航天器共振轨道研究

建立航天器非开普勒运动理论是航天技术发展的必然。提出了一类非开普勒轨道——共振轨 道。共振是自然界的一种普遍现象,当发生共振时,很小的输入可以使系统的状态产生较大 变化。研究表明航天器在推力作用下的非开普勒运动在参数平面内可以视为一种受迫振 动,也会发生共振现象。因此,可以利用共振原理来研究航天器的运动,称这样一类非开普 勒轨道为共振轨道。首先通过合理地选择轨道描述参数、时间尺度和推力描述方式建立 航天器共振轨道的动力学模型。然后讨论航天器在推力作用下轨道运动的振动规律,并给出 共振轨道的概念及轨道方程。最后提出基于共振轨道的机动轨道设计方法。
     

小行星探测最优两脉冲交会轨道设计与分析

小行星探测已经成为新世纪深空探测的一个新热点和未来世界航天发展的一个新方向。转移轨道的设计和探测目标可接近性的分析是小行星探测的关键技术之一。现利用了任意两个非共面非共轴椭圆轨道之间的最优两脉冲转移方法，对我国提出的探测Ivar小行星的交会转移轨道进行了设计与分析，给出了全局最优两脉冲交会轨道的设计参数，并利用此方法对近地小行星的可接近性进行了分析和排序，给出了可接近性较好的40颗近地小行星的转移轨道设计参数。这些研究结果对于近地小行星探测任务的目标选择和发射机会的预测都有重要的参考价值。     

自由返回轨道的P平面参数快速设计方法

针对自由返回轨道求解过程中地心轨道类型变化造成的B平面参数方法计算失败问题,提出一种基于P平面参数的自由返回轨道快速设计方法。首先,基于轨道半通径参数的普适性,给出了不同轨道类型的P平面参数定义,建立了以P平面参数为求解目标量的自由返回轨道求解模型。其次,给出了基于P平面参数的自由返回轨道快速设计方法,在构建的瞬时地月惯性系下,以平面双二体自由返回轨道作为初值,实现了高精度力模型下的自由返回轨道快速求解。对8种构型自由返回轨道的设计结果表明,P平面参数具有类似于B平面参数的大收敛域,且有效解决了轨道类型变化对计算的影响,可直接应用于中国后续月球探测任务轨道设计。     

航天器环绕小行星Ivar的运动分析

将小行星Ivar近似为三轴椭球体，给出了非球形引力势函数，建立了航天器环绕小行星Ivar的轨道动力学方程。利用Jacobi积分常数绘制了航天器在Ivar周围的零速度曲线，并分析了航天器的可能运动区域，给出了航天器不碰撞小行星Ivar的边界条件及不同偏心率下的近拱点半径。分析了小行星Ivar扁率和椭率对环绕轨道的影响，数学仿真结果表明：在一个轨道周期内，顺行轨道的开普勒能量、轨道角动量、偏心率和近拱点半径变化较大，而逆行轨道的相应参数变化较小。     

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。     

连续推力机动轨道优化设计的贝塞尔曲线法

提出一种基于贝塞尔曲线的平面机动轨道设计方法。该方法将贝塞尔曲线方程与轨道形状方程相结合，利用得到的复合函数作为轨道方程来对机动轨道进行数学描述；通过约束条件获得可行的机动轨道族，由控制点设计给出具体的优化变量，将累积速度增量作为优化指标函数；并利用优化算法完成参数优化，从而得到最优机动轨道。最后针对设计的机动轨道推力峰值较大的问题，进一步提出了分段贝塞尔曲线法，在降低推力峰值的同时，可进一步降低燃料消耗，并在平面机动转移轨道设计的基础上，通过梯度下降对自由控制点进行修正，解决了考虑时间约束的平面轨道交会问题。     

不规则形状小行星引力环境建模及 球谐系数求取方法

在实施小行星探测任务之前,需要对不规则形状小行星的引力场有一个清楚的认识,以便于进行环绕或着陆小行星的轨道设计。文章提出了一种小行星引力场建模及球谐系数的求取方法。首先,由多面体模型方法重构出小行星外部的引力环境并以此作为虚拟观测量。在此基础上,根据球谐系数与引力势能间的关系,通过求解超定线性方程组得到小行星引力场的各阶次球谐系数。与传统的将小行星近似成三轴椭球体进而计算球谐系数的方法相比,该方法可大幅度提高引力场建模的精度。通过与由NEAR探测器轨道数据解算的Eros433小行星的球谐系数比较表明,其最大误差不超过6%。计算表明,该方法可以为小行星探测任务发射前的轨道设计提供更为精确的数据。     

从月球逃逸探测小行星的发射机会搜索

从月球逃逸探测小行星的发射机会搜索因需考虑日、地、月引力的影响而使问题变得复杂。针对该多体系统的发射机会搜索问题,提出了一种分层渐近的搜索方法。该方法首先通过分析地月系质心与小行星的几何关系,搜索从地月系质心到小行星的发射机会,进而以地月运动为研究对象,推导出了从月球轨道切向逃逸机会的判别条件,并基于此判别条件及等高线图法对逃逸机会进行了搜索。同时,为提高所得发射机会在多体模型下的轨道修正收敛性,给出了基于月心逃逸轨道参数为终端约束的日-地与日-地-月动力学模型的轨道渐近修正方法。最后,以近地小行星(3908)Nyx和(190491)2000 FJ20为例,搜索其从月球逃逸的发射机会,仿真计算表明了该方法的有效性。     

地月循环轨道动力学建模与计算研究

根据地月循环轨道的概念,按照生成第二类周期轨道的弧段进行分类,并讨论了其共振性与对称性在轨道设计与应用中的作用。然后归纳了三种循环轨道的动力学建模与计算方法及其轨道延拓策略,最后总结了三种方法的利弊和应用轨道类型。对地月系统循环轨道的研究和分析,能够为我国未来载人登月工程提供一种新的思路与理论支持。     

基于脉冲初值的小推力转移轨道优化研究

针对小推力转移轨道优化过程往往忽略初值多样性的现状,研究了基于不同脉冲初值的小推力转移轨道优化问题。基于直接法的离散思想建立了小推力转移轨道优化模型,提出了基于粒子群和序列二次规划的组合优化算法,以地球1∶1共振近地小行星2016HO3交会任务为例,将3种典型的脉冲轨道作为初值设计了燃料最优小推力转移轨道。仿真结果表明:3种初值轨道优化得到了2个小推力转移发射窗口,两者燃料消耗差距不超过6%。不同的初值对小推力轨道的整体性能指标影响较小,但开关机时刻和推力方向的变化会产生较大差异,从而得到不同的最优控制曲线。     

Design of transfer trajectories between resonant orbits in the Earth–Moon restricted problem

The application of dynamical systems techniques to mission design has demonstrated that employing invariant manifolds and resonant flybys enables previously unknown trajectory options and potentially reduces the ΔV$\mathrm{\Delta }V$ requirements. In this investigation, planar and three-dimensional resonant orbits are analyzed and cataloged in the Earth–Moon system and the associated invariant manifold structures are computed and visualized with the aid of higher-dimensional Poincaré maps. The relationship between the manifold trajectories associated with multiple resonant orbits is explored through the maps with the objective of constructing resonant transfer arcs. As a result, planar and three-dimensional homoclinic- and heteroclinic-type trajectories between unstable periodic resonant orbits are identified in the Earth–Moon system. To further illustrate the applicability of 2D and 3D resonant orbits in preliminary trajectory design, planar transfers to the vicinity of L₅ and an out-of-plane transfer to a 3D periodic orbit, one that tours the entire Earth–Moon system, are constructed. The design process exploits the invariant manifolds associated with orbits in resonance with the Moon as transfer mechanisms.     

环月飞行器返回轨道设计与优化

针对传统月地返回轨道设计方法在从初始轨道直接转移的局限性，提出一种基于Lambert问题的月地转移轨道设计方法。该方法重新选取了轨道约束参数，并在笛卡尔坐标系下建立了返回轨道动力学模型，并基于该模型全面分析了返回轨道关于约束参数的变化特性。此外，针对带有约束条件的返回轨道优化设计问题，提出了快速收敛的函数构造法，并给出了有效的目标函数形式。以某一在轨环月飞行器的轨道参数作为初始轨道进行返回轨道计算，结果验证了所提出返回轨道设计方法以及函数构造法的有效性。     

A Retrospective Geometric Analysis of the Long-Term Evolution of Orbits and the Ballistic Lifetime for Satellites of the Prognoz Series

We consider the applied aspects of the geometrical analysis of solutions in a restricted circular double-averaged three-body problem that are concerned with the design of high-apogee satellite orbits. Based on the analysis of the long-term evolution and the ballistic lifetime for orbit families of the Prognoz satellites launched into their orbits in the period 1972–1995, we suggest some practical suggestions for choosing long-lived high-apogee orbits with taking into account various requirements for the domain of evolution of the orbital elements.     

State propagation in an uncertain asteroid gravity field

Various spacecraft have been and will be sent to asteroids to characterize them. Generally, an asteroid's gravity field is very irregular and not accurately known when compared to the gravity field of a major planet, Earth in particular. It has been well studied that the irregularity significantly affects the trajectory of an orbiting spacecraft, and causes it to impact or to escape from the asteroid. Complementary to that, this paper focuses on the influence of the limited knowledge of this gravity field on the evolution of the spacecraft's orbit. It develops a general method by which this influence can be quantified. This method comprises specific Monte Carlo simulations with a discrete set of low-altitude orbits, taking into account the uncertainties in the gravity-field parameters. For illustration purposes, it is applied to two different asteroids. Already after three revolutions, the gravity-field uncertainties propagate to significant position uncertainties; this specifically holds for prograde orbits, and around the smaller asteroid. Applying this robust and accurate method helps mission designers and planners to assess the risk posed by gravity uncertainties, and take appropriate measures such as choosing the most favorable orbital geometries and/or lowering the orbit more slowly.     

Analysis of the orbital motion of the asteroid Apophis’ satellite

We have analyzed the orbital disturbed spacecraft motion near an asteroid. The equations of the asteroidocentric spacecraft motion have been used with regard to three perturbations from celestial bodies, the asteroid’s nonsphericity, and solar radiation pressure. It has been shown that the orbital parameters of the main spacecraft and a small satellite with a radio beacon can be selected such that the orbits are rather stable for a fairly long period of time, i.e., a few weeks for the main spacecraft with an orbit initial radius of ~0.5 km and a few years before approaching Apophis with the Earth in 2029, for a small satellite at an orbit initial radius of ~1.5 km. The initial orientation of the spacecraft orbital plane perpendicular to the sunward direction is optimal from the point of view of the stability of the spacecraft flight near an asteroid.     

Evolution of asteroid orbits at the 3 : 1 their mean motion resonance with Jupiter (planar problem)

The 3 : 1 mean motion resonance is studied in the planar elliptic restricted three-body problem (Sun-Jupiter-asteroid). Using double numerical averaging, the equations are constructed that describe the secular evolution of eccentricity and perihelion longitude of the asteroid orbit. The region of adiabatic chaos is isolated in the phase space of the system under study.     

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.