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.     

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.     

Orbital error propagation considering atmospheric density uncertainty

Due to the influence of various errors, the orbital uncertainty propagation of artificial celestial objects while orbit prediction is required, especially in some applications such as conjunction analysis. In the orbital error propagation of artificial celestial objects in low Earth orbits (LEOs), atmospheric density uncertainty is one of the important factors that require special attention. In this paper, on the basis of considering the uncertainties of position and velocity, the atmospheric density uncertainty is also taken into account to further investigate the orbital error propagation of artificial celestial objects in LEOs. Artificial intelligence algorithms are introduced, the MC Dropout neural network and the heteroscedastic loss function are used to realize the correction of the empirical atmospheric density model, as well as to provide the quantification of model uncertainty and input uncertainty for the corrected atmospheric densities. It is shown that the neural network we built achieves good results in atmospheric density correction, and the uncertainty quantization obtained from the neural network is also reasonable. Moreover, using the Gaussian mixture model - unscented transform (GMM-UT) method, the atmospheric density uncertainty is taken into account in the orbital uncertainty propagation, by adding a sampled random term to the corrected atmospheric density when calculating atmospheric density. The feasibility of the GMM-UT method considering atmospheric density uncertainty is proved by the further comparison of abundant sampling points and GMM-UT results (with and without considering atmospheric density uncertainty).     

A deformation model of flexible,HAMR objects for accurate propagation under perturbations and the self-shadowing effects

A new type of space debris in near geosynchronous orbit (GEO) was recently discovered and later identified as exhibiting unique characteristics associated with high area-to-mass ratio (HAMR) objects, such as high rotation rates and high reflection properties. Observations have shown that this debris type is very sensitive to environmental disturbances, particularly solar radiation pressure, due to the fact that its motion depends on the actual effective area, orientation of that effective area, reflection properties and the area-to-mass ratio of the object is not stable over time. Previous investigations have modelled this type of debris as rigid bodies (constant area-to-mass ratios) or discrete deformed body; however, these simplifications will lead to inaccurate long term orbital predictions. This paper proposes a simple yet reliable model of a thin, deformable membrane based on multibody dynamics. The membrane is modelled as a series of flat plates, connected through joints, representing the flexibility of the membrane itself. The mass of the membrane, albeit low, is taken into account through lump masses at the joints. The attitude and orbital motion of this flexible membrane model is then propagated near GEO to predict its orbital evolution under the perturbations of solar radiation pressure, Earth’s gravity field (J₂), third body gravitational fields (the Sun and Moon) and self-shadowing. These results are then compared to those obtained for two rigid body models (cannonball and flat rigid plate). In addition, Monte Carlo simulations of the flexible model by varying initial attitude and deformation angle (different shape) are investigated and compared with the two rigid models (cannonball and flat rigid plate) over a period of 100?days. The numerical results demonstrate that cannonball and rigid flat plate are not appropriate to capture the true dynamical evolution of these objects, at the cost of increased computational time.     

一种板式推进剂管理装置（PMD）性能的数值仿真

板式推进剂管理装置（PMD）是板式表面张力贮箱最重要的部件之一．为分析板式PMD管理推进剂能力,以某板式贮箱为研究对象,采用三维非定常流体（VOF）体积函数的两相流模型,对不同填充比时板式PMD的推进剂管理性能进行数值仿真,得到微重力下推进剂在PMD上及贮箱内部的分布情况,仿真结果与国外空间搭载试验结果比较吻合,数值仿真结果为板式贮箱的性能提供验证依据     

Specific features of electron distributions at altitudes of 400 km

New experimental data obtained on the orbital station ‘MIR’ in 1991 during solar maximum are discussed. Electron fluxes with E_e>75 keV were registered for three different directions as well as for electrons with E_e>300 and 600 keV. Spatial and time distributions of electron fluxes in the trapping region are presented. In the inner radiation belt an additional maximum is observed at L=1.25–1.35, and the fluxes in the 22-05^h MLT interval are 2–3 orders of magnitude smaller, than during other local times. In this region a flattening of the electron spectrum is observed. The results obtained were compared with the AE-8 model.     

Pitch angle diffusion as seen by CRRES

Lifetimes and pitch angle distributions of radiation belt electrons injected into the slot region are determined from CRRES/MEA particle flux measurements. The dominant loss mechanism is presumed to be pitch angle scattering due to whistler waves, for which a theoretical formulation is available. The empirical lifetimes are compared to those from recent calculations, which rely on model whistler wave parameters. CRRES measurements of cyclotron-frequency electric fields are also presented and compared to the wave model.     

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.     

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.     

Earth encounter velocities for interplanetary meteoroids

The speed distribution of meteoroids encountering the Earth is shown to be similar for all meteoroid masses in the range 1 g to 10⁻¹² g. The speed distribution of interplanetary meteoroids encountering the Earth has usually been inferred from meteor observations. This paper reviews commonly quoted distributions and introduces more recent estimates. The influence quoted measurement uncertainties have on the distribution of Earth encounter velocities presented by Sekanina and Southworth (1975) and Erickson (1968) is presented. The Divine (1993) model of interplanetary meteoroids fits a set of orbital distributions to a wide range of spacecraft and ground based dust detector observations. By ‘flying’ the Earth through this model the distribution of geocentric encounter velocities has been obtained for typical particle masses, 10⁻⁹ and 10⁻¹² g while those at 10⁻⁴ and 10⁻⁵ g are shown to be in error.     

Wrinkling analysis for small solar-photon sails: An experimental and analytic approach for trajectory design

A good model of solar-radiation pressure induced thrust is one of the key points in sailcraft trajectory design. The sail membrane’s local topographic deformations, i.e. wrinkles and creases, are among the main aspects that such a model should include. We have analyzed the influence of wrinkles/creases, as a whole, by measuring the related deformations on small samples of sail membrane, 2.5?μm thick, consisting of CP1 and physical-vapor-deposition Aluminum. Experimental outcomes from our laboratory facility have been processed, statistically investigated, and inserted into the lightness vector formalism. We have used such formalism for accurate sailcraft trajectory computation via a non-ideal reflection sail thrust model. Finally, we computed the deviations of wrinkled-sail sailcraft final orbital states with respect to the no-wrinkle sail final orbital ones for a circular to circular 2D inward transfer. The radii of the orbits are 1?AU and the semi-major axis of Mercury, respectively. It appears that sail wrinkles and creases are no longer negligible in the sailcraft trajectory design.     

On the lunar node resonance of the orbital plane evolution of the Earth’s satellite orbits

This paper aims to investigate the effects of lunar node resonance on the circular medium Earth orbits (MEO). The dynamical model is established in classical Hamiltonian systems with the application of Lie transform to remove the non-resonant terms. Resonant condition, stability and phase structures are studied. The lunar node resonance occurs when the secular changing rates of the orbital node (with respect to the equator) and the lunar node (with respect to the ecliptic) form a simple integer ratio. The resonant conditions are satisfied for both inclined and equatorial orbits. The orbital plane would have long period (with typical timescales of several centuries) fluctuation due to the resonance.     

基于雷诺数的大气阻力模型在飞行器再入预报中的应用

随着对空间技术服务需求的增加和空间碎片主动移除技术的实现,未来空间碎片将以数量多、质量大、难分解等特点频繁再入大气层,给地面人员和财产安全造成更多威胁.因此,亟需对火箭体等大型航天器的大气再入进行预警,然而因缺乏合适的大气阻力系数模型难以实现高精度的大气再入预报.为此,在简化航天器模型的基础上引入基于雷诺数的大气动力模...     

部署retro-GEO巡视器的月球借力飞行轨道分析

retro-GEO是指逆行（retrograde）地球静止轨道（geostationary Earth orbit, GEO），该轨道与GEO轨道高度相同或相近，但倾角为180°，安装在retro-GEO卫星上的巡视器可每12h对GEO带空间资产附近碎片环境安全预警。直接西向发射retro-GEO卫星存在地面测控和发射能耗较大的困难。基于平面四体模型，为降低设计变量敏感性，以近月点参数为设计变量，建立了部署retro-GEO巡视器的月球借力飞行轨道设计模型，利用轨道动力学模型延拓策略，得到该类轨道绕月后返回地球飞行时长只能约为114.79h，该结论可用于求解该类轨道高精度轨道动力学模型解。     

一种改进的卫星星座服务可用性评价方法

针对存在缺失卫星的轨道面,将星座中的卫星分为两组,从概率角度并采用组合方法提出了星座覆盖可用性和导航精度可用性指标的统计评价模型和仿真流程,进而通过对两项可用性指标进行加权建立了形式统一的服务可用性加权评价模型。利用该模型对单个或多个轨道面有确定数量卫星缺失的状态下,星座构型和轨道参数变化对其服务可用性的影响进行了研究。结果表明,星座轨道平面数和轨道高度均对服务可用性有较大影响。提出的服务可用性评价模型物理意义明确,可有效减少指标评价时间,研究结论有助于在概念设计阶段对星座构型和轨道参数进行优选。     

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。     

SZ-5 Cabin's Height Changes during Three Super-storms in 2003

In this work, the daily height variations of SZ-5 (Shenzhou-5) cabin from 22 October to 28 November in 2003 are analyzed, which includes the period of the Halloween Storm and the Great November Storm. The significant orbital decays have been observed at the end of October and in late November due to the great solar flares and the severe geomagnetic storms. According to the equation of the air-drag-force on a spacecraft and the SZ-5 orbital decay information, the relative daily average thermospheric density changes during the three 2003 super-storms are derived and the results are compared with the Naval Research Laboratory Mass Spectrometer Incoherent Scatter Radar Extended Model (NRLMSISE-00). The results show that the daily average thermospheric density (at the altitude of SZ-5, about 350 km) in storm time enhances to approximately 200% as much as that in the quiet time but the empirical model may somewhat underestimate the average thermospheric density changes and the daily contributions of geomagnetic storms to the density enhancements during these severe space weather events.