两种J_2摄动模型下卫星编队相对位置误差分析

为了研究一个轨道周期内卫星和卫星编队的运动规律,在J2摄动理论基础之上,采用摄动加速度分析方法,给出了J2瞬时摄动模型。以近地太阳同步轨道卫星和双星编队为例,与只考虑J2一阶长期项的平均摄动模型比较,仿真分析结果表明,对卫星而言,一个轨道周期内,卫星半长轴相对平均半长轴漂移达到18km,偏心率相对平均偏心率漂移达到10-3量级,轨道倾角相对平均轨道倾角漂移达到0.01°,即由于J2瞬时摄动的影响,卫星运动发生了摄动;对双星编队而言,一个轨道周期内,两星相对位置的径向误差达到5km,沿迹向误差达到19km,法向误差相对较小,在10-2量级上,相对距离的误差达到了19km,随着时间的推移,误差会越来越大。     

人造地球卫星轨道问题的二阶解

本文给出人造地球卫星轨道问题的二阶解。地球引力场的位函数包括任意有限个带谐调和项。这个解是基于Aksnes的中间轨道获得的,并用文字形式表达出来。短周期项是完全的,二阶长周期项和三阶长期项精确到偏心率e的一阶项。用这个解来计算轨道,在几天的时间内卫星的位置误差为一米左右。     

椭圆轨道非线性相对运动模型的周期解与应用

在长期的航天器编队飞行中传统的基于线性相对运动模型设计编队保持轨道的方法会引起较多的燃料消耗.首先采用摄动法解析地求得了考虑二阶非线性项时椭圆轨道相对运动模型的周期性条件和周期解;然后以此周期解为参考轨道设计了基于Lyapunov稳定的PD保持控制律.仿真结果表明:基于椭圆轨道非线性相对运动模型的周期解较基于椭圆轨道线性相对运动模型的周期解,精度明显提高;以前者为参考轨道的保持控制与以后者为参考轨道的保持控制相比,燃耗明显降低.     

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。     

小行星远距离抵近轨道（英文）

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。     

太阳轨道运动的2400年周期与轨道周期

通过对行星会合指数运动学方程生成的数据进行傅里叶变换, 得到了从年、十年、 百年、千年、万年到十万年时间尺度的周期, 发现这些周期具有后者是前者10n 倍的特殊倍乘关系. 如果将通过傅里叶变换得到的年时间尺度最显 著的周期4.96488a设为单位时间步长代入行星会合指数方程, 则可得到稳定 的2400年周期. 在此基础上由2400年周期振幅的差异性又构成了更长时间尺度的 10万年和40～41万年太阳轨道运动特征周期. 这对于揭示太阳轨道运动与太 阳活动的关系, 以及探讨气候千年尺度和轨道周期变化规律的机制具有重要意义.      

预言：尼比鲁带来的灾难

尼比鲁一词最早见于6000年前苏美尔人的记载（古巴比伦尼l亚人称这个行星为马杜克），他们称尼比鲁是他们的母星，其轨道交错在我们太阳系已知的8个行星之间（之前称9个），公转一次需时3600年。（玛雅预言中的太阳历，其周期为3000年。5000年，和尼比鲁的公转周期接近。）     

日ETS—6卫星运行状况与今后实验计划

１９９４年８月２８日，日本从种子岛空间中心用Ｈ－２火箭把技术试验卫星－６（ＥＴＳ－６）发射升空，虽然星箭分离成功，但由于远地点发动机点火出现故障，致使卫星未能进入地球同步轨道。现卫星处于近地点高度约７８００ｋｍ、远地点高度约３８７００ｋｍ的椭圆轨道，其轨道倾角约１３°，周期约１４小时，太阳电池帆板缓慢地朝向太阳旋转（每１５分钟转一圈）。日本为了研制这颗卫星用去近４１５亿日元，为尽量减少损失，打算利用该卫星做各种实验，其计划如下。一、已进行的实验从１９９４年９月１日进入现有的轨道，进行了下列一些工…     

天外有天

近年来，科学家发现太阳系外行星的无可辩驳的事实，向世人宣示：天外有天。同时也表明，我们人类对自己所在的太阳系乃至银河系，还知之甚少。最近，天文学家又发现了一颗围绕名叫格利斯８７６恒星旋转的行星，它的质量约有５００个地球大小。由于这颗行星在一个很扁的椭圆形轨道上运行，并且旋转速率也异乎寻常，所以１年（公转１周）仅仅需要６１天。它与它所围绕的、暗淡无光的红矮星之间的距离，比太阳系最里层的行星———被太阳烤焦的水星离太阳的距离还要近。但是，它的表面很可能有气体存在，气温或许在－７５℃，按地球表面的温度…     

多行星恒星系统

开普勒计划近期发现了太阳系外首批类地行星——开普勒20e和开普勒20f,它们以一颗类似于太阳的恒星为中心做轨道运转。这两颗行星处在所谓的"宜居带"上,因为距离恒星位置非常近,星球表面有液态水存在。开普勒20f是已知跟地球体形相似的最近的行星。但就目前所知,其20天的轨道周期和427℃的表面温度并不适合生命的存在。     

考虑太阳摄动的小行星附近轨道动力学

本文研究了艳后星(216 Kleopatra)和爱神星(433 Eros)附近的周期轨道,在考虑太阳引力摄动的情况下,发现了以往所遗漏的216 Kleopatra轨道族和环绕433 Eros的12族周期轨道,并且给出了它们的特性。研究结果表明,太阳引力对小行星平衡点位置的影响很小,但是对平衡点上航天器运动的影响较大。同族不稳定轨道中,大Jacobi常数轨道更容易在摄动后保持轨道原来特性,这很好地解释了小行星卫星在较远轨道上长期存在的可能性。     

Dynamics in the Phobos environment

The dynamical environment on and about the Martian moon Phobos is explored. This planetary moon provides a unique dynamical environment in the solar system, being subject to extreme tidal forces and having a characteristically non-spherical shape. Further, it is not in a fully circular orbit, meaning that it has librations that arise from its eccentricity, contributing to a periodic forcing environment. Thus, to plan and implement missions in the vicinity of and on Phobos will require these considerations be taken into account. In this paper the latest published models of the Phobos shape and dynamics are used to characterize its dynamical environment in close proximity orbit about the body, for motion across its surface and for controlled hovering motion in its vicinity. It is found that surface motion is subject to a number of “speed limits” that can cause a moving vehicle to leave the surface and to possibly escape the moon and enter orbit about Mars. In terms of orbital stability, the existence of libration orbit families are characterized down to the surface using an exact potential, and the known stable QSO orbits are shown to be associated with families of stable quasi-periodic orbits.     

基于参考轨道的Walker星座相对相位保持策略

针对高轨道Walker全球星座相对相位保持问题,在分析星座几何结构演化规律基础上,提出了一种基于动态调整参考轨道的星座相对相位保持策略.该参考轨道的半长轴取星座所有卫星的平均轨道半长轴的平均值,通过计算各卫星相对参考轨道的相对相位偏差以及变化率,而后根据有关维持的约束条件来选择合适的卫星进行站点保持,使得所有卫星的相对参考轨道的相位偏差不超过允许值.当一旦有卫星进行了站点保持,则参考轨道就重新统计确定.文章通过一个12颗MEO卫星构成的Walker-δ星座的分析算例,表明这种相对保持策略可以减少星座的站点维持次数.本文提出的方法可以为我国今后卫星导航星座的维持提供参考.     

Low-altitude,near-polar and near-circular orbits around Europa

The dynamics of orbits around planetary satellites, taking into account the gravitational attraction of a third-body and the non-uniform distribution of mass of the planetary satellite, is studied. The Hamiltonian considered is explicitly time-dependent. Conditions for frozen orbits are presented. Low-altitude, near-polar orbits, very desirable for scientific missions to study planetary satellites such as the Jupiter’s moon Europa, are analyzed. Lifetimes for these orbits are computed through the single and double averaged method. Comparison between the results obtained by the single and double averaged method is presented. The single-averaged model is more realistic, since it does not eliminate the term due to the equatorial ellipticity of the planetary satellite as done by the double-averaged problem. Considering the single-averaged method, we found unstable frozen orbits where the satellite does not impact with the surface of Europa for at least 200 days. We present an approach using the unaveraged disturbing potential to analyze the effects of these terms in the amplitude of the eccentricity.     

连续小推力非开普勒悬浮轨道研究综述

连续小推力非开普勒悬浮轨道在深空探测与地球极地观测任务中有着重要的应用前景。归纳了电推进、太阳帆推进等连续小推力技术的发展历程与现状;阐述了日心、行星悬浮轨道的动力学特性、稳定性、轨道保持策略;分析了三体问题下人工拉格朗日点的优势及其在深空探测方面的应用;讨论了悬浮轨道编队飞行的研究方法与控制策略。最后针对小推力悬浮轨道研究发展面临的难题,提出了研究新思路和应用新方向。     

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.     

GNSS-R concept extended by a fine orbit tuning

Small changes in semimajor axis of the orbits selected for the GNSS-R [R as Reflectometry] satellites, so-called fine orbit tuning, known from the ESA’s Gravity and steady-state Ocean Circulation Explorer mission, can dramatically increase the number of nadir and off-nadir reflecting points and, in turn, can enhance the capability of the concept of bistatic altimetry (GNSS Reflectometry) without additional costs. The application of our suggestion is feasible for a satellite which will be equipped by thrusters for the orbit keeping. During the mission lifetime several orbit tunings are feasible, just to transfer from one to another orbit. Then we can study short-periodic or longer-periodic features, according to scientific goals defined for the mission. The shortest cycles (few days), corresponding to the required revisit time (defined by ESA), may be subcycles of much longer cycles (repeat periods).     

航天器相对运动的两点边界值问题解析解

针对无摄椭圆轨道,推导了表示真实相对位置速度的状态转移矩阵,进而推导出了相对运动两点边界值问题的一阶解析解。所得结果不仅可指定转移时间、还可在时间范围内进行全局的燃料优化或在时间和燃料两者间折中;对于周期和非周期的相对运动均适用。仿真结果表明此解的归一化精度达到10^－6。进一步的仿真发现相对转移过程的燃料消耗会随目标轨道偏心率的增加而增加;随长半轴的增加而减少;随初始真近点角的增加呈现周期性变化;随着转移时间增加,燃料消耗的总趋势是减少的。     

On the stabilizing effect of Solar Radiation Pressure in the Earth-Moon system

Solar sails change the natural dynamics of systems: Trajectories that are driven by gravitational forces can be displaced and changed because of the effect of Solar Radiation Pressure (SRP). Moreover, if the lightness number of the sail is large enough, the instability of certain orbits can be diminished and even removed. In this paper we modify two models for the motion of a probe in the Earth-Moon system that include the effect of Sun’s gravity to take also into account the effect of SRP. These models, the Bicircular Problem (BCP) and the Quasi-Bicircular Problem (QBCP), are periodic perturbations of the Earth-Moon Restricted Three Body Problem (RTBP). The models are modified to consider the effect of the SRP upon a solar sail. We provide examples of periodic orbits that are stabilized (or made less unstable) due to the effect of SRP.     

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.