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.     

关于共线平动点的特征及其在深空探测中的应用

系统阐述了小天体运动对应的圆型限制性三体问题共线平动点的强不稳定性特征,以及其附近的条件周期轨道——晕轨道(Halo Orbit)的存在、相应解的构造。这种特殊的轨道形式和共线平动点附近的弱稳定走廊,可分别用于在深空特殊位置附近定点有各种科学探测目标的探测器和向节能轨道过渡的通道。     

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．     

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...     

2003年10月22日太阳活动区AR0484内日浪事件的研究

利用色球Hα、TRACE／WL、SOHO／EITEuV单色像观测资料及SOHO／MDI光球磁场观测资料，对2003年10月22日太阳活动区AR0484内发生的日浪事件进行了研究．发现：(1)在Ha线心观测上，日浪包含有亮、暗2个分量，这2个分量先后出现而且并不共空间．日浪的亮分量与UV和EUV波段上观测到的喷发具有较好的同时性和共空间性．(2)日浪喷发物质沿着EUV环运动。(3)在光球层，日浪足根处的黑子和磁场有明显的变化．这些观测结果支持日浪的磁重联模型。     

地球不止一个月亮？

科学家们正关注地球附近的“拉格朗日点”,所谓拉格朗日点,即一个小质量物体与两个大质量物体组成的系统中的某些空间点,在那里小物体相对于两大物体基本保持静止。这些点的存在由法国数学家拉格朗日于1772年导出,1906年人们首次发现运动于木星轨道上的小行星（即脱罗央群小行星）在木星和太阳的作用下处于拉格朗日点上。     

观测宇宙学的新进展

微波各向异性探测器(Microwave AnisotropyProbe,简称MAP,为了纪念2002年9月逝世的微波背景测量的先驱Darid Wilkinson的功绩,现改称WMAP)是2001年6月30日从美国卡纳维拉尔角发射升空的,最终定位于距地球约150万千米处的第二拉格朗日点(L2 Lagrange Point)。在此处,太阳-地球-WMAP三点一线(太阳距地球平均距离约1.5亿千米),日、地的引力作用结合起来保持WMAP相对于地球处于稳定状态。处于这一位置的WMAP,远离人间发出的任何     

彗木相撞中的波动

1994年7月18日至24日期间，彗星苏梅克-列维9(SL-9)的超过20块碎片与木星发生了相撞．哈勃空间望远镜(HST)拍摄到的图像揭示了木星大气对撞击的动力学响应．具有重要意义的是观测到5个撞击点周围的圆环，它们以450米／秒的常速度向外运动．环的圆形性表明它们是波．因为对于不同大小的撞击，波速是常量，可以推断出传播速度与爆炸能量无关．这意味着这些波动是线性波．评述现行理论所使用的3类候选波，亦即惯性引力波、声波和地震波，介绍的重点是前面两种．     

Effect of Moon perturbation on the energy curves and equilibrium points in the Sun–Earth–Moon system

In this paper, we have considered that the Moon motion around the Earth is a source of a perturbation for the infinitesimal body motion in the Sun–Earth system. The perturbation effect is analyzed by using the Sun–Earth–Moon bi–circular model (BCM). We have determined the effect of this perturbation on the Lagrangian points and zero velocity curves. We have obtained the motion of infinitesimal body in the neighborhood of the equivalent equilibria of the triangular equilibrium points. Moreover, to know the nature of the trajectory, we have estimated the first order Lyapunov characteristic exponents of the trajectory emanating from the vicinity of the triangular equilibrium point in the proposed system. It is noticed that due to the generated perturbation by the Moon motion, the results are affected significantly, and the Jacobian constant is fluctuated periodically as the Moon is moving around the Earth. Finally, we emphasize that this model could be applicable to send either satellite or telescope for deep space exploration.     

On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem

This paper focuses on some aspects of the motion of a small particle moving near the Lagrangian points of the Earth–Moon system. The model for the motion of the particle is the so-called bicircular problem (BCP), that includes the effect of Earth and Moon as in the spatial restricted three body problem (RTBP), plus the effect of the Sun as a periodic time-dependent perturbation of the RTBP. Due to this periodic forcing coming from the Sun, the Lagrangian points are no longer equilibrium solutions for the BCP. On the other hand, the BCP has three periodic orbits (with the same period as the forcing) that can be seen as the dynamical equivalent of the Lagrangian points. In this work, we first discuss some numerical methods for the accurate computation of quasi-periodic solutions, and then we apply them to the BCP to obtain families of 2-D tori in an extended neighbourhood of the Lagrangian points. These families start on the three periodic orbits mentioned above and they are continued in the vertical (z and ż) direction up to a high distance. These (Cantor) families can be seen as the continuation, into the BCP, of the Lyapunov family of periodic orbits of the Lagrangian points that goes in the (z, ż) direction. These results are used in a forthcoming work [9] to find regions where trajectories remain confined for a very long time. It is remarkable that these regions seem to persist in the real system. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the capture of the Moon

This paper studies the possibility of lunar capture depending on variations of the solar mass under certain well specified conditions and assumptions regarding the behaviour of the three-body dynamical system formed by the Sun, Earth and Moon. It is found that a large amount of decrease in the solar mass (approximately 37%) would be required to allow capture if the model of the planar restricted problem of three bodies is assumed, if the masses of the Earth and Moon did not change and if the angular momentum of the Sun-Earth system did not change. Such large mass-changes of the Sun can not be associated with radiation mass losses only with catastrophic events, such as stellar close approaches.     

Analytic construction of periodic orbits about the collinear points

A third-order analytical solution for halo-type periodic motion about the collinear points of the circular-restricted problem is presented. The three-dimensional equations of motion are obtained by a Lagrangian formulation. The solution is constructed using the method of successive approximations in conjunction with a technique similar to the Lindstedt-Poincaré method. The theory is applied to the Sun-Earth system.     

Earth satellites in resonance with the Moon and the Sun as objects of laser ranging. Analytical solution for their motion

Distant Earth satellites repeating nearly periodically their configurations both with the Moon and the Sun may appear to be even more convenient carriers of laser retroreflectors than the Moon, when geodetic applications are of primary interest. The analytical solution for the motion of a satellite in resonance both with the Moon and the Sun has been outlined in this paper, the periodic orbit of the planar restricted four-body problem being taken as an intermediary. The Von Zeipel transformation gives the Hamiltonian not depending on the fast variables. The stationary solution for this Hamiltonian has been found. Then the non-homogeneous variation equations have been formed, taking into account the orbital eccentricities of the Moon and the Sun. The solution of these equations has been obtained and its accuracy has been tested by numerical integration.Presented at the XXII Congress of the International Astronautical Federation, Brussels, Belgium September 20–25, 1971.     

On the Transfer and Control of Space Probes Around the L1 Point of the Sun-Earth+Moon System

The motion around the collinear libration points in the restricted three body problem is unstable. But there exist conditionally stable periodic orbits around these points. Special-purpose space probes located in the vicinity of these points (e.g., ISEE-3, SOHO) can benefit from this dynamical property, in regard to maintaining the orbit in position and the energy required of placing the probe in position. As an example, we study in this paper the launch and orbital control of a space probe around the L1 libration point in the system consisting of the Sun and the Earth-Moon. We present some theoretical and numerical simulations’ results, which may serve as a basis for the realization of such a space probe in future.     

Solar wind observations on the lunar surface with the Apollo-12 ALSEP

The Apollo-12 ALSEP solar wind spectrometer obtained data from the lunar surface starting November 20, 1969. To a first approximation, the general features of the positive ion flux depend only on the instrument's orientation and location in space relative to the Sun-Earth system. However, there are some detectable effects of the interaction of the solar wind with the local magnetic field and surface, including the deceleration of incident positive ions and the enhancement of fluctuations in the plasma. The expected asymmetry of sunset and sunrise times due to the motion of the Moon about the Sun is not observed. On one occasion, the solar wind was incident on the ALSEP site as early as 36 hr (18°) before sunrise.     

A dynamical equivalent to the equilateral libration points of the earth-moon system

Consider the Earth-Moon-particle system as a Restricted Three Body Problem. There are two equilateral libration points. In the actual world system, those points are no longer relative equilibrium points mainly due to the effect of the Sun and to the noncircular motion of the Moon around the Earth. In this paper we present the problem as a perturbation of the RTBP and we look for the dynamical equivalent of L _4,5. It turns out to be a quasiperiodic orbit. It is obtained for a simplified model but the procedure to obtain it is general and can be carried out with an additional computational effort.     

Numerical models for the study of motion of lunar satellites

The present study deals with numerical modeling of the elliptic restricted three-body problem as well as of the perturbed elliptic restricted three-body (Earth-Moon-Satellite) problem by a fourth body (Sun). Two numerical algorithms are established and investigated. The first is based on the method of the series solution of the differential equations and the second is based on a 5th-order Runge-Kutta method. The applications concern the solution of the equations and integrals of motion of the circular and elliptical restricted three-body problem as well as the search for periodic orbits of the natural satellites of the Moon in the Earth-Moon system in both cases in which the Moon describes circular or elliptical orbit around the Earth before the perturbations induced by the Sun. After the introduction of the perturbations in the Earth-Moon-Satellite system the motions of the Moon and the Satellite are studied with the same initial conditions which give periodic orbits for the unperturbed elliptic problem.     

Preliminary Study on the Translunar Halo Orbits of the Real Earth–Moon System

The computation of translunar Halo orbits of the real Earth–Moon system (REMS) has been an open problem for a long time, but now, it is possible to compute Halo orbits of the REMS in a systematic way. In this paper, we describe the method used for the numerical computation of Halo orbits for a time span longer than 41 years. Halo orbits of the REMS are computed from quasi-periodic Halo orbits of the quasi-bicircular problem (QBCP). The QBCP is a model for the dynamics of a spacecraft in the Earth–Moon–Sun system. It is a Hamiltonian system with three degrees of freedom and depending periodically on time. In this model, Earth, Moon and Sun are moving in a self-consistent motion close to bicircular. The computed Halo orbits of the REMS are compared with the family of Halo orbits of the QBCP. The results show that the QBCP is a good model to understand the main features of the Halo family of the REMS.