Dynamics of Two Planets in the 2/1 Mean-Motion Resonance

The dynamics of two planets near a first-order mean-motion resonance is modeled in the domain of the general three-body planar problem. The system studied is the pair Uranus-Neptune (2/1 resonance). The phase space of the resonance and near-resonance regions is studied by means of surfaces of section and spectral analysis techniques. After a thorough investigation of the topology of the phase space, we find that several regimes of motion are possible for the Uranus-Neptune system, and the regions of transition between the regimes of motion are the seats of chaotic motion. This revised version was published online in July 2006 with corrections to the Cover Date.     

Kepler Equation solver

Kepler's Equation is solved over the entire range of elliptic motion by a fifth-order refinement of the solution of a cubic equation. This method is not iterative, and requires only four transcendental function evaluations: a square root, a cube root, and two trigonometric functions. The maximum relative error of the algorithm is less than one part in 10¹⁸, exceeding the capability of double-precision computer arithmetic. Roundoff errors in double-precision implementation of the algorithm are addressed, and procedures to avoid them are developed.     

Numerical Exploration of Chermnykh’s Problem

We study the equilibrium points and the zero-velocity curves of Chermnykh’s problem when the angular velocity ω varies continuously and the value of the mass parameter is fixed. The planar symmetric simple-periodic orbits are determined numerically and they are presented for three values of the parameter ω. The stability of the periodic orbits of all the families is computed. Particularly, we explore the network of the families when the angular velocity has the critical value ω = 2√2 at which the triangular equilibria disappear by coalescing with the collinear equilibrium point L₁. The analytic determination of the initial conditions of the family which emanate from the Lagrangian libration point L₁ in this case, is given. Non-periodic orbits, as points on a surface of section, providing an outlook of the stability regions, chaotic and escape motions as well as multiple-periodic orbits, are also computed. Non-linear stability zones of the triangular Lagrangian points are computed numerically for the Earth–Moon and Sun–Jupiter mass distribution when the angular velocity varies.     

北斗卫星导航系统实时定轨及SSR改正信息生成方法

随着GNSS应用的不断发展,实时位置服务已经成为国内外研究热点,而北斗卫星导航系统的实时服务尚处于发展阶段。本文基于卫星精密定轨基本原理,讨论了北斗导航卫星实时轨道确定策略;研究了基于北斗卫星质心和天线相位中心的SSR轨道改正值生成方法,并给出了一种适合北斗导航卫星的IODE值表达方式;基于国家基准站和全球MGEX站数据,进行了北斗导航卫星的实时轨道解算测试,结果表明,GEO卫星1D RMS精度优于400 cm,平均精度为223 cm,其径向精度优于20 cm;IGSO卫星精度优于30 cm,平均精度为22 cm,其径向精度优于10 cm;MEO卫星精度优于30 cm,平均精度为15 cm,其径向精度优于10 cm。     

New Definition of Discovery for Solar System Objects

We propose a new formal definition of discovery for a Solar System object. It is based on an objective and mathematically rigorous algorithm to assess when a set of observations is enough to constitute a discovery. When this definition is satisfied, in almost all cases the orbit is defined well enough to establish the nature of the object discovered (Main Belt vs. Near Earth Asteroid, Trans-Neptunian vs. long period comet). The frequency of occurrence of exceptions is estimated by a set of numerical experiments. The availability of a non-subjective definition of discovery allows some rules to be adopted for the assignment of discovery credit with a minimum risk of dispute. Such rules should be fair, encourage good practice by the observers and acknowledge the contribution of the orbit computers providing the identifications and the orbits, as well as the one of all the contributing observers.     

中等传输距离下的无线功率传输链路第1部分:实现工作状态最优化

中程无线功率传输（WPT）可以采用几种不同的方式实现,如通过电感或电容耦合、谐振或非谐振网络实现.本文主要研究了通过感应耦合谐振器实现的WPT链路,而且只着重研究了利用2个谐振器的链路（直接链路）并工作在主谐振频率下的情况.研究结果表明,当工作在主谐振频率下,可以根据网络参数来对传输效率或负载功率进行优化.     

基于重力卫星几何轨道线性化的地球重力场反演方法

传统动力学法的观测方程以6个初始轨道参数和先验力模型为初值进行线性化,其线性化误差随积分弧长拉长而增大.本文直接以重力卫星的几何观测轨道为初值进行线性化,其线性化误差与轨道弧长无关,且不需要初始重力场模型和初始轨道参数.导出了基于卫星轨道观测值反演重力场模型的相关公式,利用JPL公布的RL02版本2008年全年的GRACE双星轨道数据和加速度计数据解算了90阶次的地球重力场模型TJGRACE01S,并以EGM2008模型为基准与其他模型进行了比较分析,结果表明:TJGRACE01S模型直到90阶次的大地水准面累积误差为17.6 cm,优于同阶次的EIGEN-CHAMP03S和EIGEN-CHAMP05S模型,前27阶位系数整体精度优于EIGEN-GRACE01S,前15阶位系数整体精度与EIGEN-GRACE02S模型精度大致相当.利用美国8221个GPS水准点数据的分析结果也表明,本文模型也优于同阶次的EIGEN-CHAMP03S和EIGEN-CHAMP05S模型.     

利用GEOSAT／ERM卫星测高数据计算中国近海海平面

本文利用一年（１９８６年１１月８日～１９８７年１１月１７日）２２个ＥＲＭ周期的ＧＥＯＳＡＴ卫星测高数据计算出中国近海海域（１０５°～１３５°Ｅ，０°～４０°Ｎ）相对于ＧＲＳ８０参考椭球面的１°×１°年平均海平面。该海平面我们称之为ＩＧＧＭＳＳ９５平均海平面。在数据处理过程中，由于采用了混合轨道误差模型及交叠平差技术，极大地消除了在误差中占主要成分的径向轨道误差影响，使得ＩＧＧＭＳＳ９５平均海平面的总体精度达到±２０～３０ｃｍ（ＲＭＳ）水平。与ＯＳＵ９１Ａ重力大地水准面模型相比较可以发现两者具有惊人的一致性。     

基于全球MGEX数据的北斗导航星座精密轨道确定

利用全球分布的MGEX站观测数据,使用"两步法"以双差方式对北斗卫星进行精密定轨。主要研究北斗卫星轨道确定的处理策略,重点分析轨道确定的流程,并通过实验评价了3种不同类型轨道的精度。结果显示,MEO和IGSO卫星的定轨内符合精度优于0.2m,其中径向优于10cm,外符合精度优于30cm;GEO(以C05号为例)卫星外符合精度优于0.7m,且径向优于10cm。     

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