SGP4/SDP4模型用于空间碎片轨道预测的精度分析

为保证航天任务的顺利完成 ,必须采用一定的模型 ,对可能威胁目标轨道的空间碎片进行跟踪预测。文中首先给出标称轨道的计算模型 ;接着介绍两行轨道根数 (TLE)和考虑了简化常规 /深空扰动的近似解析解模型 (SGP4/SDP4) ,并提供TLE使用的坐标系和惯性系之间的转换 ;然后以典型轨道为例 ,分析SGP4/SDP4与标称轨道的偏差。运算结果表明SGP4/SDP4运算速度快 ,满足一定精度 ,可以用于空间碎片的轨道预测和初步威胁评估。     

基于驻留时间比的近地空间碎片环境建模

为分析近地空间碎片的分布规律,提出了一种以碎片在空间网格内驻留时间为基础的碎片环境统计建模方法.该方法利用多项式拟合和求根方法统计碎片在空间网格内的停留时间,获取模型基础数据,并据此采用多项式预测、插值和时间序列分析等技术,综合分析空间碎片的分布与演化规律.给出了一个基于双行根数(TLE,Two Line Elements)数据的建模实例,该实例通过了ORDEM2000模型的对比验证,并获得了一些更精细的近地空间碎片环境特征.所得建模方法和分析结论可为长期运行的近地航天器轨道设计、碰撞风险评估及防护等提供技术支撑.     

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。     

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.      

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。     

基于目标特性的航天器太阳光压面积计算方法

太阳光压是影响深空探测航天器轨道确定与预报精度最主要的摄动力.针对实际任务需求，采用了一种基于目标特性的光压面积建模与计算方法，根据航天器形状、尺寸、表面材料以及材料光学特性等信息，实现了分析型光压模型的建立与求解，提高了计算效率和精度，可快速计算目标在光照方向上的光压面积、投影面积以及光压比例因子等参数.通过长方体光压面积理论值与仿真值的对比，验证了该方法的准确性和有效性.针对复杂结构探测器开展了光压面积计算，可为深空探测航天器精密定轨中的光压模型解算、定轨及预报提供参考.      

雷达波束驻留模式下空间碎片数量的置信区间估计

碎片数量估计是空间碎片环境统计特征描述的重要内容之一,对于空间碎片环境模型验证、航天器碰撞风险分析以及碎片数量增长趋势预测有重要意义.针对波束指向正东、正南任意仰角的雷达波束驻留(Beam-park)模式(天顶指向是波束指向仰角为90°时的特例),给出了一种估计碎片数量置信区间的方法.对于给定轨道高度范围内一个具有穿越雷达波束可能性(即雷达散射截面足够大,且轨道倾角相对测站纬度足够大)的碎片,将其是否真正穿越波束这一随机事件用(0-1)分布来建模,根据所采集的轨道高度和倾角数据,计算出该轨道高度范围内碎片穿越波束的平均概率,进而采用中心极限定理来估计碎片数量的置信区间.仿真结果表明了方法的有效性.      

载人月球极地探测定点返回轨道设计

针对载人月球极地探测任务，对定点返回轨道优化设计问题进行了研究。根据月球极地轨道的特性，介绍了三种返回轨道机动方案。结合三脉冲变轨方案，采用了从初步计算到精确计算的串行求解策略，对定点返回轨道进行优化设计。初步计算阶段，建立了基于近月点伪参数的三段二体拼接模型，将三脉冲机动段与月球逃逸段解耦，求解轨道初值；精确计算阶段，提出了两段拼接方法，分别进行逆向和正向高精度数值积分。经过仿真测试，验证了该策略求解的有效性和准确性。最后，通过大量的仿真计算，分析了定点返回轨道的特性。研究结论对未来载人月球极地探测定点返回轨道方案的设计具有重要的参考价值。     

基于期望最大算法的空间事件及异常值探测

美国ELSET数据库提供的TLE数据是目前使用最广泛的数据,在热层大气密度反演、弹道系数估计、碰撞预警等领域具有重要作用。受空间环境扰动、空间事件以及TLE产生过程等共同影响,ELSET数据库包含大量亟待清理的异常值和识别的空间事件,例如发布错误的TLE、轨道根数异常和Bstar异常。现有方法在清理异常轨道根数时缺乏统一性,需要使用不同的技术,清理流程较为繁杂,并且仅适用于特定轨道区域的少数目标。为克服现有方法的弊端,提出了一种基于期望最大算法的滑动窗口–多项式拟合预报方法,对含有轨道机动的碎片以及受空间环境影响的碎片进行异常值与空间事件探测。研究表明,该方法能够灵活处理不同空间环境下的异常值与空间事件探测,具有普适性,适用于所有轨道碎片。      

基于相控阵雷达波束篱笆的空间碎片数量与分布估计方法

随着载人航天与空间站等航天活动的增多,不能有效防护、也无法定期跟踪和编目的小尺寸(尤其是1～10 cm)碎片的危害越来越受到关注,这些碎片信息的获取依赖于统计采样技术.针对简化的相控阵雷达波束篱笆空间碎片探测模式,提出了一种采用统计技术估计空间碎片总数量以及高度和倾角分布的方法.将碎片穿越波束篱笆的过程用Poisson分布来建模,根据观测时段内穿越波束篱笆目标的平均到达率及测量的轨道高度和倾角数据来估计给定轨道高度范围或倾角范围内碎片的数量,进而得到碎片的总数量以及碎片数量随轨道高度或倾角的分布.在获取雷达散射截面信息时,该方法还可用于估计碎片数量随尺寸的分布.通过仿真实验验证了该方法的有效性.      

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．     

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).     

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.     

一种高效的计算卫星轨道寿命的方法

关于在大气阻力作用下卫星生存寿命的估计 ,提出了一种高效的数值方法 ,称为微分 -积分法。它的实质是以轨道要素的平均变化率为基础的微分方程 ,而方程的右端包含定积分。与传统方法比较验证了此新方法的正确性 ,并且显示了它的极高效率。在诸如空间碎片减缓这种需要非常大量的计算卫星寿命的问题中 ,新方法的价值得到充分体现。     

Analysis of the orbit lifetime of CubeSats in low Earth orbits including periodic variation in drag due to attitude motion

It is estimated that more than 22,300 human-made objects are in orbit around the Earth, with a total mass above 8,400,000 kg. Around 89% of these objects are non-operational and without control, which makes them to be considered orbital debris. These numbers consider only objects with dimensions larger than 10 cm. Besides those numbers, there are also about 2000 operational satellites in orbit nowadays. The space debris represents a hazard to operational satellites and to the space operations. A major concern is that this number is growing, due to new launches and particles generated by collisions. Another important point is that the development of CubeSats has increased exponentially in the last years, increasing the number of objects in space, mainly in the Low Earth Orbits (LEO). Due to the short operational time, CubeSats boost the debris population. One of the requirements for space debris mitigation in LEO is the limitation of the orbital lifetime of the satellites, which needs to be lower than 25 years. However, there are space debris with longer estimated decay time. In LEÓs, the influence of the atmospheric drag is the main orbital perturbation, and is used in maneuvers to increment the losses in the satellite orbital energy, to locate satellites in constellations and to accelerate the decay.The goal of the present research is to study the influence of aerodynamic rotational maneuver in the CubeSat?s orbital lifetime. The rotational axis is orthogonal to the orbital plane of the CubeSat, which generates variations in the ballistic coefficient along the trajectory. The maneuver is proposed to accelerate the decay and to mitigate orbital debris generated by non-operational CubeSats. The panel method is selected to determine the drag coefficient as a function of the flow incident angle and the spinning rate. The pressure distribution is integrated from the satellite faces at hypersonic rarefied flow to calculate the drag coefficient. The mathematical model considers the gravitational potential of the Earth and the deceleration due to drag. To analyze the effects of the rotation during the decay, multiple trajectories were propagated, comparing the results obtained assuming a constant drag coefficient with trajectories where the drag coefficient changes periodically. The initial perigees selected were lower than 400 km of altitude with eccentricities ranging from 0.00 to 0.02. Six values for the angular velocity were applied in the maneuver. The technique of rotating the spacecraft is an interesting solution to increase the orbit decay of a CubeSat without implementing additional de-orbit devices. Significant changes in the decay time are presented due to the increase of the mean drag coefficient calculated by the panel method, when the maneuver is applied, reducing the orbital lifetime, however the results are independent of the angular velocity of the satellite.     

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。     

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.     

Apparent rotation properties of space debris extracted from photometric measurements

Knowledge about the rotation properties of space debris objects is essential for the active debris removal missions, accurate re-entry predictions and to investigate the long-term effects of the space environment on the attitude motion change. Different orbital regions and object’s physical properties lead to different attitude states and their change over time.Since 2007 the Astronomical Institute of the University of Bern (AIUB) performs photometric measurements of space debris objects. To June 2016 almost 2000 light curves of more than 400 individual objects have been acquired and processed. These objects are situated in all orbital regions, from low Earth orbit (LEO), via global navigation systems orbits and high eccentricity orbit (HEO), to geosynchronous Earth orbit (GEO). All types of objects were observed including the non-functional spacecraft, rocket bodies, fragmentation debris and uncorrelated objects discovered during dedicated surveys. For data acquisition, we used the 1-meter Zimmerwald Laser and Astrometry Telescope (ZIMLAT) at the Swiss Optical Ground Station and Geodynamics Observatory Zimmerwald, Switzerland. We applied our own method of phase-diagram reconstruction to extract the apparent rotation period from the light curve. Presented is the AIUB’s light curve database and the obtained rotation properties of space debris as a function of object type and orbit.