Space debris measurements in Japan

This paper describes the present status of space debris measurements in Japan, focusing on the recent achievements of existing systems and the design of new systems. Issues concerning the Leonids meteoroid storm in November 1998/99 will be also discussed.     

Space debris: Electrodynamic effects

It is shown that electrodynamic forces play a crucial role in the orbital dynamics of the small Al₂O₃ particles that are injected into the terrestrial magnetosphere during solid rocket propellent burns. Due to the simplified model that is used to describe the plasma distribution in the magnetosphere, the present results are necessarily preliminary. Even so, it appears that the smallest particles (a = 0.1 μm) will be rapidly eliminated from the magnetosphere. Evaluation of the fate of the somewhat larger (a = 1 μm) particles awaits the construction of a more complete and realistic model of the magnetospheric plasma.     

Space debris mitigation in geosynchronous orbit

In order to preserve the geosynchronous region, the Inter-Agency Space Debris Coordination Committee (IADC) proposed and endorsed a re-orbiting strategy for spacecraft at the end-of-life: they should be disposed above the synchronous altitude and passivated, to reduce the risk of inadvertent explosions. The recommended perigee altitude of the disposal orbit took into account all relevant perturbations and was a function of the expected perturbing acceleration induced by solar radiation pressure. It was intended to prevent any further interference with a properly defined geostationary protected region.     

Space debris: Assessing risk and responsibility

We model the orbital debris environment by a set of differential equations with parameter values that capture many of the complexities of existing three-dimensional simulation models. We compute the probability that a spacecraft gets destroyed in a collision during its operational lifetime, and then define the sustainable risk level as the maximum of this probability over all future time. Focusing on the 900- to 1000-km altitude region, which is the most congested portion of low Earth orbit, we find that – despite the initial rise in the level of fragments – the sustainable risk remains below 10^-3${10}^{-3}$ if there is high (>98%) compliance to the existing 25-year postmission deorbiting guideline. We quantify the damage (via the number of future destroyed operational spacecraft) generated by past and future space activities. We estimate that the 2007 FengYun 1C antisatellite weapon test represents ≈1%$\approx 1\%$ of the legacy damage due to space objects having a characteristic size of ?10$?10$ cm, and causes the same damage as failing to deorbit 2.6 spacecraft after their operational life. Although the political and economic issues are daunting, these damage estimates can be used to help determine one-time legacy fees and fees on future activities (including deorbit noncompliance), which can deter future debris generation, compensate operational spacecraft that are destroyed in future collisions, and partially fund research and development into space debris mitigation technologies. Our results need to be confirmed with a high-fidelity three-dimensional model before they can provide the basis for any major decisions made by the space community.     

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.      

Space debris cumulative flux considering the Interval Distance-based method

The availability of engineering models to estimate the risk from space debris is essential for space missions. According to current research, cumulative flux calculation is mostly carried out based on the equal-width interval discretization. The method discretizes the volume around the Earth into cells defined in earth centered inertial coordinates. The resulting debris flux onto a target object is shown to depend on the chosen size of the cells. To avoid a discretization error, this must be accounted for. In order to present reliable flux predictions for space mission, the algorithm improvement is an ongoing topic for the related research field. The aim of this study was to examine the discretization error during the cumulative flux determination process. Both the effect of interval step length and the orbital boundary are under investigation. Several typical orbits are selected as examples here and the 2018/01/03 TLE (Two Line Element) data published by the US Space Surveillance Network is used as the debris background in this paper. Furthermore, the Interval Distance-Based method for Discretization (IDD) is adopted in this paper. A position-centered flux determination method is introduced based on the IDD method. According to the example analysis, the IDD used in the flux calculation process provides results which are less affected by the interval step-size setup; and the orbital boundary has no effect on the calculation process. In other words, the discretization error is significantly reduced. The position-centered method provided a possible suggestion for the improvement of space debris environment models.     

Space debris mitigation strategies and practices in geosynchronous transfer orbits

Missions to geosynchronous orbits remain one of the most important elements of space launch traffic, accounting for 40% of all missions to Earth orbit and beyond during the four-year period 2000–2003. The vast majority of these missions leave one or more objects in geosynchronous transfer orbits (GTOs), contributing on a short-term or long-term basis to the space debris population. National and international space debris mitigation guidelines seek to curtail the accumulation of debris in orbits which penetrate the regions of low Earth orbit and of geosynchronous orbit. The orbital lifetime of objects in GTO can be greatly influenced by the initial values of perigee, inclination, and right ascension of the orbital plane, leading to orbital lifetimes of from less than one month to more than 100 years. An examination of the characteristic GTOs employed by launch vehicles from around the world has been conducted. The consequences of using perigees above 300 km and super-synchronous apogees, typically above 40,000 km, have been identified. In addition, the differences in orbital behavior of launch vehicle stages and mission-related debris in GTOs have been investigated. Greater coordination and cooperation between space launch service providers and spacecraft designers and owners could significantly improve overall compliance with guidelines to mitigate the accumulation of debris in Earth orbit.     

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.     

Space debris observations with the Slovak AGO70 telescope: Astrometry and light curves

The Faculty of Mathematics, Physics and Informatics of Comenius University in Bratislava, Slovakia (FMPI) operates its own 0.7-m Newtonian telescope (AGO70) dedicated to the space surveillance tracking and research, with an emphasis on space debris. The observation planning focuses on objects on geosynchronous (GEO), eccentric (GTO and Molniya) and global navigation satellite system (GNSS) orbits. To verify the system’s capabilities, we conducted an observation campaign in 2017, 2018 and 2019 focused on astrometric and photometric measurements. In last two years we have built up a light curve catalogue of space debris which is now freely available for the scientific community. We report periodic signals extracted from more than 285 light curves of 226 individual objects. We constructed phase diagrams for 153 light curves for which we obtained apparent amplitudes.     

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.     

Removing orbital debris with lasers

Orbital debris in low Earth orbit (LEO) are now sufficiently dense that the use of LEO space is threatened by runaway collision cascading. A problem predicted more than thirty years ago, the threat from debris larger than about 1 cm demands serious attention. A promising proposed solution uses a high power pulsed laser system on the Earth to make plasma jets on the objects, slowing them slightly, and causing them to re-enter and burn up in the atmosphere. In this paper, we reassess this approach in light of recent advances in low-cost, light-weight modular design for large mirrors, calculations of laser-induced orbit changes and in design of repetitive, multi-kilojoules lasers, that build on inertial fusion research. These advances now suggest that laser orbital debris removal (LODR) is the most cost-effective way to mitigate the debris problem. No other solutions have been proposed that address the whole problem of large and small debris. A LODR system will have multiple uses beyond debris removal. International cooperation will be essential for building and operating such a system.     

Yarkovsky-Schach effect on space debris motion

The Yarkovsky-Schach effect is a small perturbation affecting Earth satellites and space debris illuminated by the Sun. It was first applied to the orbit of LAGEOS satellites as an explanation of the residuals in orbital elements. In this work, we carry out several numerical integration tests taking into consideration various orbit and rotation parameters, in order to analyse this effect in a broader context. The semi-major axis variations remain small and depend on the spin axis attitude with respect to the Sun. We show that the force amplitude is maximised for orbits inclined with $i\approx$?20–30°. We also observe the influence on other orbital elements, notably on the orbit inclination. However, these effects are clearly observed only on long timescales; in our simulations, we propagated the orbits for 200?y. The Yarkovsky-Schach effect is thus confirmed to have a minuscule magnitude. It should be taken into account in studies requiring high-precision orbit determination, or on expanded timescales.     

Real-time space debris monitoring with EISCAT

Following a feasibility study in 2000–2001 on using the EISCAT ionospheric research radars to detect centimetre-sized space debris in the frame of an ESA contract, we are now finishing a continuation study, aimed at achieving debris detection and parameter estimation in real-time. A requirement is to “piggy-back” space debris measurements on top of EISCAT’s normal ionospheric work, without interfering with that work, and to be able to handle about 500 h of measurements per year. We use a special digital receiver back-end in parallel with EISCAT’s standard receiver. We sample fast enough to correctly band-pass sample the EISCAT analog frequency band. To increase detection sensitivity, we use coherent pulse-to-pulse integration. The coherent integration is built-in in our method of parameter estimation, which we call the match function (MF) method. The method is derived from Bayesian statistical inversion, but reduces, with standard assumptions about noise and prior, to minimizing the least squares norm ∥z(t) − bχ(R,v,a;t)∥, where z is the measured signal and {bχ} is a set of model signals. Because the model signals depend linearly on the amplitude b, it is sufficient to maximize the magnitude of the inner product (cross correlation) between z and χ, the amplitude estimate is then determined by direct computation. The magnitude of the inner product, when properly normalized, is the MF. To construct the set of model signals, we sample the EISCAT transmission, in the same way as we sample the received signal, and apply linearly changing Doppler-shifts to it. Our initial implementation of the MF-method in 2001 was about four orders of magnitude too slow for real-time applications, but we have now gained the required speed factors. A factor of ten comes from using faster computers, another factor of ten comes from coding our key algorithms in C instead of Matlab. The largest factor, typically 100–300, comes from using a special, approximative, but in practice quite sufficient, method of finding the MF maximum. Test measurements show that we get real-time speed already when using a single dual-processor 2 GHz G5 Macintosh to do the detection computations.     

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.     

Value analysis for orbital debris removal

This paper presents methods for deriving first order monetary benefits from removing individual debris objects in high value sun-synchronous orbits. These analyses are intended to serve as an economic metric by which competing debris removal methods can be evaluated.     

Bounding the risk of crew loss following orbital debris penetration of the International Space Station at assembly stages 1J and 1E.

Orbital debris impacts on the International Space Station occur frequently. To date, none of the impacting particles has been large enough to penetrate manned pressurized volumes. We used the Manned Spacecraft Crew Survivability code to evaluate the risk to crew of penetrations of pressurized modules at two assembly stages: after Flight 1J, when the pressurized elements of Kibo, the Japanese Experiment Module, are present, and after Flight 1E, when the European Columbus Module is present. Our code is a Monte-Carlo simulation of impacts on the Station that considers several potential event types that could lead to crew loss. Among the statistics tabulated by the program is the probability of death of one or more crew members in the event of a penetration, expressed as the risk factor, R. This risk factor is dependent on details of crew operations during both ordinary circumstances and decompression emergencies, as well as on details of internal module configurations. We conducted trade studies considering these procedure and configuration details to determine the bounds on R at the 1J and 1E stages in the assembly sequence. Here we compare the R-factor bounds, and procedures could that reduce R at these stages.     

An adaptive strategy for active debris removal

Many parameters influence the evolution of the near-Earth debris population, including launch, solar, explosion and mitigation activities, as well as other future uncertainties such as advances in space technology or changes in social and economic drivers that effect the utilisation of space activities. These factors lead to uncertainty in the long-term debris population. This uncertainty makes it difficult to identify potential remediation strategies, involving active debris removal (ADR), that will perform effectively in all possible future cases. Strategies that cannot perform effectively, because of this uncertainty, risk either not achieving their intended purpose, or becoming a hindrance to the efforts of spacecraft manufactures and operators to address the challenges posed by space debris.     

Analysis of IRAS data for orbital debris

The Infrared Astronomical Satellite (IRAS) was launched in 1983 for the purpose of surveying the sky in a broad area of the infrared portion of the spectrum. While the primary objects of interest of IRAS were stars and nebulae, other types of space-related objects could also be observed. These include comets, asteroids, and Earth orbiting objects. Theoretical analysis indicates that IRAS could observe objects with a diameter of 1-mm at a range of 100-km and objects with a diameter of 1-cm at a range of 1000-km, while current ground-based observations of particles in low Earth orbit are limited to objects larger than 1-cm. Thus, these data offer a unique opportunity to ascertain the number density of particles below the present observable limit. At NASA/JSC a preliminary analysis of an IRAS data set has been performed to detect and describe this population, and the results of this study are presented.     

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.