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Analytical Study of the Co-orbital Motion in the Circular Restricted Three-body Problem

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Research in Astronomy and Astrophysics 2023年第4期23卷 121-132页

作者： Xinhe Shen Tao Liu xinhao liao Shanghai Astronomical Observatory Chinese Academy of SciencesShanghai 200030China Key Laboratory of Planetary Sciences Chinese Academy of SciencesShanghai 200030China University of Chinese Academy of Sciences Beijing 100049China School of Physical Science and Technology ShanghaiTech UniversityShanghai 201210China

In the restricted three-body problem(RTBP), if a small body and a planet stably orbit around a central star with almost exactly the same semimajor axis, and thus almost the same mean motion, this phenomenon is called the coorbital motion, or equivalently, the 1:1 mean motion resonance. The classical expansion of the disturbing function is divergent when the semimajor axis ratio of the small body to the planet is close to unity. Thus, most of the previous studies on the co-orbital dynamics were carried out through numerical integrations or semi-analytical approaches. In this work, we construct an analytical averaged model for the co-orbital motion in the framework of the circular RTBP. This model is valid in the entire coorbital region except in the vicinity of the collision singularity. The results of the analytical averaged model are in good agreement with the numerical averaged model even for moderate eccentricities and inclinations. The analytical model can reproduce the tadpole, horseshoe and quasi-satellite orbits common in the planar problem. Furthermore, the asymmetry of 1:1 resonance and the compound orbits(Icarus 137:293–314) in the general spatial problem can also be obtained from the analytical model.

关键词： celestial mechanics-methods analytical-minor planets-asteroids general

Electromagnetic induction in a conducting D" layer-Ⅰ:Effects of boundary charge accumulation and the boundary conditions

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Geodesy and Geodynamics 2019年第3期10卷 187-195页

作者： Ming Fang xinhao liao Department of EAPS Massachusetts Institute of TechnologyCambraidge MA02139USA Shanghai Observatory Chinese Academy of SciencesShanghai200030China

In response to the primary electric field originated by the fluid-core-dynamo, electric charges accumulate at the boundaries of a solid conducting D″ layer due to the poor circuitry conditions until the irrotational primary electric field is neutralized. The neutralization undoes the internal induction excited by the primary electric field and, as a result, eliminates the secondary toroidal magnetic field inside the D″. The primary magnetic field generated by the fluid-core-dynamo gives rise to a sustainable secondary poloidal magnetic field inside the conducting D″ layer. We introduce the general kinematic boundary conditions that are valid with different induction processes and parameter jumps across the core mantle *** find by dimensional analysis that the strength of the secondary poloidal magnetic field is much weaker, by a factor of ~10-2, than the irrotational primary. These findings indicate that the D' is in effect an insulator for the geodynamo regardless of its material composition. Any mechanism for the coremantle magnetic coupling should take this fact into consideration.

关键词： D' layer Magnetic induction Boundary conditions

Movement of earth rotation and activities of atmosphere and ocean

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Chinese Science Bulletin 2001年第11期46卷 881-888页

作者： ZHOU Yonghong ZHENG Dawei YU Nanhua liao xinhao Shanghai Astronomical Observatory Chinese Academy of SciencesShanghai 200030China National Astronomical Observatories Chinese Academy of SciencesBeijing 100012China United Center for Astro-geodynamics Research Chinese Academy of SciencesShanghai 200030China

The rotation of the earth, including the variation of the rotational rate and polar motion, represents the statement of the earth’s overall movement and interactions among the solid earth, atmosphere and ocean on a variety of space-time scales. They make the earth’s complex dynamical system under the conservation of angular momentum. The application and development of recent space geodetic techniques greatly promote the researches on the interactions between the earth rotation and the activities of atmosphere and ocean. This review will mainly report the progress in researches on the earth rotation and the activities of atmosphere and ocean as well as the air-sea interaction in the tropics, and prospect the direction for future theoretical investigations.

关键词： earth rotation atmospheric activity oceanic activity ENSO.

Premonitory phenomenon of El Nino event reflected in the observations of LOD and sea level

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Chinese Science Bulletin 2000年第24期45卷 2231-2236页

作者： ZHENG Dawei DING Xiaoli ZHOU Yonghong CHEN Yongqi LI Zhilin liao xinhao Shanghai Astronomical Observatory Chinese Academy of SciencesShanghai 200030China Center of National Astronomical Observation Chinese Academy of SciencesBeijing 100012China Department of Land Surveying and Geo-Informatics Hong Kong Polytechnic UniversityHung HornKowloonHong KongChina

Data sets of the changes of the length of day, the sea surface temperature in the eastern Pacific and of the sea level in Hong Long from tide gauge observations are used to analyze and reveal the reflections in the observations of the length of day and the sea level changes concerned with the premonitory phenomenon of next El Nino event. The results from this study indicate that a new El Nino event has been brewing with the ending of the strong La Nina event that started in early summer of 1998. The estimated formation period of the new El Nino event will begin before the end of 2000, and the peak period may be reached at around the end of 2001.

关键词： change of the length of day sea level change El Nino event.

On the Integrable Motion Equations in FOC by GSSH

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On the Integrable Motion Equations in FOC by GSSH

作者： Chengli HUANG xinhao liao Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China

For the equations of the infinitesimal elastic-gravitational motion for a rotating, slightly elliptical Earth, one can, with the tool of generalized surface spherical harmonics (GSSH, or GSH), transfer the motion equations from ellipsoidal domain to an effective spherical domain (ESD), and then from vector form to scalar form, so that it is numerically integrable. In the fluid outer core (FOC), due to the cancellation of rigidity in fluid, the tangential tractions vanish identically and the differential equations for the transverse displacement fields do not hold any longer as in solid medium, but they are needed in some work. In this paper, we derive the derivative of the transverse displacements and other motion equations for FOC, they are explicit and in scalar, and the scheme to encode to program is also presented at the end of this paper

关键词： Motion equation Fluid outer core Displacement field Generalized spherical harmonics Elastic-gravitational excitation

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行星科学和深空探测研究与发展

中国科学院院刊 2011年第5期26卷 504-510页

作者：廖新浩中国科学院上海天文台上海200023

文章介绍了行星科学已取得的重要研究进展和当前存在的主要科学问题,对未来我国行星科学和深空探测研究与发展提出了若干建议。

关键词：行星科学深空探测研究与发展

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人造卫星运动中的轨道共振

天文学进展 1991年第4期9卷 298-308页

作者：刘林廖新浩赵长印南京大学天文系

本文采用受摄理想共振模型,对人造卫星运动中所发生的各类轨道共振作一具体分析,给出相应的共振特征及其演化性态,为摄动计算中考虑共振项的取舍提供理论依据。

关键词：人造卫星运动轨道共振

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常微分方程数值解法在动力天文中的应用

系统仿真学报 1993年第3期5卷 48-55页

作者：刘林廖新浩赵长印南京大学天文系

在动力天文中,利用常微数值解法求解运动方程时,通常会出现两个问题——解的定性性质受到歪曲和轨道沿迹误差的严重累积。本文将介绍利用运动本身的一些力学性质作为控制条件,能够有效地解决这些问题,特别是对Hamiltom系统,采用保持辛... 详细信息

在动力天文中,利用常微数值解法求解运动方程时,通常会出现两个问题——解的定性性质受到歪曲和轨道沿迹误差的严重累积。本文将介绍利用运动本身的一些力学性质作为控制条件,能够有效地解决这些问题,特别是对Hamiltom系统,采用保持辛结构的差分格式——半积分器(Symplectic Imtegrators),有它独特的优点,而且可以将相应的差分格式稍作修改,就可用于小耗散系统,这对动力天文而言也是很重要的。

关键词：动力天文天体天体运动常微分方程数值解法

Interannual variations in the length of day and ENSO events in 1982-1983 and 1997-1998

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Science China Mathematics 2001年第1期44卷 128-136页

作者：郑大伟廖新浩赵志弘李志林丁晓利周永宏陈永奇 1. Shanghai Astronomical Observatory Chinese Academy of Sciences 200030 Shanghai China 2. National Astronomical Observatories Chinese Academy of Sciences 100012 Beijing China 3. Department of Land Surveying and Geo-Informatics Hong Kong Polytechnic University Hung Hom Kowloon Hong Kong China

The length of day series during the period of 1962.0-2000.0, the atmospheric angular momentum and the Southern Oscillation Index are adopted to analyze the relationships among the EN-SO events that have occurred since 1960, the changes in the length of day and the atmospheric angular momentum. Attention is particularly given to the different effects of the 1982-1983 and 1997-1998 ENSO events on the variations of Earth rotation. The synthetic excitation effects of multi-scale atmospheric oscillations on the anomalous variations of the interannual rates of Earth rotation are revealed by means of the time-frequency spectrum of the wavelet transform.

关键词： change in length of day atmospheric angular momentum ENSO events.