Characterizing space debris longitude-dependent distribution based on RAAN perturbation rate

The space debris environment is one of the major threats against payloads. Space debris orbital distribution is of great importance for space debris environment modeling. Due to perturbation factors, the Right Ascension of Ascending Node (RAAN) of space objects changes consistently, causing regular rotation of the orbit plane around Earth’s axis. Based on the investigation of the RAAN perturbation rate of concerned objects, this paper proposes a RAAN discretization method in order to present the space debris longitude-dependent distribution. Combined with two line element (TLE) data provided by the US Space Surveillance Network, the estimated value from RAAN discretization method is compared with the real case. The results suggest that using only the initial orbital data at the beginning of the time interval of interest, the RAAN discretization method is able to provide reliable longitude distribution of concerned targets in the next following period. Furthermore, spacecraft cumulative flux against space debris is calculated in this paper. The results suggest that the relevance between spacecraft RAAN setup and flux output is much smaller for LEO targets than MEO targets, which corresponds with the theory analysis. Since the nonspherical perturbation is the major factor for RAAN variation, the RAAN perturbation rate has little connection with the size of orbital objects. In other words, the RAAN discretization method introduced in this paper also applies to space debris of different size range, proposing a possible suggestion for the improvement of space debris environment engineering models.     

空间目标预警阈值确定分析

针对目前通常采用计算碰撞概率来进行空间目标碰撞预警的方法,为提高其评判标准的精度以达到提高航天器精准预警的目的,分析了目前空间目标碰撞概率阈值确定过程的总体框架.对阈值确定过程中所涉及的误差协方差矩阵确定方法、碰撞概率计算以及碎片通量计算方法进行了研究.以国际空间站（ISS）为例,通过计算其所在空间的碎片通量,分析其轨道受空间环境的影响情况,并与早期结果进行比较,得出其以往的碰撞概率阈值可能被高估的结论.      

基于多项式近似的空间碎片群体轨道预报算法

快速准确地分析空间碎片群轨道演化行为对于其他在轨航天器碰撞规避至关重要。在各摄动力的作用下,空间碎片群演化运动呈现出复杂的非线性特征。空间碎片群体个体数量巨大,如果通过对空间碎片群中每个空间碎片进行轨道积分来分析群体预报的方法会导致计算量过大。针对该问题,提出一种基于多项式近似的轨道快速预报分析方法。该方法将空间碎片群分为少量的标称碎片和其他大量关联碎片。针对标称碎片的轨道预报采用数值积分求解保证预报精度;而针对其他大量的关联碎片轨道预报问题,采用多项式泰勒展开半解析方法求解,从而在保证预报精度的前提下有效减少空间碎片群轨道预报的计算量。为了验证方法的有效性,对不同空间碎片群进行了轨道预报仿真。仿真结果表明,当轨道预报精度设定在1m范围内时,多项式近似算法的计算量较蒙特卡洛方法计算效率提高了2.2~17.2倍,验证了所提出方法的有效性。     

Debris flux comparisons from the Goldstone Radar,Haystack Radar,and Hax Radar prior,during, and after the last solar maximum

The continual monitoring of the low Earth orbit (LEO) debris environment using highly sensitive radars is essential for an accurate characterization of these dynamic populations. Debris populations are continually evolving since there are new debris sources, previously unrecognized debris sources, and debris loss mechanisms that are dependent on the dynamic space environment. Such radar data are used to supplement, update, and validate existing orbital debris models. NASA has been utilizing radar observations of the debris environment for over a decade from three complementary radars: the NASA JPL Goldstone radar, the MIT Lincoln Laboratory (MIT/LL) Long Range Imaging Radar (known as the Haystack radar), and the MIT/LL Haystack Auxiliary radar (HAX). All of these systems are highly sensitive radars that operate in a fixed staring mode to statistically sample orbital debris in the LEO environment. Each of these radars is ideally suited to measure debris within a specific size region. The Goldstone radar generally observes objects with sizes from 2 mm to 1 cm. The Haystack radar generally measures from 5 mm to several meters. The HAX radar generally measures from 2 cm to several meters. These overlapping size regions allow a continuous measurement of cumulative debris flux versus diameter from 2 mm to several meters for a given altitude window. This is demonstrated for all three radars by comparing the debris flux versus diameter over 200 km altitude windows for 3 nonconsecutive years from 1998 to 2003. These years correspond to periods before, during, and after the peak of the last solar cycle. Comparing the year to year flux from Haystack for each of these altitude regions indicate statistically significant changes in subsets of the debris populations. Potential causes of these changes are discussed. These analysis results include error bars that represent statistical sampling errors.     

空间碎片自然衰减和太阳活动

分析研究了空间碎片数随太阳辐射流量Ｆ１０．７的变化;给出预报Ｆ１０．７长期变化的计算方法和预测空间碎片数的数学模型。结果显示：①强太阳活动造成空间碎片年增长率下降;②空间碎片数与太阳活动１１年变化密切相关,相关数为０．９;③空间碎片增长率约为发射率的两倍;④若发射率保持不变,则到２０２０年,大于１０ｃｍ的碎片数将达到１４５００;⑤若小碎片的增长为大碎片增长的两倍,则到２０２０年,大于１ｃｍ的碎片数可达１２５０００。     

Atmospheric drag modelling for orbital micro-debris at LEO altitudes

Data from satellite impact experiments and the scanning of recovered spacecraft offers an extended timebase to examine, using a consistent methodology, the microparticle fluxes. New penetration data from the TiCCE experiment on Eureca /1, 2/ adds to this database and shows that - despite an expected growth in the micro-debris flux - the observed flux is not greater than either LDEF or SMM. The question arises: “is this consistent with the micro particle flux being dominated by space debris or by meteoroids”.

To assist this assessment, numerical modelling using the Gear method /3/ of explicit time integration of the atmospheric drag lifetime of micron dimensioned orbital debris in both circular (LEO) and eccentric (GTO) orbits has been performed for the relevant space exposures. Results are applied to the data to examine whether the recent variations in flux can be attributed to varying levels of, orbital micro-debris caused by atmospheric drag and its changes during the solar cycle.     

基于解体事件的空间碎片轨道演化算法研究

针对航天器解体事件所生成的空间碎片的演化过程,进行了数学分析,确定了新生成的空间碎片的速度增量,在该增量作用下碎片轨道会发生变更,本文根据该增量得出了空间碎片在轨道变更后的轨道根数,分析了在大气阻力摄动作用下,空间碎片的数目和轨道分布的演化情况,给出了相关结果,结果表明此算法可行。     

LEO空间碎片甚短弧角度数据初轨确定方法对比

光学观测是空间目标观测中最常见的一种观测方式。采用扫描模式工作时光学观测得到的观测弧段弧长通常很短,有时甚至不到被观测空间目标运行周期的1%,这样的角度数据被称为甚短弧角度数据。基于近圆LEO空间碎片地基实测场景,研究比较仅利用角度数据进行初始轨道确定常用方法的性能差异,分析观测弧长对不同初轨确定算法的定轨成功率和误差的影响,为初轨确定工作提供参考。对比分析了常用的几种方法,包括Laplace方法、Gauss方法、Gooding方法和近几年提出的距离搜索算法等。大规模实测数据处理结果显示,距离搜索算法的成功率高于90%,初轨半长轴统计误差仅为25 km。初轨结果表明,距离搜索算法定轨成功率高于其他算法。研究成果可为解决空间碎片初轨确定问题提供参考。      

卫星在轨太阳辐射热流的简化计算方法

针对卫星在轨太阳辐射热流计算过程中计算参数多,计算过程复杂的问题,提出了一种简化的计算方法。该方法在分析卫星、地球和太阳三者之间空间几何关系的基础上,建立了新的计算坐标系,在计算坐标系中对卫星、地球和太阳的位置进行了重新规定,并在此坐标系中推导了卫星太阳辐射热流的计算公式。运用此方法对卫星太阳辐射热流进行分析求解时,轨道参数之间的空间角度关系更为简单,仅需对7个主要参数进行计算,与传统方法相比较计算量减少了约2/3。     

Improved orbit predictions using two-line elements

The density of orbital space debris constitutes an increasing environmental challenge. There are two ways to alleviate the problem: debris mitigation and debris removal. This paper addresses collision avoidance, a key aspect of debris mitigation. We describe a method that contributes to achieving a requisite increase in orbit prediction accuracy for objects in the publicly available two-line element (TLE) catalog. Batch least-squares differential correction is applied to the TLEs. Using a high-precision numerical propagator, we fit an orbit to state vectors derived from successive TLEs. We then propagate the fitted orbit further forward in time. These predictions are validated against precision ephemeris data derived from the international laser ranging service (ILRS) for several satellites, including objects in the congested sun-synchronous orbital region. The method leads to a predicted range error that increases at a typical rate of 100 m per day, approximately a 10-fold improvement over individual TLE’s propagated with their associated analytic propagator (SGP4). Corresponding improvements for debris trajectories could potentially provide conjunction analysis sufficiently accurate for an operationally viable collision avoidance system based on TLEs only.     

空间碎片的空间密度算法研究

由于空间碎片的影响, 空间环境日益恶劣,有必要建立空间碎片环境工程模型对空间碎片撞击航天器进行风险评估.本文研究了空间碎片环境模型中的重要环节, 即碎片的空间密度问题,在统计理论与椭圆轨道理论基础上,分析及推导了空间碎片在空间中的分布状况及空间密度,并得出了碎片空间密度的空间坐标函数解析表达式.同时对引入假设条件的合理性进行了讨论,并利用双行元数据对结论进行了验证, 利用本文方法得出的结果与双行元数据吻合.      

Analysis of laser ranges and angular measurements data fusion for space debris orbit determination

In the framework of space debris, the orbit determination process is a fundamental step, both, for researchers and for satellite operators. The accurate knowledge of the orbit of space debris objects is needed to allow space debris characterization studies and to avoid unnecessary collision avoidance maneuvers.The accuracy of the results of an orbit determination process depends on several factors as the number, the accuracy, the kind of processed measurements, their distribution along the orbit, and the object-observer relative geometry. When the observation coverage of the target orbit is not homogeneous, the accuracy of the orbit determination can be improved processing different kind of observables. Recent studies showed that the satellite laser ranging technique can be successfully applied to space debris.In this paper, we will investigate the benefits of using laser ranges and angular measurements for the orbit determination process. We will analyze the influence of the number of used observations, of the covered arc of orbit, of each observable, and of the observation geometry on the estimated parameters. Finally, using data acquired on short observation arcs, we analyze the achievable accuracies for the orbital regimes with the highest space debris density, and to the consequences of the data fusion on catalog maintenance operations. The results shown are obtained using only real data (both angular and laser measurements) provided by sensors of the Swiss Optical Ground Station and Geodynamics Observatory Zimmerwald owned by the Astronomical Institute of the University of Bern (AIUB) and for some studies also using ranges provided from other stations of the International Laser Ranging Service (ILRS).     

姿态异常下的星体自旋角速度确定方法

摘要： 针对在轨姿态异常后星体高速自旋情况,开展星体自旋角速度确定方法研究.提出一种基于太阳敏感器测量数据确定自旋角速度的方法,并对自旋角速率确定误差进行分析,得到各误差源对确定精度的影响关系;基于角速率确定误差分析结论,给出根据角速度大小选取不同时间间隔测量数据的策略,通过大时间间隔测量数据的选取,保证小角速度情况下的确定精度.所提出方法的有效性通过数学仿真验证,并在实际应用中基于太阳敏感器遥测数据获取在轨姿态异常卫星角速度.     

基于引力场不对称性的三体系统轨道自主导航

以月球背面的中继通信为背景,提出了基于三体系统引力场不对称特性的星–星测距自主定轨方案。该方案以环月极轨卫星和地–月L2点Halo轨道卫星组成中继通信网,以实现对月球两极和背面的覆盖。通过采集极轨卫星与Halo轨道卫星的测距信息,结合卡尔曼滤波在日–地–月动力学模型下获得两颗卫星的绝对轨道。数值仿真结果表明:本文方法能将导航的位置精度和速度精度分别提高到百米和厘米/秒量级。该自主导航方法还可以扩展到不规则引力场小天体附近星群运动的自主导航。     

空间碎片碰撞预警研究

介绍了空间碎片的分布和危害，阐明了航天器进行碎片预警规避的必要性，讨论了碎片碰撞预警技术中的关键问题，用已有的碰撞和规避实例对自行研制的软件进行了计算检验，结果证明了软件的正确性，也说明了国内进行碎片预警工作的可行性．     

Assessment of the close approach frequency and collision probability for satellites in different configurations of large constellations

The Earth orbital environment is drastically changing due to an intensification of the space activities. In particular, several projects of large constellations, proposed for the next years for communications purpose like global internet access, Internet of Things, or for Earth observations, will lead to the deployment of several thousands of new satellites at an unprecedented rate. It is a crucial challenge for space traffic management, which will deal with a great number of satellite conjunctions, potentially causing a collision with damaging consequences for the constellation itself and the space environment sustainability.In this paper, we investigate the close approach frequency and the cumulative collision probability for each referenced constellation. For this purpose, we compute the orbital evolution of satellites in different constellations during the lifecycle, from the deployment to the decommissioning, and we apply the CUBE algorithm and the Foster method to assess the collision probability with the background space debris population assuming a constant uncertainty in position. We show the variation of risk defined by the close approach frequency and the cumulative collision probability as a function of the proposed configuration. In particular, satellites of the Iridium and Kuiper constellation, but also satellite of the Telesat constellation on polar orbits are the most exposed at a collision. Moreover, the decommissioning phase contribute for a major part to the final cumulative collision probability.     

空间系绳碎片碰撞生存能力研究

空间系绳结构和几何尺寸对其在复杂空间环境中抵抗碎片碰撞的能力有显著影响.本文根据系绳-碎片碰撞模型和泊松分布,计算了双股系绳和带状系绳被碎片割断的概率,分析了太空碎片对系绳生存能力可能造成的影响.双股系绳是由两条平行系绳每隔一段距离打结连接构成,带状系绳可视为一种横截面为矩形的特殊单股系绳.首先对单股系绳被碎片割断的概率进行建模,然后构建双股系绳和带状系绳生存能力函数,最后根据空间碎片环境模型,对比分析具有不同结构、不同尺寸的系绳的生存能力.仿真结果表明,相较于单股系绳,双股系绳和带状系绳的生存能力有明显提高.      

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.