从日地系统L2出发借力月球飞越近地小行星

对于停留在日地系统L2的“嫦娥2号”探测器,其后续飞行方案有多个选项,例如主动撞月或重返月球轨道、返回地球轨道或再入大气、飞往地月系统L1/L2或日地系统L1、进入深空飞越近地小行星(最终,“嫦娥2号”于2012年12月13日成功地实现了对Toutatis小行星的近距离飞越)。探讨上述的飞行方案需要对飞行轨道进行初步设计,总的速度脉冲限制在100 m/s以内并且需要考虑探测器同时受到太阳、地球、月球的引力作用。本研究设计了探测器从日地系统L2出发借力月球实现Toutatis小行星飞越的飞行方案,与直接飞越方案相比,借力月球可以进一步节省探测器的燃料消耗,其等效速度脉冲设计值为58.47 m/s。     

小行星远距离抵近轨道

讨论了小行星引力一阶项可被忽略情况下的小行星远距离轨道设计及动力学。此时,航天器的运动受太阳引力和太阳光压的影响。航天器和小行星的加速度之差在这两者之间形成的独特的相对动力学,为航天器在小行星附近停驻与观测提供特定轨道。完整解决了小行星处于圆形日心轨道这一较简单情况,也考虑和阐述了椭圆轨道情况,并取得了一些初步结果。     

Dynamics of a spacecraft and normalization around Lagrangian points in the Neptune–Triton system

The problem of a spacecraft orbiting the Neptune–Triton system is presented. The new ingredients in this restricted three body problem are the Neptune oblateness and the high inclined and retrograde motion of Triton. First we present some interesting simulations showing the role played by the oblateness on a Neptune’s satellite, disturbed by Triton. We also give an extensive numerical exploration in the case when the spacecraft orbits Triton, considering Sun, Neptune and its planetary oblateness as disturbers. In the plane a × I (a = semi-major axis, I = inclination), we give a plot of the stable regions where the massless body can survive for thousand of years. Retrograde and direct orbits were considered and as usual, the region of stability is much more significant for the case of direct orbit of the spacecraft (Triton’s orbit is retrograde). Next we explore the dynamics in a vicinity of the Lagrangian points. The Birkhoff normalization is constructed around L₂, followed by its reduction to the center manifold. In this reduced dynamics, a convenient Poincaré section shows the interplay of the Lyapunov and halo periodic orbits, Lissajous and quasi-halo tori as well as the stable and unstable manifolds of the planar Lyapunov orbit. To show the effect of the oblateness, the planar Lyapunov family emanating from the Lagrangian points and three-dimensional halo orbits are obtained by the numerical continuation method.     

Resonant quasi-periodic near-rectilinear Halo orbits in the Elliptic-Circular Earth-Moon-Sun Problem

Motivated by the near-future re-exploration of the cislunar space, this paper investigates dynamical substitutes of the Earth-Moon’s resonant Near-Rectilinear Halo Orbits (NRHOs) under the Elliptic-Circular Restricted Four-Body Problem formulation of the Earth-Moon-Sun system. This model considers that the Earth and Moon move in elliptical orbits about each other and that a third body, the Sun, moves in a circular orbit about the Earth-Moon barycenter. By making use of this higher-fidelity dynamical model, we are able to incorporate the Sun’s influence and the Moon’s eccentricity, two of the most significant perturbations of the cislunar environment. As a result of these perturbations, resonant periodic NRHOs of the Earth-Moon Circular Restricted Three-Body Problem (CR3BP) are hereby replaced by two-dimensional quasi-periodic tori that better represent the dynamical evolution of satellites near the vicinity of the Moon. We present the steps and algorithms needed to compute these dynamical structures in the Elliptic-Circular model and subsequently assess their utility for spacecraft missions. We focus on the planned orbit for the NASA-led Lunar Gateway mission, a 9:2 synodic resonant L₂ southern NRHO, as well as on the 4:1 synodic and 4:1 sidereal resonances, due to the proximity to the nominal orbit and their advantageous dynamical properties. We verify that the dynamical equivalents of these orbits preserve key dynamical attributes such as eclipse avoidance and near-linear stability. Furthermore, we find that the higher dimensionality of quasi-periodic solutions offers interesting alternatives to mission designers in terms of phasing maneuvers and low-altitude scientific observations.     

Configuration space and stability analysis of solar sail near-vertical earth-trailing orbits

Regions outside the reach of traditional propulsion systems or the ones that require significant propellant, may be reached by harnessing the solar radiation pressure and leveraging coupled dynamics to maneuver a sail-based spacecraft. Earth-trailing orbits have recently been investigated for getting a unique perspective of the Sun while maintaining the spacecraft in close proximity to Earth. Vertical orbits trailing the Earth exhibit the additional capability to view the Sun from above and below the ecliptic plane. In this work, families of sail-based orbits are explored for varying Earth-trailing angles and Z amplitudes in the Sun-Earth circular restricted three-body problem. Optimization is carried out to ensure that the non-traditional vertical orbits exhibit a constant pitch angle control history, as well as symmetry across the X-Y plane. The stability of the resulting orbit families is assessed using an extension of Flouquet theory to Differential Algebraic Equations. Results indicate that sail-based Earth-trailing vertical orbits can be more stable than traditional sub-L₁ sail-based vertical orbits.     

Synergistic approach of asteroid exploitation and planetary protection

The asteroid and cometary impact hazard has long been recognised as an important issue requiring risk assessment and contingency planning. At the same time asteroids have also been acknowledged as possible sources of raw materials for future large-scale space engineering ventures. This paper explores possible synergies between these two apparently opposed views; planetary protection and space resource exploitation. In particular, the paper assumes a 5 tonne low-thrust spacecraft as a baseline for asteroid deflection and capture (or resource transport) missions. The system is assumed to land on the asteroid and provide a continuous thrust able to modify the orbit of the asteroid according to the mission objective. The paper analyses the capability of such a near-term system to provide both planetary protection and asteroid resources to Earth. Results show that a 5 tonne spacecraft could provide a high level of protection for modest impact hazards: airburst and local damage events (caused by 15–170 m diameter objects). At the same time, the same spacecraft could also be used to transport to bound Earth orbits significant quantities of material through judicious use of orbital dynamics and passively safe aero-capture manoeuvres or low energy ballistic capture. As will be shown, a 5 tonne low-thrust spacecraft could potentially transport between 12 and 350 times its own mass of asteroid resources by means of ballistic capture or aero-capture trajectories that pose very low dynamical pressures on the object.     

Encounter trajectories for deep space mission ASTER to the triple near Earth asteroid 2001-SN263. The laser altimeter (ALR) point of view

In cooperation with Russia, the Brazilian deep space mission ASTER plans to send a small spacecraft to investigate the triple asteroid 2001-SN263. The nearest launch opportunities for this project include June 2022 and June 2025. One main exploration campaign is being planned with focus on the largest asteroid (Alpha). Among the instruments under development, a laser altimeter (named ALR) was preliminarily designed and presented in 2010–2011. Many studies to define mission and instruments requirements were performed aiming at the characterization of important issues for the successful realization of the mission. Among them, the identification of a suitable trajectory that could be followed by the ASTER spacecraft in the encounter phase, when the main campaign will take place. This paper describes the effort undertaken with focus on the laser altimeter operation. Possible encounter trajectories were modelled and simulated to identify suitable approach parameters and conditions allowing the accomplishment of the intended investigation. The simulation also involves the instrument operation, considering approach geometry, attitude, relative motion, time/date, and the dynamics of the main asteroid. From the laser altimeter point of view, keeping in mind the desired coverage results (50% minimum surface coverage of asteroid Alpha, complying with horizontal and vertical resolution requirements), results point out crucial features for the encounter trajectory, like the need for a small inclination (10^-6 degrees; with respect to the asteroid's orbit), the most favourable spacecraft positioning (between the Sun and the asteroid) and pointing condition (back to the Sun), the minimum amount of achievable surface coverage (58%, focused on central areas), and the most proper time to conduct the main campaign (January 2025). Concerning the instrument, results offer refined values for divergence angle (500 to 650 μrad, half-cone), pulse repetition frequencies (from 1/20 to 1 Hz), and consequent data generation rates. A simulation tool that can use any 3D generated trajectories as input data was created for the analyses presented here. Although created for the ALR in this mission, this simple analysis tool can be adapted to other instruments in this or other missions.     

近距离空间交会动力学

首先研究两个飞行器在近距离相对运动的动力学方程,包括简易（线性化）和精确模型;其次推导出一个工程实用在轨道平面内保持点轨迹椭圆方程;最后讨论保持点的动力学特性和轨道摄动对保持点的影响。     

单个航天器对Walker星座中多卫星的近距离接近

通过设计航天器轨道,可使航天器发射入轨后无需机动即实现对Walker星座中非共轨的多颗卫星的快速、近距离接近.给出了该轨道的搜索方法以及基于星座特性的代换法,并给出了仿真示例.      

Optimal station-keeping near Earth–Moon collinear libration points using continuous and impulsive maneuvers

In this study the gravitational perturbations of the Sun and other planets are modeled on the dynamics near the Earth–Moon Lagrange points and optimal continuous and discrete station-keeping maneuvers are found to maintain spacecraft about these points. The most critical perturbation effect near the L₁ and L₂ Lagrange points of the Earth–Moon is the ellipticity of the Moon’s orbit and the Sun’s gravity, respectively. These perturbations deviate the spacecraft from its nominal orbit and have been modeled through a restricted five-body problem (R5BP) formulation compatible with circular restricted three-body problem (CR3BP). The continuous control or impulsive maneuvers can compensate the deviation and keep the spacecraft on the closed orbit about the Lagrange point. The continuous control has been computed using linear quadratic regulator (LQR) and is compared with nonlinear programming (NP). The multiple shooting (MS) has been used for the computation of impulsive maneuvers to keep the trajectory closed and subsequently an optimized MS (OMS) method and multiple impulses optimization (MIO) method have been introduced, which minimize the summation of multiple impulses. In these two methods the spacecraft is allowed to deviate from the nominal orbit; however, the spacecraft trajectory should close itself. In this manner, some closed or nearly closed trajectories around the Earth–Moon Lagrange points are found that need almost zero station-keeping maneuver.     

基于最小轨道交叉距离的小行星顺访探测目标预筛选方法

小行星探测有助于研究太阳系演化等重要科学问题,在深空探测任务转移途中实施小行星顺访探测可增加科学研究回报。直接通过轨道递推筛选小行星探测目标计算量大、效率低,针对该问题提出了基于最小轨道交叉距离的目标预筛选方法。在推导出适用于计算双曲线轨道的最小轨道交叉距离公式后,将此理论应用到小行星顺访探测目标筛选中。首先基于探测器与小行星轨道的形状、空间位置计算二者轨道在空间中的几何最近距离,预筛选出可能满足接近距离标准的小行星目标;然后基于轨道递推模型,筛选出真实最近距离小于可接近标准的目标小行星。仿真结果显示,基于最小轨道交叉距离的预筛选方法可有效减少计算量,降低计算时间,提高小行星顺访目标筛选的效率。      

Orbital stability close to asteroid 624 Hektor using the polyhedral model

We investigate the orbital stability close to the unique L4-point Jupiter binary Trojan asteroid 624 Hektor. The gravitational potential of 624 Hektor is calculated using the polyhedron model with observational data of 2038 faces and 1021 vertexes. Previous studies have presented three different density values for 624 Hektor. The equilibrium points in the gravitational potential of 624 Hektor with different density values have been studied in detail. There are five equilibrium points in the gravitational potential of 624 Hektor no matter the density value. The positions, Jacobian, eigenvalues, topological cases, stability, as well as the Hessian matrix of the equilibrium points are investigated. For the three different density values the number, topological cases, and the stability of the equilibrium points with different density values are the same. However, the positions of the equilibrium points vary with the density value of the asteroid 624 Hektor. The outer equilibrium points move away from the asteroid’s mass center when the density increases, and the inner equilibrium point moves close to the asteroid’s mass center when the density increases. There exist unstable periodic orbits near the surface of 624 Hektor. We calculated an orbit near the primary’s equatorial plane of this binary Trojan asteroid; the results indicate that the orbit remains stable after 28.8375?d.     

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.     

Solar sails for perturbation relief: Application to asteroids

A major cause of spacecraft orbital variation comes from natural perturbations, which, in close proximity of a body, are dominated by its non-spherical nature. For small bodies, such as asteroids, these effects can be considerable, given their uneven (and uncertain) mass distribution. Solar sail technology is proposed to reduce or eliminate the net secular effects of the irregular gravity field on the orbit. Initially, a sensitivity analysis will be carried out on the system which will show high sensitivity to changes in initial conditions. This presents a challenge for optimisation methods which require an initial guess of the solution. As such, the Genetic Algorithm (GA) is proposed as the preferred optimisation method as this requires no initial guess from the user. A multi-objective optimisation is performed which aims to achieve a periodic orbit whilst also minimising the effort required by the sail to do so. Given the system sensitivity, the control law for one orbit is not necessarily applicable for any subsequent orbit. Therefore, a new method of updating the control law for subsequent orbits is presented, based on linearisation and use of a Control Transition Matrix (CTM). The techniques will later find application in a multiple asteroid rendezvous mission with a solar sail as the primary propulsion system.     

气动辅助异面变轨在多碎片清除中的应用分析

碎片清除飞行器异面变轨需要消耗大量燃料.从气动辅助异面变轨优化设计及被清除碎片轨道高度差值、倾角差值等参数对变轨性能的影响出发,比较分析了优化气动辅助异面变轨与双脉冲霍曼轨道转移的燃料节约量,研究了不同轨道高度差对于实施气动辅助变轨燃料节约量的影响.当地球静止轨道（GEO）与低地轨道（LEO）间气动辅助变轨优化速度增量约为1.55km·s-1、质量面积比172kg·m-2、比冲310s、轨道倾角变化16°时,燃料节约率约为45%.对比研究了不同轨道高度差LEO轨道间实施气动辅助变轨的燃料节约情况.结果表明:随着轨道高度的增加,气动辅助优化效率逐渐降低;在相同高度轨道间实施异面变轨,随着轨道倾角的增加,气动辅助变轨燃料节约率先增大后减小,倾角改变量约为20°时,燃料节约率最大;当轨道倾角为5°时,采用气动辅助变轨和双脉冲变轨的燃料消耗量相同.      

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。     

Collision probability and spacecraft disposition in the geostationary orbit

Since 1963 approximately 300 satellites have been launched into the geostationary orbit, followed possibly by another additional 200 satellites up to the year 2000. Ground surveillance with radar and optical sensors able to detect objects of 1 m minimum size in the geostationary ring indicates a total population of several hundred which includes active and defunct satellites and spent upper stages. In addition, a population of untrackable objects is conjectured, whose size can only be estimated, possibly several thousand of smaller objects.

The purpose of this paper is to review the long-term evolution of orbits in the geostationary ring and at higher altitude, the collision probabilities and disposition options.

The major perturbations are considered including attitude-orbit cross-coupling effects which could cause secular orbit perturbations.

Collision probabilities for current and projected populations are reviewed considering different approaches, such as a deterministic treatment of the uncontrolled population and a stochastic modeling for the controlled satellites. Also, colocation, that is sharing of the same longitude slot by several operational satellites, is a potential source for collision, if no preventive measures are taken.

As regards spacecraft disposition options, the conclusion is that reorbiting is currently the only practical measure to safeguard the geostationary orbit. In this recommended procedure the defunct satellites are inserted into a so-called graveyard orbit, located suffieciently high above the geostationary orbit.     

Measurements of LET spectra and comparison to models.

We present measurements of LET spectra for near earth orbits with various inclinations and altitudes. A comparison with calculated LET spectra shows that the contribution from direct ionizing galactic cosmic rays is well described by the models. An additional contribution to the spectra originates from stopping protons and from nuclear interactions of particles with material. In the case of an interaction a large amount of energy is deposited in a small volume by target recoils or target fragments. These events will be called short range (SR) events. For a low inclination orbit radiation belt protons are the main source of these events while galactic protons become more important when increasing the inclination to near polar orbits. We show that the contribution of SR events for orbits with low altitude (324 km) and 57 degrees inclination is comparable to that for an orbit with 28 degrees inclination at a high altitude (510 km).     

Stability of relative equilibria of the full spacecraft dynamics around an asteroid with orbit–attitude coupling

The full dynamics of spacecraft around an asteroid, in which the spacecraft is considered as a rigid body and the gravitational orbit–attitude coupling is taken into account, is of great value and interest in the precise theories of the motion. The spectral stability of the classical relative equilibria of the full spacecraft dynamics around an asteroid is studied with the method of geometric mechanics. The stability conditions are given explicitly based on the characteristic equation of the linear system matrix. It is found that the linearized system decouples into two entirely independent subsystems, which correspond to the motions within and outside the equatorial plane of the asteroid respectively. The system parameters are divided into three groups that describe the traditional stationary orbit stability, the significance of the orbit–attitude coupling and the mass distribution of the spacecraft respectively. The spectral stability of the relative equilibria is investigated numerically with respect to the three groups of system parameters. The relations between the full spacecraft dynamics and the traditional spacecraft dynamics, as well as the effect of the orbit–attitude coupling, are assessed. We find that when the orbit–attitude coupling is strong, the mass distribution of the spacecraft dominates the stability of the relative equilibria; whereas when the orbit–attitude coupling is weak, both the mass distribution and the traditional stationary orbit stability have significant effects on the stability. We also give a criterion to determine whether the orbit–attitude coupling needs to be considered.