轨道要素奇异问题的改进四元数方法

运用四元数方法可以在一定范围内解决描绘飞行器轨道运动时轨道要素的奇异问题。但四元数固有的双值性使得在对运动方程进行积分时,其正负选取很困难。为了解决这一问题,采用了改进约束方程的四元数方法,并用该方法描述了拉格朗日行星摄动方程,然后研究了地球扁率摄动对地球同步卫星轨道的影响。仿真结果表明：当偏心率小于1时,四元数可以很好地解决轨道要素奇异性问题。与改进的春分点轨道要素相比,四元数的方法有着更加明确的物理意义和几何意义,用四元数表示的运动变量方程的计算更为简单,积分计算效率更高,而且其计算误差也能达到精度要求。     

The use of Gaussian equations of motions of a satellite for local gravity anomaly recovery

The orbital elements of a low Earth orbiting satellite and their velocities can be used for local determination of gravity anomaly. The important issue is to find direct relations among the anomalies and these parameters. Here, a primary theoretical study is presented for this purpose. The Gaussian equations of motion of a satellite are used to develop integral formulas for recovering the gravity anomalies. The behaviour of kernels of the integrals are investigated for a two-month simulated orbit similar to that of the Gravity field and steady-state ocean circulation explorer (GOCE) mission over Fennoscandia. Numerical investigations show that the integral formulas have neither isotropic nor well-behaved kernels. In such a case, gravity anomaly recovery is not successful due to large spatial truncation error of the integral formulas. Reformulation of the problem by combining the orbital elements and their velocities leads to an integral with a well-behaved kernel which is suitable for our purpose. Also based on these combinations some general relations among the orbital elements and their velocities are obtained which can be used for validation of orbital parameters and their velocities.     

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.     

一组新的四元数轨道要素建模方法

针对传统以欧拉角为参数的轨道要素的奇异性、不确定性以及计算效率低等问题,提出了一种新的四元数轨道要素。建立了新轨道要素与经典轨道要素,以及新轨道要素与惯性系下位置、速度的相互转换关系,推导了基于新轨道要素的高斯摄动方程。以J₂项摄动下的轨道推演为例进行仿真验证,结果表明新轨道要素不仅在圆轨道与赤道平面轨道处不存在奇异性和不确定性,而且由于新轨道要素不涉及三角函数运算,新高斯摄动方程积分效率和计算精度明显提高。     

探测器垂直击中月球的轨道设计

本文讨论了探测器从低高度圆形地球停泊轨道入轨点出发、在停泊轨道上滑行一段后、沿速度方向加速进入登月轨道、自由飞行击中月球的轨道设计．在着月的速度、角度、时间、区域、停泊轨道和能量限制等约束下,首先借助二体、双二体理论,不仅提供了轨道初值的近似值,而且说明了轨道的特性．然后利用广义限制性四体动力学模型,进行3点边值搜索,得到高精度的探测器轨道．     

飞行器轨道交会的H_∞次优控制问题

研究了近圆轨道上两个飞行器轨道交会的控制问题。通过对最优控制理论设计最优交会轨线的研究 ,提出了利用 H∞控制理论设计实际控制器的方法 ,给出了仿真结果 ,验证了这种方法的正确性。说明了该方法具有鲁棒的控制效果以及次优的轨道特性。     

平均轨道要素及其在卫星星座设计中的应用

平均轨道要素在卫星轨道设计及星座仿真中具有非常重要的作用。在综合国内外现有研究成果的基础上，给出了一整套简单实用、没有奇点的密切要素与平均要素间的相互转化方法，用此法进行的星座设计及仿真工作表明该方法非常有用。同时给出了利用平均轨道要素得以的关于赤道平面圆轨道的一个有意义的结论。     

遗传算法在星座多星接近轨道优化中的应用

以三颗非共轨的Walker星座卫星为研究对象, 对航天器无需变轨与其接近的可能性进行研究. 将Lambert方法得到的航天器轨道作为初始轨道, 利用遗传算法对初始轨道进行优化. 对初始轨道在参考时刻位置和速度的改变量进行编码,形成对应的种群. 以航天器与星座卫星之间的最近距离为适应度函数, 通过种群的繁殖得到优化结果. 结合仿真算例, 分析了最小二乘算法和遗传算法在轨道优化中的优劣以及接近过程中轨道摄动的影响. 结果表明, 遗传算法适用于所提出的轨道改进问题. 研究结果可为单航天器无需变轨对星座多星接近问题提供理论依据.      

地球静止卫星电推进轨道保持策略优化

针对电推力器控制弧段长、传统轨道保持计算常用的脉冲假设不能适用的问题,提出了静止卫星轨道保持的平运动动力学模型和长期控制策略优化方法。由于轨道保持控制的是平均轨道要素,文章提出了一种基于春分点轨道要素的高精度平根外推动力学模型,与STK-HPOP模型比对高度吻合;提出了综合考虑轨道东西和南北控制的耦合控制优化模型,设计了基于序列二次规划的优化求解方法。仿真算例中研究了二推力器配置的静止卫星4周轨道保持问题,仿真结果表明,该方法可以优化长期轨道保持控制策略。     

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。     

Velocity pointing error analysis for symmetric spinning thrusting Cubesat

To solve the problem of thrust vector misalignment from the Cubesat center of mass during orbital maneuver, spin-stabilized method is applied to eliminate velocity pointing error. Spinning thrusting Cubesat model involves the effects of mass variation and jet damping is established. Analytical solutions for the angular velocity, nutation angle, Euler angle, and inertial velocity with nonzero initial conditions are derived. Simulations show that the analytical solutions closely match numerical simulations. Based on the analytical solutions, the velocity pointing error influencing factors is analyzed. The results show that the velocity pointing error caused by initial transverse velocity, nutation angle and transverse disturbance torque can be reduced by raising the spin rate, but the initial Euler angle need to be limited. Also, the spinning thrusting maneuver can allow for a lower spin rate by increasing the axial moment of inertia.     

Observation campaign dedicated to 1968-081E fragments identification

This paper proposes a comprehensive approach to associate origins of space objects newly discovered during optical surveys in the geostationary region with spacecraft breakup events. A recent study has shown that twelve breakup events would be occurred in the geostationary region. The proposed approach utilizes orbital debris modeling techniques to effectively conduct prediction, detection, and classification of breakup fragments. Two techniques are applied to get probable results for origin identifications. First, we select an observation point where a high detection rate for one breakup event among others can be expected. Second, we associate detected tracklets, which denotes the signals associated with a physical object, with the prediction results according to their angular velocities. The second technique investigates which breakup event a tracklet would belong to, and its probability by using the k-nearest neighbor (k-NN) algorithm.     

伴随轨道拟合技术

航天器的伴随轨道可以执行各种特殊任务。文中给出一种从伴随轨道确定两个航天器轨道要素的方法,这一方法也可推广应用于多个航天器的情况。     

An alternative representation of the relative motion: The local orbital elements

The study of the relative motion between two very-close non-massive objects has been usually done through Hill equations. More recent approaches use the differences of orbital elements to extrapolate relative motion. In this paper, we present another possible representation of the relative motion. This representation takes advantage of the very particular most common relative trajectory: the ellipse. Our representation induces a better temporal comprehension of the motion but it also provides the topology of the natural relative motions. Our approach is useful for circular and slightly eccentric reference orbits.     

Excavation of artificial caverns inside asteroids by leveraging rotational self-energy

Future space ventures will likely require exploitation of near-Earth asteroid resources. Moreover, it can be envisaged that asteroids may host habitats in their interiors. In fact, a cavern inside an asteroid would be a natural radiation shield against cosmic radiation and may also serve as a confined environment for storage of mined material such as water ice or other processed volatiles such as propellants. To this end, this paper proposes to leverage the asteroid rotational self-energy to remove material from the asteroid interiors and create a spherical cavern, by means of the orbital siphon concept. The siphon is a chain of tether-connected payload masses (the asteroid material), which exploits the rotation of the asteroid for the delivery of mass from the asteroid to escape. Under certain conditions the siphon can be initiated to ensure self-sustained flow of mass from the asteroid to escape. A net orbital siphon effect is generated by connecting new payloads at the bottom of the chain while releasing the upper payloads. Key parameters are discussed, such as the required siphon dimension and the maximum size of the internal cavity that can be excavated, as a function of the asteroid rotational period. Moreover, assuming elastic material behaviour, a closed-form expression for the stress tensor is found and a failure criterion is used to identify regions in the asteroid interiors subjected to the larger stresses. It is shown that the conditions for failure are relaxed as the radius of the internal void increases.     

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.     

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.     

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。