The fast debris evolution model

The ‘particles-in-a-box’ (PIB) model introduced by Talent [Talent, D.L. Analytic model for orbital debris environmental management. J. Spacecraft Rocket, 29 (4), 508–513, 1992.] removed the need for computer-intensive Monte Carlo simulation to predict the gross characteristics of an evolving debris environment. The PIB model was described using a differential equation that allows the stability of the low Earth orbit (LEO) environment to be tested by a straightforward analysis of the equation’s coefficients. As part of an ongoing research effort to investigate more efficient approaches to evolutionary modelling and to develop a suite of educational tools, a new PIB model has been developed. The model, entitled Fast Debris Evolution (FADE), employs a first-order differential equation to describe the rate at which new objects ?10 cm are added and removed from the environment. Whilst Talent [Talent, D.L. Analytic model for orbital debris environmental management. J. Spacecraft Rocket, 29 (4), 508–513, 1992.] based the collision theory for the PIB approach on collisions between gas particles and adopted specific values for the parameters of the model from a number of references, the form and coefficients of the FADE model equations can be inferred from the outputs of future projections produced by high-fidelity models, such as the DAMAGE model.     

Influence of Earth’s shadowing effects on space debris stability

Solar radiation pressure affects the evolution of high area-to-mass geostationary space debris. In this work, we extend the stability study of Valk et al. (2009) by considering the influence of Earth’s shadows on the short- and long-term time evolutions of space debris. To assess the orbits stability, we use the Mean Exponential Growth factor of Nearby Orbits (MEGNO), which is an efficient numerical tool to distinguish between regular and chaotic behaviors. To reliably compute long-term space debris motion, we resort to the Global Symplectic Integrator (GSI) of Libert et al. (2011) which consists in the symplectic integration of both Hamiltonian equations of motion and variational equations. We show how to efficiently compute the MEGNO indicator in a complete symplectic framework, and we also discuss the choice of a symplectic integrator, since propagators adapted to the structure of the Hamiltonian equations of motion are not necessarily suited for the associated variational equations. The performances of our method are illustrated and validated through the study of the Arnold diffusion problem. We then analyze the effects of Earth’s shadows, using the adapted conical and cylindrical Earth’s shadowing models introduced by Hubaux et al. (2012) as the smooth shadow function deriving from these models can be easily included into the variational equations. Our stability study shows that Earth’s shadows greatly affect the global behaviour of space debris orbits by increasing the size of chaotic regions around the geostationary altitude. We also emphasize the differences in the results given by conical or cylindrical Earth’s shadowing models. Finally, such results are compared with a non-symplectic integration scheme.     

利用TLE数据分析LEO卫星轨道异常的新方法——————综合判据法

及时准确地发现在轨卫星的轨道异常意义重大. 通过有效的异常算法, 能够找出发生轨道异常的碎片或航天器, 为空间碎片碰撞预警系统分析和验证碰撞事件提供数据支持. 通过对利用TLE (Two Line Elements)数据分析LEO在轨卫星轨道异常的方法研究, 提出了一个利用单个卫星相邻根数时间差控制加综合判据的判别方法. 分析表明, 相对于取单一因素阈值的判别方法, 综合判据法能够最大限度地减少漏判, 并且保持相对较高的判断准确率.      

The bistatic radar capabilities of the Medicina radiotelescopes in space debris detection and tracking

An accurate measurement of the position and trajectory of the space debris fragments is of primary importance for the characterization of the orbital debris environment. The Medicina Radioastronomical Station is a radio observation facility that is here proposed as receiving part of a ground-based space surveillance system for detecting and tracking space debris at different orbital regions (from Low Earth Orbits up to Geostationary Earth Orbits). The proposed system consists of two bistatic radars formed by the existing Medicina receiving antennas coupled with appropriate transmitters. This paper focuses on the current features and future technical development of the receiving part of the observational setup. Outlines of possible transmitting systems will also be given together with the evaluation of the observation strategies achievable with the proposed facilities.     

Properties of the high area-to-mass ratio space debris population at high altitudes

In the framework of its space debris research activities ESA established an optical survey program to study the space debris environment at high altitudes, in particular in the geostationary ring and in the geostationary transfer orbit region. The Astronomical Institute of the University of Bern (AIUB) performs these surveys on behalf of ESA using ESA’s 1-m telescope in Tenerife. Regular observations were started in 1999 and are continued during about 120–140 nights per year. Results from these surveys revealed a substantial amount of space debris at high altitudes in the size range from 0.1 to 1 m. Several space debris populations with different dynamical properties were identified in the geostationary ring. During the searches for debris in the geostationary transfer orbit region a new population of objects in unexpected orbits, where no potential progenitors exist, was found. The orbital periods of these objects are clustered around one revolution per day; the eccentricities, however, are scattered between 0 and 0.6. By following-up some of these objects using the ESA telescope and AIUB’s 1-m telescope in Zimmerwald, Switzerland, it was possible to study the properties of this new population. One spectacular finding from monitoring the orbits over time spans of days to months is the fact that these objects must have extreme area-to-mass ratios, which are by several orders of magnitudes higher than for ‘normal-type’ debris. This in turn supports the hypothesis that the new population actually is debris generated in or near the geostationary ring and which is in orbits with periodically varying eccentricity and inclination due to perturbations by solar radiation pressure. In order to further study the nature of these debris, multi-color and temporal photometry (light curves) were acquired with the Zimmerwald telescope. The light curves show strong variations over short time intervals, including signals typical for specular reflections. Some objects exhibit distinct periodic variations with periods ranging from 10 to several 100 s. All this is indicative for objects with complicated shapes and some highly reflective surfaces.     

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.     

Reducing variability in short term orbital lifetime prediction

Within the last year three major re-entries occurred. The satellites UARS, ROSAT and Phobos-Grunt entered Earth’s atmosphere with fragments reaching the surface. Due to a number of uncertainties in propagating an object’s trajectory the exact place and time of a satellite’s re-entry is hard to determine. Major influences when predicting the re-entry time are the changing precision of the available orbital data, the satellite’s ballistic coefficient, the activity of the sun which influences the Earth’s atmosphere and the underlying quality of the atmospheric model. In this paper a method is presented which can reduce the variability in short-term orbital lifetime prediction induced by fluctuating orbital data accuracies. A re-entry campaign is used as a reference for this purpose. For a window of a few weeks before the re-entry the position data of a synthetic object is disturbed considering different degrees of orbital data errors. As a result different predictions will exist for the generated position data of a given day. Using a regression algorithm on the available data an average position is obtained, which is then used for the orbital lifetime prediction. The effect of this measure is a more consistent prediction of the orbital lifetime. The paper concludes with the comparison of the generated re-entry windows in various test cases for the original and the averaged data.     

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.     

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。     

空间碎片云演变过程的阶段划分

根据碎片云从破碎点开始向空间扩散过程中碎片密度和形状的变化规律,以几何形状和起主要作用的因素为特征,定义了球形、椭球形、绳形、螺旋线形、全方位弥漫直至球壳形六个演变阶段.论述了在各个阶段的主要特征和对演变过程起主要作用的因素.总结了与演变过程相关的轨道运动理论和研究方法,分析了各个阶段演变的动力学原理.在球形阶段起主要作用的是分离速度;椭球形阶段可以利用线性化相对运动方程进行分析;绳形与螺旋线形在几何上有质变,但都有结点和结线,并可以利用速度增量理论分析和解释其存在的原因.轨道摄动力消除了结点和结线,导致碎片云的全方位弥漫,并最终使碎片云趋于球壳形.推导和罗列了各阶段转换标志点时刻的计算公式,利用计算机仿真的方法,给出了近地轨道各个阶段碎片云分布示意图,验证了演变过程阶段划分的合理性.     

An adaptive threshold method for improving astrometry of space debris CCD images

Optical survey is a main technique for observing space debris, and precisely measuring the positions of space debris is of great importance. Due to several factors, e.g. the angle object normal to the observer, the shape as well as the attitude of the object, the variations of observed characteristics for low earth orbital space debris are distinct. When we look at optical CCD images of observed objects, the size and brightness are varying, hence it’s difficult to decide the threshold during centroid measurement and precise astrometry. Traditionally the threshold is given empirically and constantly in data reduction, and obviously it’s not suitable for data reduction of space debris. Here we offer a solution to provide the threshold. Our method assumes that the PSF (point spread function) is Gaussian and estimates the signal flux by a directly two-dimensional Gaussian fit, then a cubic spline interpolation is performed to divide each initial pixel into several sub-pixels, at last the threshold is determined by the estimation of signal flux and the sub-pixels above threshold are separated to estimate the centroid. A trail observation of the fast spinning satellite Ajisai is made and the CCD frames are obtained to test our algorithm. The calibration precision of various threshold is obtained through the comparison between the observed equatorial position and the reference one, the latter are obtained from the precise ephemeris of the satellite. The results indicate that our method reduces the total errors of measurements, it works effectively in improving the centering precision of space debris images.     

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.     

On the effect of considering more realistic particle shape and mass parameters in MMOD risk assessments

One of the primary mission risks tracked in the development of all spacecraft is that due to micro-meteoroids and orbital debris (MMOD). Both types of particles, especially those larger than 0.1 mm in diameter, contain sufficient kinetic energy due to their combined mass and velocities to cause serious damage to crew members and spacecraft. The process used to assess MMOD risk consists of three elements: environment, damage prediction, and damage tolerance. Orbital debris risk assessments for the Orion vehicle, as well as the Shuttle, Space Station and other satellites use ballistic limit equations (BLEs) that have been developed using high speed impact test data and results from numerical simulations that have used spherical projectiles. However, spheres are not expected to be a common shape for orbital debris; rather, orbital debris fragments might be better represented by other regular or irregular solids. In this paper we examine the general construction of NASA’s current orbital debris (OD) model, explore the potential variations in orbital debris mass and shape that are possible when using particle characteristic length to define particle size (instead of assuming spherical particles), and, considering specifically the Orion vehicle, perform an orbital debris risk sensitivity study taking into account variations in particle mass and shape as noted above. While the results of the work performed for this study are preliminary, they do show that continuing to use aluminum spheres in spacecraft risk assessments could result in an over-design of its MMOD protection systems. In such a case, the spacecraft could be heavier than needed, could cost more than needed, and could cost more to put into orbit than needed. The results obtained in this study also show the need to incorporate effects of mass and shape in mission risk assessment prior to first flight of any spacecraft as well as the need to continue to develop/refine BLEs so that they more accurately reflect the shape and material density variations inherent to the actual debris environment.     

Estimation of orbital parameters of broken-up objects from in-situ debris measurements

Even sub-millimeter-size debris could cause a fatal damage on a spacecraft. Such tiny debris cannot be followed up or tracked from the ground. Therefore, Kyushu University has initiated IDEA the project for In-situ Debris Environmental Awareness, which conducts in-situ measurements of sub-millimeter-size debris. One of the objectives is to estimate the location of on-orbit satellite fragmentations from in-situ measurements. The previous studies revealed that it is important to find out the right nodal precession rate to estimate the orbital parameters of a broken-up object properly. Therefore, this study derives a constraint equation that applies to the nodal precession rate of the broken-up object. This study also establishes an effective procedure to estimate properly the orbital parameters of a broken-up object with the constraint equation.     

The ratio of hazardous meteoroids to orbital debris in near-Earth space

Orbital debris is known to pose a substantial threat to Earth-orbiting spacecraft at certain altitudes. For instance, the orbital debris flux near Sun-synchronous altitudes of 600–800 km is particularly high due in part to the 2007 Fengyun-1C anti-satellite test and the 2009 Iridium-Kosmos collision. At other altitudes, however, the orbital debris population is minimal and the primary impactor population is not man-made debris particles but naturally occurring meteoroids. While the spacecraft community has some awareness of the risk posed by debris, there is a common misconception that orbital debris impacts dominate the risk at all locations. In this paper, we present a damage-limited comparison between meteoroids and orbital debris near the Earth for a range of orbital altitude and inclination, using NASA’s latest models for each environment. Overall, orbital debris dominates the impact risk between altitudes of 600 and 1300 km, while meteoroids dominate below 270 km and above 4800 km.     

Active debris removal of multiple priority targets

Today’s space debris environment shows major concentrations of objects within distinct orbital regions for nearly all size regimes. The most critical region is found at orbital altitudes near 800 km with high declinations. Within this region many satellites are operated in so called sun-synchronous orbits (SSO). Among those, there are Earth observation, communication and weather satellites. Due to the orbital geometry in SSO, head-on encounters with relative velocities of about 15 km/s are most probable and would thus result in highly energetic collisions, which are often referred to as catastrophic collisions, leading to the complete fragmentation of the participating objects. So called feedback collisions can then be triggered by the newly generated fragments, thus leading to a further population increase in the affected orbital region. This effect is known as the Kessler syndrome.     

Practical guidelines for electro-dynamic tethers to survive from orbital debris impacts

Japan Aerospace Exploration Agency (JAXA) has proposed an active debris removal using electro-dynamic tether to reduce large space debris in the low-Earth orbit. However, a tether strand is thin but long enough to have a large area so that it is vulnerable to small particles. This vulnerability might be the weakest point of a tether system against orbital debris. In order to overcome this weakest point, a double tether system, in which two tether strands are tied together at even intervals to form equally spaced loops, has been suggested as one of the promising candidates. This paper provides a mathematical approach to estimate the survival probability of a double tether system and then apply the approach to evaluate the mission success rate of the active debris removal using electro-dynamic tether that JAXA has proposed. It can be concluded the countermeasure to get enough success rate can be obtained. The result is simulated for Advanced Earth Observing Satellite II (ADEOS-II) re-entry from 800 km sun synchronized orbit to atmosphere. The simulation shows that mission success rate over 90% can be obtained with number of loops over 1000 and 10 mm clearance between two strands.     

Dynamical evolution of debris clouds in geosynchronous orbit

Optical observations have discovered a substantial amount of decimeter sized objects in orbits close to the geosynchronous altitude. Most of these are probably the result of a still undetermined number of explosions occurred to spacecraft and upper stages. So far, however, only two or three fragmentations have been confirmed near GEO and the identification of further explosions at a so high altitude is made difficult by the long time passed since the occurrence of the events and by the effects of the orbital perturbations on the resulting debris clouds. In order to assist the optical observers in identifying debris clouds due to explosions in proximity of the geosynchronous region, a set of fragmentations has been simulated, taking into account a reasonable range of ejection velocities as a function of the fragment size. The resulting debris clouds have been propagated, including all the relevant orbital perturbations, for several decades and the results obtained are presented as snapshots, at given post-explosion times, in the orbital elements space.     

空间飞行器碎片防护结构的简化设计

给出一种基于实验和理论分析的航天器碎片防护结构简化设计方法 ,该方法可用于进行大型空间飞行器碎片防护结构的方案选择和初步结构设计。利用空间碎片的工程环境模型和防护结构几何经验公式 ,采用“设计碎片”的概念 ,对防护结构进行几何结构设计和质量估算 ,并采用改进的防护性能验证算法进行空间碎片的风险评估。通过对惠式防护结构的计算 ,得到的计算结果基本符合实际要求。