基于圆型限制性三体模型的借力飞行机理研究

针对星际探测中的借力飞行技术,基于圆型限制性三体模型,深入研究了全相位角情况下借力飞行自由参数与借力飞行轨道变化之间的关系。在圆型限制性三体问题的假设下,通过正向与逆向积分相结合的方法,给出了圆型限制性三体系统中,通过借力飞行实现逃逸与俘获以及顺行轨道与逆行轨道转变的条件,并以地月系统为例,给出了通过月球借力飞行实现地月系统俘获与逃逸的借力飞行参数选择区域。同时,也给出了通过月球借力飞行实现轨道类型转变的参数变化范围。最后,讨论分析了借力飞行高度、速度和借力相位角对借力飞行轨道能量变化量的影响,进一步揭示借力飞行自由参数与借力飞行轨道变化之间的关系。     

基于地球引力变轨的日冕探测器轨道设计

研究了相对黄道面有一定倾角的探测器轨道设计的问题。以金星借力轨道设计为例,分析了轨道偏心率与轨道倾角增量之间的关系。根据C3匹配原理搜索了“地球-中间天体-地球”多天体交会的发射窗口。最后,设计了与地球轨道周期相等的三次地球借力轨道,该轨道倾角可以达到黄纬30°以上。理论分析及仿真结果表明:基于地球引力设计此类轨道时,应采用多天体交会方案,才能既保证地球逃逸能量低,又保证首次飞入地球影响球前轨道偏心率较大的双重指标;同时应采用多次地球借力方案,该方案具有每次借力后轨道偏心率逐渐减小的特点,当其减小到零时,再次借力后轨道倾角不会继续增加。     

星际探测借力飞行轨道的混合设计方法研究

以金星借力探测火星为背景,针对传统借力飞行轨道设计方法中存在的问题,提出了 一种星际探测借力飞行轨道的混合设计方法。该方法在分析借力天体特性的基础上,采用等 高线图给出可能出现借力参数匹配的区域,提出“软匹配”策略进行轨道拼接,采用混合优 化设计方法得到轨道优化设计参数,有效地解决了传统方法对一些满足约束条件转移轨道方 案的遗漏问题。本文以2017-2018年金星借力探测火星为例给出了设计结果,设计参数与 M.Okutsu给出的一致,同时还得到了该参数区域一个新的借力轨道转移方案。此外,本文还 对2010-2018年采用金星借力探测火星的转移轨道进行了研究,给出了金星借力探测火星 较好的设计参数区域,这些研究对于未来可能的火星探测任务的设计与规划具有重要的参考 意义。
     

地月空间NRHO与DRO在月球探测中的应用研究

针对地月系统三体问题低能往返轨道转移在月球探测中的应用研究，结合天体借力飞行技术与混合优化技术，系统分析了不同目标轨道与借力方位对任务飞行时间与燃料消耗等关键参数的影响，给出了往返轨道设计初值的选择策略。针对轨道设计初值猜想问题，首先采用遗传算法与二体Lambert转移快速确定轨迹拼接点初值。在同时考虑近月点与近地点多约束条件下，基于序列二次规划算法与多重打靶法进一步对燃料最优的地月往返轨道进行研究，并推导了约束方程解析梯度提高设计效率。最后分析近月点高度、不同目标轨道的转移时间与燃耗变化特性，对于考虑月球借力的地月空间轨道往返转移设计及参数选取具有重要的参考价值。     

基于金星借力的黄道面外日冕探测器轨道设计

针对向太阳高纬发射日冕探测器科学任务,对借金星引力探测器轨道设计进行了研究。用圆锥曲线拼接法给出了地球逃逸轨道参数中的升交点赤径和近地点幅角的解析解,保证了快速设计轨道。分析数组飞往金星的日心过渡轨道发现:首次飞入金星影响球前探测器日心轨道偏心率较大,是保证多次借金星引力提高倾角的关键;当探测器日心轨道偏心率接近零时,借力后轨道倾角不会继续提高。设计了与金星轨道周期相等的三次金星借力轨道,倾角最终达到黄纬20°以上。     

面向木星卫星交会任务的探测器飞行路径规划

针对探测器在木星系统内多次借力的飞行路径和轨道优化设计问题,提出了一种基于三层优化思想的飞行路径规划方法,该方法可根据给定的任务约束和交会目标,自动搜索探测器在木星系统内的借力飞行序列,同时完成标称飞行轨道的优化设计。首先,文章在给定轨道动力学模型和木卫借力模型基础上,建立了面向木卫交会任务的两次借力飞行轨道优化设计模型和求解方法;然后,采用结合遗传算法、全局遍历和贪婪算法的三层优化设计思路,给出了一种环木飞行路径规划方法;最后,以木星四颗卫星的交会任务为例进行了仿真分析。仿真结果表明：针对木卫的交会任务,探测器速度增量需求随木卫借力次数的增多,呈现先显著减小后逐渐增大的现象;探测器采用多次木卫借力的策略,可显著降低探测器的速度增量需求;探测器速度增量达到最优之后,借力目标收敛于交会目标,且速度增量随借力次数的进一步增多而逐渐增大。     

不同月球借力约束下的地月Halo轨道转移轨道设计

针对地月系L2点不同任务需求下的低耗能转移轨道设计问题,基于不变流形理论与混合优化技术,深入研究了不同月球借力约束与不同幅值Halo轨道的入轨点（简称HOI点）对转移轨道飞行时间与燃料消耗的影响,给出了HOI点选择策略。首先结合任务要求并考虑月球引力影响,在月球借力点施加不同约束条件,通过微分修正算法调整Halo轨道的稳定流形,设计月球到Halo轨道的转移轨道。采用遗传算法与微分修正算法相结合的混合优化策略,在同时考虑地球停泊轨道高度、倾角、升交点赤经与航迹角等多约束条件下,对燃料最优的地月转移轨道进行研究。最后,分析月球借力高度、借力方位角和不同HOI点对平动点转移轨道飞行时间与燃耗变化量的影响,对于考虑月球借力的地月平动点转移轨道设计与应用具有重要的参考价值。     

火星探测无动力借力飞行轨道研究

对无动力情形的借金星引力辅助变轨进行了研究,并完成了火星探测轨道的设计;首 先使用Jacobi积分得到了蒂塞朗准则,在利用速度矢量图对借力飞行轨道的特性进行分析后 ,得到了Williams提出的C3匹配法,证明了蒂塞朗准则和C3匹配的同一性;在 搜索借力飞行的可行性转移轨道中,采用C3匹配对借金星引力的火星探测轨道进行了 仿真,并对结果进行了分析,最后使用蒂塞朗准则对C3匹配的仿真结果进行了检验。     

气动-引力辅助转移轨道研究及在星际探测中的应用

借力飞行是减小星际探测任务发射能量和总的速度增量的有效途径,然而,借力飞行前后,探测器速度矢量转角的变化往往受到借力星体体积、质量等因素的影响,而不能达到理想的要求。若在借力飞行中引入气动辅助变轨,即气动-引力辅助转移(AGA),则这一问题可以得到有效解决。现通过对AGA转移轨道的分析,给出了AGA转移轨道设计的拼接条件,此拼接条件是对AGA转移轨道进行设计和分析的重要准则。同时还以探测Ivar小行星为例,提出了一种将绘制等高线图和圆锥曲线拼接相结合的设计AGA转移轨道的方法,并给出了设计探测Ivar小行星转移轨道的参数。数值计算表明:AGA转移方法不但可以降低远程星际探测任务的发射能量和总的速度增量,而且可以找到更多的探测机会。     

考虑建模误差的某型火箭末级制导方法研究

运载火箭末级发动机点火后,在制导系统的导引下,火箭最终抵达入轨位置、取得入轨速度,卫星进入运行轨道。火箭末级飞行动力学模型为非线性微分方程形式,难以利用解析方法得到火箭姿态变化特性,进而控制火箭飞行过程中的状态变量。将火箭入轨约束条件转化为最优控制的性能指标函数,利用庞德里亚金极小值原理与牛顿梯度法相结合的方式来解决动力学方程求解问题,得到末级飞行标准轨道;火箭动力学建模过程中,由于参数难以精确计量等的影响,存在建模误差,导致火箭实际飞行轨道会偏离标准轨道。对模型进行线性化处理,引入状态反馈,可以使实际飞行轨道接近于标准轨道,提高卫星荷载入轨要求精度。仿真结果表明:该制导算法可较好地减小火箭载荷入轨误差。     

中低轨道卫星控制方法

针对中低轨道卫星，对平面内卫星半长轴α、偏心率e和近地点幅角w联合调整，以及平面外轨道倾角调整等进行了理论推导.用α，e，w联合修正法对初始轨道捕获、轨道保持和轨道倾角调整进行的仿真实验结果表明，用α，e，w同时修正可实现高精度的平面内轨道调整。另外，平面外倾角调整应尽可能在近地点和远地点完成，以使对升交点赤经的影响最小。     

小偏心率低轨卫星的星历参数拟合法

研究了小偏心率低轨卫星参数拟合理论,数据来源于某星载GPS接收机定位数据。通过对小偏心率近地卫星的轨道根数进行频谱分析,建立了对应的数学模型,用采样数据对数学模型中的参数用最小二乘法进行估计。对算法进行了模拟仿真,结果表明,该方法简单有效,计算速度快,拟合和短时间（10min）预报误差在100m量级。     

Nonlinear Evolution of a Balloon Satellite Orbit

The motion of a spherically symmetric balloon satellite near the equatorial plane is considered. Taking the Earth's oblateness and solar light pressure into account, the integral of motion can be obtained under certain simplifications. The eccentricity is related to the solar angle which represents an angle between pericenter and the Sun. This analytical approximation describes a large and complicated evolution of the eccentricity in corresponding areas of the phase space and the space of parameters. Phase portraits contain fixed saddle points and separatrices that divide different types of oscillations of the eccentricity. In the unsimplified problem, separatrices break down, and specific stochastic motions arise. The aims of the present study are (1) evaluation of the accuracy of analytical approximation with the help of numerical integration using a sufficiently complete model of motion and (2) numerical investigation of stochastic motions and dimensions of stochastic zones in the region of broken separatrices for an adequate model of motion. For a balloon satellite with a semimajor axis of 2.15 Earth's radii and a windage of 30 cm²/g the dimensions of a stochastic zone in eccentricity and solar angle are 10^–5and 0.1°, respectively. The analytical approximation describes the orbit evolution in the right way, except for the cases of large eccentricities, e> 0.4, which corresponds to a pericenter height of less than 1400 km, where the atmospheric drag is already significant.     

On the Precession of Saturn

The precession of Saturn under the effect of the gravity of the Sun, Jupiter and planet’s satellites has been investigated. Saturn is considered to be an axisymmetric (A = B) solid body close to the dynamically spherical one. The orbits of Saturn and Jupiter are considered to be Keplerian ellipses in the inertial coordinate system. It has been shown that the entire set of small parameters of the problem can be reduced to two independent parameters. The averaged Hamiltonian function of the problem and the integrals of evolutionary equations are obtained disregarding the effect of satellites. Using the small parameter method, the expressions for the precession frequency and the nutation angle of the planet’s axis of rotation caused by the gravity of the Sun and Jupiter are obtained. Considering the planet with satellites as a whole preceding around the normal to the unmovable plane of Saturn’s orbit, the satellites effect on the Saturn rotation is taken into account via the corrections in the formula for the undisturbed precession frequency. The satellites are shown to have no effect on the nutation angle (in the framework of the accepted model), and the disturbances from Jupiter to make the main contribution to the nutation angle evolution. The effect of Jupiter on the nutation angle and the precession period is described with regard to the attraction of satellites.     

嫦娥二号月球卫星CCD立体相机在轨图像分析

嫦娥二号月球卫星从2010年10月1日发射至今,已在轨运行近2年,除全部完成预定的工程与科学目标外,还完成了若干扩展科学试验。CCD立体相机获得了月球虹湾地区的35轨空间分辨率约为1．3m的局域立体图像,以及7m空间分辨率、100％覆盖的全月立体图像,是迄今为止国际上分辨率最高、最清晰的全月立体图像。文章在简要介绍在轨图像获取情况的基础上,对15km／100km椭圆轨道及100km圆轨道上获取的图像进行了分析,重点讨论了拍摄时的太阳高度角对图像视觉效果以及图像信息量的影响,可为中国今后探测其他星球提供一定的参考。     

On the one-body problem in the field of a tall cylinder in orbit

We describe the motion of a material point that is attracted by a tall, homogeneous cylinder. The cylinder moves on a circular orbit and points in the radial direction. The finite solution can be expanded in powers of two small parameters: the initial eccentricity of the orbital motion about the cylinder and the coupling parameter of the Coriolis force. Such expansions are given for the case of the indifferent longitudinal location. Solutions periodic in the polar angle are constructed. We do not find resonance effects or other large cumulative amplitude variations that might be due to the gravity-gradient and Coriolis force.     

Evolution of Motion of a Binary Planet

A model of a binary planet, consisting of a material point of small mass and a deformable viscoelastic sphere, is suggested. The center of mass of the binary planet moves in the gravitational field of a central body in the plane, which contains planets forming the binary planet. A deformable spherical planet rotates around the axis orthogonal to the plane of planetary motion. Planet deformations are described by the linear theory of viscoelasticity. It is shown that with an appropriate approximation of the gravitational potential, there is a class of quasicircular orbits, when the eccentricities of an orbit of the center of mass of a binary planet and an orbit, describing mutual planet motion, are equal to zero. The further evolution of motion is investigated in this class of orbits with the use of the canonical Poincare–Andoyer variables. Corresponding averaged equations are found, and phase pictures are constructed; the stability of stationary solutions is investigated on the basis of equations in variations. For the Solar system planets with their satellites, forming binary planets, the application of the presented model allows us to conclude that satellites sooner or later will fall on the corresponding planets.     

Pervasive orbital eccentricities dictate the habitability of extrasolar earths

The long-term habitability of Earth-like planets requires low orbital eccentricities. A secular perturbation from a distant stellar companion is a very important mechanism in exciting planetary eccentricities, as many of the extrasolar planetary systems are associated with stellar companions. Although the orbital evolution of an Earth-like planet in a stellar binary system is well understood, the effect of a binary perturbation on a more realistic system containing additional gas-giant planets has been very little studied. Here, we provide analytic criteria confirmed by a large ensemble of numerical integrations that identify the initial orbital parameters leading to eccentric orbits. We show that an extrasolar earth is likely to experience a broad range of orbital evolution dictated by the location of a gas-giant planet, which necessitates more focused studies on the effect of eccentricity on the potential for life.     

Parametric study of the diversion of a near Earth object on an Earth intersecting trajectory

To date, NASA's “Near Earth Object Program” has discovered over 5500 comets and asteroids on trajectories that bring them within “the neighborhood” of Earth's orbit. Nearly 1000 of these objects are classified as “potentially hazardous,” passing within 0.05 astronomical units of Earth's orbit. Discovery rates of such threatening bodies increase each year. Given this multitude of threats, in addition to evidence that the planet has absorbed many impacts over its history, it is reasonable to assume that another object will strike the Earth at some point in the future. Consequently, researchers have studied and proposed several mitigation techniques for such an occurrence. This study seeks to determine how effectively the attachment of a tether and ballast mass would divert the trajectory of such threatening objects. Specifically, the study analyzes the effects over time of such a system on objects of varying orbital semimajor axis and eccentricity, using various tether lengths and ballast masses. It was determined that the technique is most effective for NEOs with high eccentricity and small semimajor axis, and that system performance increases as tether length and ballast mass increase.