关于空间探测器定位在太阳系中特殊点上的有关问题

WSO／UV(世界空间紫外天文台)以及监测太阳活动的特殊探测器(Solar Sentinel)都需要在日-地(月)系的平动点附近运行，且相对日-地(月)系要求其几何位置几乎保持不变，因此有必要阐明平动点的动力学特征及其附近的运动状况。基于这一点，对限制性三体模型下，日-地(月)系中平动点附近扰动运动的稳定性作了详尽的分析，尤其讨论了共线平动点具有不稳定动力学特征时，如何使WSO／UV这类空间探测器保持在其附近的情况；同时阐明了轨道保持不变的条件和相应的轨控措施。     

三角平动点在深空探测中的应用前景

与共线平动点不同,圆型限制性三体问题中的两个三角平动点在一定条件下,无论是线性意义下还是非线性意义下,都是稳定的,其附近存在着周期与拟周期轨道,在深空探测中有应用前景.该文首先简单介绍三角平动点附近运动的动力学特征,然后以日-(地+月)系和地-月系两个三体系统为例,进一步阐述真实引力模型下三角平动点附近的运动状态,最后以这两个三体系统为例,探讨了三角平动点探测器的发射和定点轨道控制问题.     

定点在日-地(月)系L1点附近的探测器的发射及维持

在限制性三体问题中共线平动点附近的运动虽然是不稳定的,但可以是有条件稳定的,该动力学特征使得一些有特殊目的的探测器只需消耗较少的能量即可定点在这些点附近(如ISEE-3、SOHO).以日-地(月)系的L1点为例,根据其附近的运动特征,探讨定点探测器的发射与轨道控制问题,给出了相应的数值模拟结果,为工程上的实现提供理论依据.     

利用Halo轨道仿真开展嫦娥四号中继星与月面设备干涉基线的研究

初步建立了嫦娥四号中继星的晕轨道(Halo轨道)数值模型,将其应用于空间低频射电天文观测的干涉测量仿真,以地月拉格朗日平动点L2区域的Halo轨道为基础,以发布的嫦娥四号中继星理论轨道为参考,校准和调整模型参数,通过时间和空间参考系统的变换,把轨道数据转换到L2点旋转坐标系.然后对比Halo轨道模型与理论轨道数据之间的...     

地-月系平动点轨道的特征及其相关问题

当探测器定点在地-月系共线平动点L_1、L_2附近的halo轨道或Lissajous轨道时,由于其固有的动力学特征,通常是被人们置于地-月系质心旋转坐标系中展现其几何特征.其实,它们同样是环绕地球运行的Kepler轨道,这类探测器实为地球的远地卫星.但由于其自身所具有的不稳定性特征,在轨道外推中,初值误差的传播程度远比一般的环绕型探测器轨道外推显著.这在轨道设计、运行控制和地面测控等领域都是需要重视的问题.尽管如此,除在构造这类轨道变化的受摄分析解时遇到困难外,对其定轨等问题,与一般远地卫星类似,并无其他特殊要求.将具体给出该类轨道由于不稳定特性引起误差快速传播的定量状态和相应的理论分析,以及实际应用中的短弧定轨和相应的高精度轨道预报方法,并附有实测资料进行定轨结果的检验.     

关于星座小卫星的编队飞行问题

从轨道力学角度来看星座小卫星编队飞行和星星跟踪中的伴飞，遵循着如下动力学机制：(1)在各小卫星绕地球运动过程中轨道摄动变化的主要特征决定了星-星之间的空间构形，(2)当星星之间相互距离较近时，在退化的限制性三体问题(实为限制性二体问题)中，共线秤动点附近的条件周期运动亦可在一定时间内制约星-星之间的空间构形．将具体阐明这两种动力学机制的原理和相应的星星之间的相对构形，并用仿真计算来证实这两种动力学机制的适用范围，为星座小卫星编队飞行和在伴飞运动过程中进行轨控提供理论依据和具体的轨控条件．     

任务轨道设计

本文首先说明太空任务与轨道设计的关系，接着介绍轨道的基本性质。从地球重力势的观点看各种常用的绕地轨道，包括地球和太阳同步轨道及Molniya轨道。从扰动的观点看常用的星际轨道，包括LISA，ASTROD，SOHO轨道。最后对星际轨道设计，说明二点边界值问题的数值解法，飞掠星体的应用，最佳化的考虑，并用以设计2015年发射的ASTROD初步任务轨道。     

月球卫星轨道力学综述

月球探测器的运动通常可分为3个阶段，这3个阶段分别对应3种不同类型的轨道：近地停泊轨道、向月飞行的过渡轨道与环月飞行的月球卫星轨道。近地停泊轨道实为一种地球卫星轨道；过渡轨道则涉及不同的过渡方式(大推力或小推力等)；环月飞行的月球卫星轨道则与地球卫星轨道有很多不同之处，它决不是地球卫星轨道的简单克隆。针对这一点，全面阐述月球卫星的轨道力学问题，特别是环月飞行中的一些热点问题，如轨道摄动解的构造、近月点高度的下降及其涉及的卫星轨道寿命、各种特殊卫星(如太阳同步卫星和冻结轨道卫星等)的轨道特征、月球卫星定轨等。     

任务轨道设计

本文首先说明太空任务与轨道设计的关系 ,接着介绍轨道的基本性质。从地球重力势的观点看各种常用的绕地轨道 ,包括地球和太阳同步轨道及Molniya轨道。从扰动的观点看常用的星际轨道 ,包括LISA、ASTROD、SOHO轨道。最后对星际轨道设计 ,说明二点边界值问题的数值解法、飞掠星体的应用、最佳化的考虑 ,并用以设计 2 0 1 5年发射的ASTROD初步任务轨道。     

双星系统中的轨道偏心率分布

讨论了１４３颗早型和１２５个晚型双星系统轨道偏心率与轨道周期间的关系。结果表明：几乎所有Ｐ〈１．７ｄ的早型主序双星都具有圆或近圆轨道（ｅ≤０．０５）,即早型主序双星和晚型主序,晚型巨星组双星的圆轨道临界周期约为１．７ｄ;而早型巨星,特殊和１０ｄ。比较理论预期与实测统计关系,动力学潮汐机制及粘滞理论与实测数据较好地吻合,而纯流体动力学理论与我们的统计不太一致。     

On quasi-periodic motions around the collinear libration points in the real Earth–Moon system

Due to various perturbations, the collinear libration points of the real Earth–Moon system are not equilibrium points anymore. Under the assumption that the Moon’s motion is quasi-periodic, special quasi-periodic orbits called dynamical substitutes exist. These dynamical substitutes replace the geometrical collinear libration points as time-varying equilibrium points. In the paper, the dynamical substitutes of the three collinear libration points in the real Earth–Moon system are computed. For the points L ₁ and L ₂, linearized motions around the dynamical substitutes are described, and the variational equations of the dynamical substitutes are reduced to a form with a near constant coefficient matrix. Then higher order analytical formulae of the central manifolds are constructed. Using these analytical solutions as initial seeds, Lissajous orbits and halo orbits are computed with numerical algorithms.     

High-order solutions of invariant manifolds associated with libration point orbits in the elliptic restricted three-body system

High-order analytical solutions of invariant manifolds, associated with Lissajous and halo orbits in the elliptic restricted three-body problem (ERTBP), are constructed in this paper. The equations of motion of ERTBP in the pulsating synodic coordinate system have five equilibrium points, and the three collinear libration points as well as the associated center manifolds are unstable. In our calculation, the general solutions of the invariant manifolds associated with Lissajous and halo orbits around collinear libration points are expressed as power series of five parameters: the orbital eccentricity, two amplitudes corresponding to the hyperbolic manifolds, and two amplitudes corresponding to the center manifolds. The analytical solutions up to arbitrary order are constructed by means of Lindstedt–Poincaré method, and then the center and invariant manifolds, transit and non-transit trajectories in ERTBP are all parameterized. Since the circular restricted three-body problem (CRTBP) is a particular case of ERTBP when the eccentricity is zero, the general solutions constructed in this paper can be reduced to describe the dynamics around the collinear libration points in CRTBP naturally. In order to check the validity of the series expansions constructed, the practical convergence of the series expansions up to different orders is studied.     

The effect of photogravitational force and oblateness in the perturbed restricted three-body problem

The model of restricted three-body is generalized to include the effects of the oblateness, the radiation pressure and fictitious forces. The positions of libration points, their stability, the critical mass ratio and periodic orbits emanating from these points are analyzed under the influence of these effects. The results obtained are more generalized. In addition the locations of the out of plane equilibrium points are studied. We also observe that there is no explicit effect for the perturbation of Coriolis force on the positions of the out of plane equilibrium points. It is worth mentioning that this model can be degraded into 128 special cases.     

Long-term capture orbits for low-energy space missions

This research aims at ascertaining the existence and characteristics of natural long-term capture orbits around a celestial body of potential interest. The problem is investigated in the dynamical framework of the three-dimensional circular restricted three-body problem. Previous numerical work on two-dimensional trajectories provided numerical evidence of Conley’s theorem, proving that long-term capture orbits are topologically located near trajectories asymptotic to periodic libration point orbits. This work intends to extend the previous investigations to three-dimensional paths. In this dynamical context, several special trajectories exist, such as quasiperiodic orbits. These can be found as special solutions to the linear expansion of the dynamics equations and have already been proven to exist even using the nonlinear equations of motion. The nature of long-term capture orbits is thus investigated in relation to the dynamical conditions that correspond to asymptotic trajectories converging into quasiperiodic orbits. The analysis results in the definition of two parameters characterizing capture condition and the design of a capture strategy, guiding a spacecraft into long-term capture orbits around one of the primaries. Both the results are validated through numerical simulations of the three-dimensional nonlinear dynamics, including fourth-body perturbation, with special focus on the Jupiter–Ganymede system and the Earth–Moon system.     

Cylindrical isomorphic mapping applied to invariant manifold dynamics for Earth–Moon Missions

Several families of periodic orbits exist in the context of the circular restricted three-body problem. This work studies orbital motion of a spacecraft among these periodic orbits in the Earth–Moon system, using the planar circular restricted three-body problem model. A new cylindrical representation of the spacecraft phase space (i.e., position and velocity) is described, and allows representing periodic orbits and the related invariant manifolds. In the proximity of the libration points, the manifolds form a four-fold surface, if the cylindrical coordinates are employed. Orbits departing from the Earth and transiting toward the Moon correspond to the trajectories located inside this four-fold surface. The isomorphic mapping under consideration is also useful for describing the topology of the invariant manifolds, which exhibit a complex geometrical stretch-and-folding behavior as the associated trajectories reach increasing distances from the libration orbit. Moreover, the cylindrical representation reveals extremely useful for detecting periodic orbits around the primaries and the libration points, as well as the possible existence of heteroclinic connections. These are asymptotic trajectories that are ideally traveled at zero-propellant cost. This circumstance implies the possibility of performing concretely a variety of complex Earth–Moon missions, by combining different types of trajectory arcs belonging to the manifolds. This work studies also the possible application of manifold dynamics to defining a suitable, convenient end-of-life strategy for spacecraft placed in any of the unstable orbits. The final disposal orbit is an externally confined trajectory, never approaching the Earth or the Moon, and can be entered by means of a single velocity impulse (of modest magnitude) along the right unstable manifold that emanates from the Lyapunov orbit at \(L_2\) .     

Disturbance compensating control of orbit radially aligned two-craft Coulomb formation

This paper investigates the orbit radial stabilization of a two-craft virtual Coulomb structure about circular orbits and at Earth–Moon libration points. A generic Lyapunov feedback controller is designed for asymptotically stabilizing an orbit radial configuration about circular orbits and collinear libration points. The new feedback controller at the libration points is provided as a generic control law in which circular Earth orbit control form a special case. This control law can withstand differential solar perturbation effects on the two-craft formation. Electrostatic Coulomb forces acting in the longitudinal direction control the relative distance between the two satellites and inertial electric propulsion thrusting acting in the transverse directions control the in-plane and out-of-plane attitude motions. The electrostatic virtual tether between the two craft is capable of both tensile and compressive forces. Using the Lyapunov’s second method the feedback control law guarantees closed loop stability. Numerical simulations using the non-linear control law are presented for circular orbits and at an Earth–Moon collinear libration point.     

Some analytical results about periodic orbits in the restricted three body problem with dissipation

We present some analytical results about the existence of periodic orbits for the planar restricted three body problem with dissipation considered recently by Celletti et?al. (CMDA 109, 265, 2011) We show that, under fairly general conditions on the dissipation term, the circular orbits cannot be continued to the dissipative framework. Moreover, we give general conditions for the occurrence or not of a Hopf bifurcation around the libration points L ₄ and L ₅. Our results are consistent with the numerical findings of Celletti et?al.     

A note on the dynamics around the Lagrange collinear points of the Earth–Moon system in a complete Solar System model

In this paper we study the dynamics of a massless particle around the L _1,2 libration points of the Earth–Moon system in a full Solar System gravitational model. The study is based on the analysis of the quasi-periodic solutions around the two collinear equilibrium points. For the analysis and computation of the quasi-periodic orbits, a new iterative algorithm is introduced which is a combination of a multiple shooting method with a refined Fourier analysis of the orbits computed with the multiple shooting. Using as initial seeds for the algorithm the libration point orbits of Circular Restricted Three Body Problem, determined by Lindstedt-Poincaré methods, the procedure is able to refine them in the Solar System force-field model for large time-spans, that cover most of the relevant Sun–Earth–Moon periods.     

Symmetric doubly-asymptotic periodic orbits at collinear equilibria

A systematic search for periodic orbits doubly-asymptotic to the collinear equilibrium points of the restricted three-body problem is carried out and many such orbits are found, each of them existing for a specific value of the mass parameter. These may be useful as reference orbits and seem to be special limit orbits representing period discontinuities in the evolution of the families of periodic orbits.