Local debris congestion in the geosynchronous environment with population augmentation

Forecasting of localized debris congestion in the geostationary (GEO) regime is performed to investigate how frequently near-miss events occur for each of the longitude slots in the GEO ring. The present-day resident space object (RSO) population at GEO is propagated forward in time to determine current debris congestion conditions, and new probability density functions that describe where GEO satellites are inserted into operational orbits are harnessed to assess longitude-dependent congestion in “business-as-usual” launch traffic, with and without re-orbiting at end-of-life. Congestion forecasting for a 50-year period is presented to illustrate the need for appropriately executed mitigation measures in the GEO ring. Results indicate that localized debris congestion will double within 50 years under current 80% re-orbiting success rates.     

基于测距观测的静地卫星定轨精度分析

在卫星动力法定轨的协方差分析基础上,提出了一种针对地球静止轨道(GEO)卫星的简化定轨精度分析方法。根据GEO卫星的线性化状态转移方程,通过设定地面跟踪网坐标和卫星星下点经度计算叠加矩阵,由观测弧长和采样间隔直接计算定轨精度评定公式中的主要部分。公式扩展后,能比较各种系统误差源对定轨精度的影响,并将影响较大的作为附加参数纳入估计过程并重新评价定轨精度。用该法对10 m定轨精度的测距跟踪网优化设计和测距偏差对定轨精度的影响特性进行分析的结果表明,测量系统中的系统性误差可能以近20的放大倍率传播到卫星沿迹方向和法向,且不能通过自校准测距常值偏差提高定轨精度。     

New insights on the orbital debris collision hazard at GEO

An analysis is performed of the orbital debris collision hazard to operational spacecraft at geosynchronous orbit (GEO). As part of the examination, the contribution of individual components of the population are considered and presented to provide a clearer linkage between object characteristic and resulting risk. Our examination of GEO collision risk reveals several critical new insights: (1) the current probability of collision in GEO is relatively low, yet the future is difficult to predict due to our limited ability to observe objects in GEO and the uncertainty in past and future debris-generating events in GEO; (2) the probability of collision in GEO is not uniform by longitude — it is seven times greater in regions centered about the geopotential wells; (3) the probability of a mission-terminating collision is greatly dependent upon the approximately 2200 objects in the 10 cm–1 m range observed in GEO but not yet cataloged; (4) hardware relocated to GEO “graveyard” disposal orbits pose a potential additional, but not fully understood, collision hazard to operational GEO satellites; and (5) the collision hazard throughout the course of a day or year is highly episodic (i.e. non-uniform).     

Specific features of motion of geosynchronous satellites in the neighborhood of unstable stationary points

A study of peculiarities of the motion of equatorial circular geosynchronous satellites is performed in the neighborhoods of unstable stationary points with longitudes of 165° and 345°. The maps of initial conditions are constructed on the phase plane “longitude of subsatellite point-semi-major axis of orbit” corresponding to various types of regular motions and to quasi-random solutions. The dimensions of zones of the quasi-random solutions are within the limits from decimal fractions of a degree to a few degrees (in longitude) and from hundreds of meters up to several kilometers (along the semi-major axis).     

International Practices to Protect the Geostationary Ring

Since more than 20 years reorbiting of geostationary satellites at the end of their mission is recommended and partially performed to protect the GEO environment. Now a worldwide accepted reorbiting altitude was defined by the Inter-Agency Space Debris Coordination Committee (IADC). Still only one-third of the aging satellites follow this IADC rule. Based on orbital data in the DISCOS database, the situation in the geostationary ring is analyzed. From 878 known objects, 305 are controlled inside their longitude slots, 353 are drifting above, below or through GEO, and 125 are in a libration orbit (status of January 2001). In the last four years (1997–2000) 58 spacecraft reached end-of-life. Twenty of them were reorbited in compliance with the IADC recommendations, 16 were reorbited below this recommendation and 22 were abandoned without any end-of-life disposal manoeuvre.     

Orbit design for the Spektr-R spacecraft of the ground-space interferometer

In order to carry out tasks of the RadioAstron mission, a high-apogee orbit was designed. On average, the period of its satellite’s orbit around the Earth is 8.5 days with evolution due to gravitational perturbations produced by the Moon and the Sun. The perigee and apogee of this orbit vary within the limits 7500–70000 km and 270000–333000 km, respectively. The basic evolution of the orbit represents a rotation of its plane around the line of apsides. Over 3 years, the plane normal to the orbit draws on the celestial sphere an oval with a semi-major axis of about 150° and semi-minor axis of about 45°.     

Recovery of long-wavelength mean gravity anomalies for the dedicated gravitational satellite (gravsat) mission

This paper describes a computer simulation study that was undertaken to determine how well long-wavelength variations in the Earth's gravitational field can be recovered using data from the Dedicated$\text{Grav}$itational $\text{Sat}$ellite (GRAVSAT) mission. This mission is to consist of two low altitude (160 km) spacecraft in essentially the same orbit but separated in phase by 100–300 km. Geodetic data are measurements of the relative range rate to an accuracy of about 1 μm/s at 4 sec intervals. Specifically, a Bayesian covariance simulation was used to investigate simultaneous recovery of the spacecraft ephemerides and a global distribution of 20° × 20° mean gravity anomaly blocks. Sources of errors considered were tracking station positions, gravitational constant, Earth body tides, tropospheric modeling and measurement noise. It should be noted that this simulation does not include as an error source variations in the gravity field that have a character different from what was modeled. Consequently, this study demonstrates the potential of the low-low system as configured to recover the long-wavelength variations in the gravity field.Using only one days worth of data, the mean of the standard deviations of the 162 20° × 20° gravity anomaly blocks is about 1 μgal. For a 6 month mission (assuming a reduction proportional to the square root of the data intervals) this projects to < 0.1 μgal. Because of the potential of increased measurement precision at shorter separation distances, and the relative insensitivity of the recovery process to separation distance, it should be possible to recover both long and short wavelength variations with a modest distribution of separation distances tailored primarily to the short wavelength recovery. Effects of the uncertainty in the gravitational constant and Love's numbers are negligible. In a simulation not reported on, increasing the altitude of the orbit to 200 km from 150 km, degraded, as expected, the accuracy of the recovered parameters by only 7%.     

Two-craft tether formation relative equilibria about circular orbits and libration points

The relative equilibria of a two spacecraft tether formation connected by line-of-sight elastic forces moving in the context of a restricted two-body system and a circularly restricted three-body system are investigated. For a two spacecraft formation moving in a central gravitational field, a common assumption is that the center of the circular orbit is located at the primary mass and the center of mass of the formation orbits around the primary in a great-circle orbit. The relative equilibrium is called great-circle if the center of mass of the formation moves on the plane with the center of the gravitational field residing on it; otherwise, it is called a nongreat-circle orbit. Previous research shows that nongreat-circle equilibria in low Earth orbits exhibit a deflection of about a degree from the great-circle equilibria when spacecraft with unequal masses are separated by 350 km. This paper studies these equilibria (radial, along-track and orbit-normal in circular Earth orbit and Earth–Moon Libration points) for a range of inter-craft distances and semi-major axes of the formation center of mass. In the context of a two-spacecraft Coulomb formation with separation distances on the order of dozens of meters, this paper shows that the equilibria deflections are negligible (less than 10^?6°) even for very heterogeneous mass distributions. Furthermore, the nongreat-circle equilibria conditions for a two spacecraft tether structure at the Lagrangian libration points are developed.     

32颗GPS卫星星座空间覆盖特性建模与仿真

GPS卫星要准确完成定位功能可见卫星数应不少于4颗.通过建立针对低轨、中高轨和大椭圆轨道目标卫星的GPS信号空间几何覆盖模型,利用Matlab计算针对低轨、中高轨和大椭圆轨道的可见卫星数,对目前美国32颗GPS卫星星座的空间覆盖特性进行仿真.仿真结果显示,32颗GPS卫星星座不仅可以对低轨目标实现全轨道覆盖,而且对中高轨和大椭圆轨道也有所覆盖,大大扩展了24颗GPS卫星星座的空间应用.     

Biobjective planning of GEO debris removal mission with multiple servicing spacecrafts

The mission planning of GEO debris removal with multiple servicing spacecrafts (SScs) is studied in this paper. Specifically, the SScs are considered to be initially on the GEO belt, and they should rendezvous with debris of different orbital slots and different inclinations, remove them to the graveyard orbit and finally return to their initial locations. Three key problems should be resolved here: task assignment, mission sequence planning and transfer trajectory optimization for each SSc. The minimum-cost, two-impulse phasing maneuver is used for each rendezvous. The objective is to find a set of optimal planning schemes with minimum fuel cost and travel duration. Considering this mission as a hybrid optimal control problem, a mathematical model is proposed. A modified multi-objective particle swarm optimization is employed to address the model. Numerous examples are carried out to demonstrate the effectiveness of the model and solution method. In this paper, single-SSc and multiple-SSc scenarios with the same amount of fuel are compared. Numerous experiments indicate that for a definite GEO debris removal mission, that which alternative (single-SSc or multiple-SSc) is better (cost less fuel and consume less travel time) is determined by many factors. Although in some cases, multiple-SSc scenarios may perform worse than single-SSc scenarios, the extra costs are considered worth the gain in mission safety and robustness.     

天问一号环绕器中继轨道受摄共振特性分析

“天问一号”环绕器在环火中继轨道为“祝融”火星车提供中继服务时,星下点出现了过着陆点纬度时的经度先增大再减小的特殊漂移现象,需要对该现象产生的原因进行深入分析。基于摄动理论设计了一系列数值实验,提出了一种星下点过指定纬度时经度的简化计算方法;并结合对田谐项引力场位函数的解析推导发现,由于中继轨道周期与火星自转周期比接近1:3,导致3阶3次田谐项产生了轨道共振,从而使得半长轴长周期运动有着较为显著的振荡,进而与带谐项摄动联合导致了该特殊现象。研究揭示了“天问一号”环绕器的轨道共振现象,发现了高阶田谐项对非同步轨道上的环火卫星仍能产生较为明显的轨道共振现象。研究结果可为后续火星环绕探测任务轨道设计提供重要参考。     

The effectiveness of end-of-life re-orbiting for debris mitigation in geostationary orbit

The effect of satellite breakups over 72 years, as a function of the end-of-life re-orbiting altitude (0–2000km), was analyzed in terms of fragment contribution to the object density in the geostationary orbit (GEO) ring, both in the short- and long-term. In the short-term, the explosions in GEO are the most detrimental for the GEO ring environment, though the average fragment density in the ring is never higher than 1/5 of the background, decreasing to less than 1/100 of the existing environment after 4 years (apart from a density rebound 5 decades later, due to luni-solar perturbations). Spacecraft end-of-life re-orbiting is a possible mitigation solution. But the re-orbiting altitude is critical if explosions continue to occur. In order to reduce the post-event average density by 1 order of magnitude with respect to an explosion occurring in GEO, more than 500km of re-orbiting is needed. Concerning the long-term environmental impact, the re-orbiting strategy supported by Inter-Agency Space Debris Coordination Committee (IADC) seems adequate to guarantee, after 2–3 years, a long-term average density of fragments in the GEO ring of at least 2 orders of magnitude below the existing background. But at least 1000km of re-orbiting are needed to stay below that threshold in the short-term too. In conclusion, the re-orbiting strategy recommended by IADC is totally adequate in the long-term, but only if satellite passivation is extensively carried out.     

Stochastic motion of geosynchronous satellites

Long-period evolution of the orbital elements of geosynchronous objects moving in the neighborhood of separatrices of the region of libration resonance is studied. At the phase plane “the longitude of the subsatellite point-semi-major axis” the regions of migration of separatrices where the separatrices can move due to the influence of perturbations are isolated. The dimensions of these regions and the distances between them have the same order of magnitude, several kilometers along the semi-major axis. The regions of migration do not overlap at the initial value of the orbit inclination 0°. When inclination increases, gradual overlapping of these regions takes place. On average, the width of the zones of stochasticity increases when the area to mass ratio increases and decreases when inclination of the orbit increases. The zones of stochasticity corresponding to different separatrices are separated from each other. A catalog of the passive geosynchronous objects moving in the neighborhood of separatrices is compiled. The evolution of the objects of the catalog is studied.     

等质量立体五星库仑编队飞行的分析与控制

分析了立体五星编队在静电力和万有引力作用下的静态构型。分别讨论了五星编队在共线和平面情况下的静态构型,着重研究了五星构成立体双直角六棱锥构型时各个卫星所带的静电荷量。由于地球同步轨道的卫星所受到的作用力不仅是万有引力与静电库仑力,还有空气阻力等摄动力,因此只有对其施加控制,卫星才能在静态平衡点保持编队构型的稳定性。本文采用线性二次型最优控制方法来保持编队的静态构型稳定,并通过Matlab实现了五星立体库伦编队飞行控制仿真。     

地球静止轨道在轨服务技术研究现状与发展趋势

地球静止轨道(GEO)是人类仅有的一条独特卫星轨道,是极其珍贵的轨道资源。首先分 析了GEO环境现状和未来趋势,然后从“GEO轨道保护”和“GEO卫星在轨维护”两方面论述 了GEO在轨服务技术的内涵、服务机会和效益,介绍了世界各国GEO在轨服务技术的主要研究 进展,归纳了其中的关键技术。最后,对未来的发展趋势进行了展望。
     

Further analysis of infrared spectrophotometric observations of high area to mass ratio (HAMR) objects in GEO

Optical surveys have identified a class of high area-to-mass ratio (HAMR) objects in the vicinity of the Geostationary Earth Orbit (GEO) ring^. The exact origin and nature of these objects are not well known, although their proximity to the GEO belt poses a hazard to active GEO satellites. The prevalent conjecture is that many of these objects may be thermal materials shed from derelict spacecraft in ‘graveyard’ orbits above the GEO ring. Due to their high area-to-mass ratios and unknown attitude dynamics and material characteristics, solar radiation pressure (SRP) perturbs their orbits in ways that makes it difficult to predict their orbital trajectories over periods of time exceeding a week or less. To better understand and track these objects and infer their origins, we have made observations that allow us to determine physical characteristics that will improve the non-conservative force modeling used for orbit determination (OD) and prediction. Information on their temperatures, areas, emissivities, and albedos may be obtained from thermal infrared and visible measurements. Simultaneous observations in the thermal infrared and visible wavelengths may allow disentangling of projected area, albedo, and object emissivity.Further analysis and modeling of observational data on certain of the HAMR objects collected at the AMOS observatory 3.6 m AEOS telescope are presented. The thermal-IR spectra of these geosynchronous orbit objects acquired by the Broadband Array Spectrograph System (BASS) span wavelengths 3 to 13 μm and constitute a unique data set, providing a means of measuring object fluxes in the infrared and visible wavelengths. These, in turn, allow temperatures and emissivity-area products to be calculated, and in some cases provide information on rotation rates. We compare our observational results with the outputs of simple models, in terms of visible and infrared flux and orbital characteristics. The resulting temperatures and rotation rates are used in SRP acceleration models to demonstrate improvements in OD and prediction performance relative to models which assume default ambient temperature and static attitude dynamics. Additionally, we have the capability and plans to measure material properties with the same instrument in the lab as used at the telescope to facilitate direct comparisons.     

我国数据中继卫星系统发展建议

天链一号数据中继卫星在轨成功运行,标志着我国在天基信息传输领域的重大突破,今后发展方向是建设中继卫星组网系统,以满足数据中继不断增长的需求.分析表明:经度间距约为180°的地球静止轨道(GEO)双星组网系统,只需在我国本土设立控管站,利用地面高速光纤干线,双星就能对离地高度大于95km的航天器实现100%轨道覆盖的中继...     

天基照相跟踪空间碎片批处理轨道确定研究

随着国内外天基观测空间碎片研究的展开,文章提出了利用跟踪卫星的CCD(Charge
Coupled Device)相机对空间碎片进行轨道探测的方法,首先建立了CCD照相观测模型和基于 照相观测 的空间碎片批处理轨道确定模型。通过对CCD相机底片归算方法的分析可知,利用
CCD相机所获得的观测数据与跟踪卫星的姿态无关,且其精度只与测量和坐标转换计算的精 度有关,在测量和计算中可获得较高的精度。分别对分布密度较高的低轨道和地球同步 轨道区域的空间碎片进行了定轨分析。仿真结果表明,定轨时采用两个跟踪弧段的照相数据 定轨精度大大高于一个弧段照相数据的定轨精度;跟踪卫星距离空间碎片越近,定轨精度越 高;低轨道空间碎片的定轨精度高于地球同步轨道上的空间碎片定轨精度。
     

Exposure estimates for repair satellites at geosynchronous orbit

Communications and weather satellites in geosynchronous (GEO, altitude: 35,793 km.) and geostationary orbits (GSO) are revolutionizing our ability to almost instantly communicate with each other, capture high resolution global imagery for weather forecasting and obtain a multitude of other geophysical data for environmental protection purposes. The rapid increase in the number of satellites at GEO is partly due to the exponential expansion of the internet, its commercial potential and the need to deliver a large amount of digital information in near real time. With the large number of satellites operating at GEO and particularly at GSO, there is a need to think of viable approaches to retrieve, rejuvenate and perhaps repair these satellites. The first step in this process is a detailed understanding of the ionizing radiation environment at GEO. Currently, the most widely used trapped particle radiation environment definition near Earth is based on the NASA’s static AP8/AE8 models which define the trapped proton and electron intensities. These models are based on a large number of satellite measurements carried out in the 1960s and 1970s. In this paper, the AP8/AE8 models as well as a heavy ion galactic cosmic ray (GCR) model are used to define the radiation environments for protons, electrons and heavy ions at low Earth orbit (LEO), medium Earth orbit (MEO) and GEO. LEO and MEO dosimetric calculations are included in the analysis since any launch platform capable of delivering a payload to GEO will accumulate exposure during its transit through LEO and MEO. The computational approach (particle transport) taken in this paper is to use the static LEO, MEO, GEO and geomagnetically attenuated GCR environments as input to the NASA Langley Research Center (LaRC) developed deterministic particle transport codes high charge and energy transport (HZETRN) and coupled electron photon transport (CEPTRN). This is done through exposure prediction within a spherical shell, a legacy Apollo era command service module (CSM) configuration, and a large modular structure represented by a specific configuration of the international Space Station (ISS-11A, circa 2005). Based on the results of the simulations, conclusions are drawn on the exposure levels accumulated by these geometries throughout a mission to GEO.     

MEO卫星内部充电环境及典型材料充电特征分析

文章利用通用模型DICTAT,计算了恶劣期地球中高轨道(MEO)高能电子通量随卫星运行位置的变化情况以及日均积分能谱,之后选择4种参数具有代表性的电介质材料,分析了其在MEO环境下的充电特征,并将上述结果与地球同步轨道(GEO)情况进行了对比。结果表明,通常而言MEO卫星的内部充电风险更高,平均充电电位是GEO的3倍左右,而且充电电位在整个轨道周期内起伏变化明显,电位达到最高值的时间相对于高能电子通量最大值有0.3~0.9 h的延迟,具体的变化特征由电介质材料时间常数决定。