffusion that leads to a reduction of the diamagnetic current. The signature of a fast ion diffusion is indeed regularly observed during the early breakup; it coincides with the sudden development of large amplitude transient fluctuations, ballooning modes, observed at much lower frequencies (fH+). These results suggest that the HF waves, generated by field-aligned electron beams, provide the dissipation which is necessary to destabilize low frequency (ballooning) modes.