分点和赤道改正的分离摄动项求解法

本文所提出的分离摄动项求解法,是利用小行星在整个轨道上分布的不少于9次的位置测定值,与用该小行星的轨道根数初值计算出的列表位置进行比较,将由太阳系其它天体摄动力对小行星位置、速度的影响进行分离,求解出分点及赤道改正,小行星轨道根数改正,地球轨道根数改正和由摄动力引起的小行星位置和速度改正。这种方法的优点在于:(1)列表位置仅需根据小行星的轨道根数初值计算出,不考虑摄动力的作用,这样可避免小行星运动理论不完善对确定分点和赤道改正的影响;(2)在解算中,可以单独地求出摄动力对小行星运动速度和位置的影响,通过对摄动函数的数值积分,可求得任一时刻的小行星的真位置。     

摄动函数高阶展开与长期共振

研究三体系统的长期共振效应,有助于了解系统的稳定性。在雅可比坐标系下建立了第三体摄动一般运动模型,将摄动函数按照半长径之比展开到十六极矩。通过对摄动函数进行轨道双重平均,消除了内外轨道的短周期项。基于限制性三体模型,分别在内摄和外摄两类情形下进行讨论。外摄情形下十六极矩项对系统结构的演化只有微弱的影响,而内摄情形下系统会出现新的共振和混沌现象。在圆型内摄情形下,系统出现了类似于Lidov-Kozai效应的近点共振。区别于Lidov-Kozai效应只在近心点幅角ω2=±90?时可能存在平衡点,十六极矩近似下,在ω2为0?和180?时也可能存在平衡点。角动量Z轴分量的取值会影响共振平衡点的数量、位置和稳定性。在椭圆型内摄情形下,系统在十六极矩近似下激发出新的轨道翻转,且翻转没有周期性,呈现混沌现象。十六极矩近似下的轨道翻转明显区别于八极矩近似下的轨道翻转,特别是,当半长径之比相当大时,十六极矩近似下偏心率的振幅明显大于八极矩近似下偏心率的振幅。     

近地卫星运动的坐标系附加摄动在拟平均根数法中的处理

在常用的历元地心天球坐标系中研究和处理近地卫星的轨道问题,就必须考虑由于地球赤道面摆动所引起的坐标系附加摄动,正因为如此,给实际工作带来一些麻烦.关于这一问题,曾提出了一种针对瞬根数和平根数之间的转换(仅与坐标系附加摄动的短周期项有关)的解决途径,但并未涉及采用分析法进行轨道外推的有关问题(这与坐标系附加摄动的长期和长周期项有关),这对处理近地卫星的轨道问题而言显然是不完整的.这里结合拟平均根数法进一步改进原提出的方法,较完善地解决这一坐标系附加摄动的计算问题.在此前提下,对于卫星定轨和预报及其相关工作,无论是采用数值法还是分析法,均可采用同一坐标系,即历元(目前是J2000.0)地心天球坐标系.     

关于海卫Ⅱ运动理论的探讨

本工作试图建立轨道偏心率特别大(e=0.75)的海卫H(Nereid)的运动理论,并用适当方法避免摄动函数的一阶部分中含有长周期项的困难,给出相应的一阶摄动解。     

Hansen系数及其导数的直接计算方法

回顾总结了7种Hansen系数及其导数的直接计算方法,比较分析了这些方法的计算效率和计算稳定性.研究表明:Hansen系数的递推关系可以用来判别计算结果的稳定性.最后指出, Wnuk方法(双精度计算)和McClain方法(4精度计算)是稳定的,可以用来计算人造卫星轨道摄动.由于大多数人造卫星采用小偏心率轨道,需要计算无奇点摄动,推荐使用McClain方法1 (4精度计算).     

摄动势对第一类周期解稳定性的影响

本文以极坐标为广义坐标,首先讨论了摄动势对第一类周期解存在性的影响,然后利用KAM理论讨论了摄动势对第一类Poincaré周期轨道稳定性的影响。对于在实际情况中常用的形式为(n_1≤n_2为二个正整数)的摄动势,得到当小天体相对旋转坐标系的运动角速度ω≠0,和时由圆轨道所延拓生成的第一类Poincaré周期轨道是轨道稳定的。作为例子,文中还给出了当大主星体具有扁率或者是带有光环时,第一类Poincaré周期轨道稳定的条件。最后对本文所得到的结果进行了讨论。     

日月轨道计算对TLE深空编目目标预报精度的影响

双行根数(Two Line Element, TLE)作为一类广泛使用的空间物体编目数据, 其预报精度和误差特性是TLE编目 在空间碎片研究中所要关注的问题之一. TLE编目需要配合SGP4/SDP4 (Simplified General Perturbations 4/Simplified Deep Space 4)模型进行轨道预报, 对深空物体来说, 主要考虑带谐项$J_2$、$J_3$、$J_4$摄动、 第三体日月摄动和特殊轨道共振问题修正等. 其中, SGP4/SDP4模型第三体摄动计算时, 对日月轨道近似采用了长期进动根数和 简单平运动的方式, 在外推10d时存在约2$^\circ$--3${^\circ     

密近双星动力学的几个问题

本文用一种比较简单的方法导出了食双星的轨道周期和恒星周期间的关系式,指出Kopal在文[1]推导中忽略r~2/h摄动变化的不合理性.本文还讨论了考虑形状摄动的密近双星系统的一种简单模型,推出了求解该模型平动解的方程;同时针对扁率因子β_1、β_2为小量的特点,提出了两种求解直线平动解的方法.     

北斗卫星地球辐射压摄动建模研究

在对卫星所受的非保守摄动力研究中,对太阳辐射压摄动建模的研究发展迅速,而对地球辐射压摄动的研究相对缺乏,特别是其对中高轨卫星轨道影响的研究。在高精度人造卫星轨道确定中,地球辐射压摄动对于具有大面质比的导航卫星的影响越来越不可忽略。针对中国北斗导航卫星,基于地球辐射压的原理和影响机制,探讨了地球辐射压摄动建模的方法。针对北斗导航系统特点,利用地球表层的反照率和红外发射率的分布格网数据,建立了精确的地球辐射压模型,并利用全球MGEX站观测数据和中国区域监测站数据,进行了对北斗卫星引入地球辐射压模型的验证试验,分析了其定轨精度,检验了模型的正确性和可靠性。试验表明,对北斗卫星来说,在加入地球辐射压模型ERPM2(Earth radiation pressure model 2)后,轨道精度比不加入地球辐射压模型提高约4 mm;加入ERPM1模型则相应提高约2 mm。对部分卫星,加入地球辐射压模型后,其轨道精度修正量可达5～10 mm。通过卫星激光测距(satellite laser ranging,SLR)检核发现,加入ERPM2模型后,北斗中轨道地球卫星正常姿态时的轨道径向精度提高3.1 cm,GPS 036卫星轨道径向精度改善0.8～1.4 cm。因此,地球辐射压摄动模型在北斗导航卫星高精度轨道确定研究中具有一定的意义。     

地球非球形引力位中田谐项摄动的有关问题

在人造卫星绕地球运动中,地球非球形引力摄动是最重要的讨论了容易被忽视的田谐项摄动,尽管它对低轨卫星的影响,只相当于J2项的二阶量,又是短周期效应,但它却包含了大10多倍的地球自转项,必须给以重视.还导出包含全部阶次田谐项的摄动解,并分离出地球自转项,对轨道半长径a还增加了(J2×Jlm)联合摄动的地球自转项,既为理论分析提供依据又可用于分析法定轨和预报.     

Research on the Stability of the Circular Restricted Three-body Problem with Radiation and Oblateness

The velocity scaling factor method based on the least squares principle is regarded as the most efficient, stable, and widely-used method among all the manifold correction methods. The stability of the restricted three-body problem where the primary body is a source of radiation and the secondary body is an oblate spheroid is discussed by using the velocity scaling factor method. The numerical simulations suggest that (1) the number of the chaotic orbits will increase if only the oblate spheroid perturbation is considered; (2) the number of the regular orbits will increase if only considering the radiation pressure; (3) when both the radiation and oblateness perturbation exist, the radiation plays a dominant role, and the probability of regular motion of the system will increase.     

Computation of the Liapunov Orbits in the Photogravitational RTBP with Oblateness

We study the periodic motion around the collinear equilibrium points of the restricted three-body problem when the primary is a source of radiation and the secondary is an oblate spheroid. In particular, the Liapunov families of two and three dimensional periodic orbits are computed. In order to gain the appropriate initial conditions a third-fourth order Lindstedt-Poincaré local analysis is used. The stability of these families is also computed.     

Periodic orbits in the Chermnykh-like restricted problem of oblate bodies with radiation

In this paper, the periodic orbits around triangular points in the range of linear stability of the restricted three body problem, when the smaller primary and the test particle have the shape of an oblate spheroid and the larger primary is a radiation emitter with the allowance for the gravitational potential from the belt, is studied. It is observed that the orbits around these points are elliptical and have long and short periodic orbits. The period, orientation, eccentricities, the semi-major and semi-minor axis of the elliptic orbits are found. The study includes some numerical examples in the case of the Sun-Earth and Sun-Jupiter systems.     

Secular Solutions at Triangular Equilibrium Point in the Generalized Photogravitational Restricted Three Body Problem

In this paper we have found secular solutions at the triangular equilibrium point in the generalized photogravitational restricted three body problem. The problem is generalised in the sense that smaller primary is an oblate spheroid and more massive primary as source of radiation. The triangular point has long or short-period retrograde elliptical orbits. The critical mass parameter decreases with the increase in oblateness and radiation pressure. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effect of oblateness on triangular solutions at critical mass

At critical mass the triangular equilibria in the planar restricted three-body problem, when the more massive primary is an oblate spheroid with its equatorial plane coincident with the plane of motion, are in general unstable due to the presence of secular terms in the solutions of linearized equations of motion in the vicinity of these points. Existence of retrograde elliptic periodic orbits is established through suitable velocity components. The eccentricity of these orbits increases with the oblateness.     

Critical Periodic Orbits in the Restricted Three–Body Problem With Oblateness

In a recent paper in this journal series of horizontally critical symmetric periodic orbits of the six basic families of the photogravitational restricted three–body problem were computed (Perdios, 2003). In this paper, such series are determined in the framework of the restricted three–body problem when the more massive primary is an oblate spheroid. The vertical stability of the horizontally critical orbits is also computed.     

Hannay angles for relativistic polar orbits around an oblate spheroid

The Hannay adiabatic angles are computed for polar orbits in the gravitational field of an oblate spheroid described in the post-Newtonian framework of general relativity.     

Periodic orbits around an oblate spheroid

The general properties of certain differential systems are used to prove the existence of periodic orbits for a particle around an oblate spheroid.In a fixed frame, there are periodic orbits only fori=0 andi near /2. Furthermore, the generating orbits are circles.In a rotating frame, there are three families of orbits: first a family of periodic orbits in the vicinity of the critical inclination; secondly a family of periodic orbits in the equatorial plane with 0<e<1; thirdly a family of periodic orbits for any value of the inclination ife=0.     

Periodic orbits of the second kind in the restricted three-body problem when the more massive primary is an oblate spheroid

Utilizing secular perturbing potential due to oblateness, the existence of periodic orbits of the second kind is established through analytic continuation using Delaunay's canonical variables in the planar restricted three-body problem when the more massive primary is an oblate spheroid with its equatorial plane coincident with the plane of motion.     

The periodic orbits of the second kind in terms of Giacaglia's variables with oblateness

Utilizing secular perturbing potential due to oblateness, the existence of periodic orbits of the second kind is established through analytic continuation using Giacaglia's canonical variables in the planar restricted three-body problem when the more massive primary is an oblate spheroid with its equatorial plane coincident with the plane of motion.