The stability and evolution of the solar system

The known history of the solar system is discussed, also the types of dynamical problems exhibited by members of the solar system and the solutions suggested for a number of such problems. The recent work of Walker, Emslie and Roy, on Empirical Stability Criteria in Many Body Problems is also mentioned.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

Recent progress in the theory and application of symplectic integrators

In this paper various aspect of symplectic integrators are reviewed. Symplectic integrators are numerical integration methods for Hamiltonian systems which are designed to conserve the symplectic structure exactly as the original flow. There are explicit symplectic schemes for systems of the formH=T(p)+V(q), and implicit schemes for general Hamiltonian systems. As a general property, symplectic integrators conserve the energy quite well and therefore an artificial damping (excitation) caused by the accumulation of the local truncation error cannot occur. Symplectic integrators have been applied to the Kepler problem, the motion of minor bodies in the solar system and the long-term evolution of outer planets.     

Review of planetary and satellite theories

Planetary and satellite theories have been historically and are presently intimately related to the available computing capabilities, the accuracy of observational data, and the requirements of the astronomical community. Thus, the development of computers made it possible to replace planetary and lunar general theories with numerical integrations, or special perturbation methods. In turn, the availability of inexpensive small computers and high-speed computers with inexpensive memory stimulated the requirement to change from numerical integration back to general theories, or representative ephemerides, where the ephemerides could be calculated for a given date rather than using a table look-up process. In parallel with this progression, the observational accuracy has improved such that general theories cannot presently achieve the accuracy of the observations, and, in turn, it appears that in some cases the models and methods of numerical integration also need to be improved for the accuracies of the observations. Planetary and lunar theories were originally developed to be able to predict phenomena, and provide what are now considered low accuracy ephemerides of the bodies. This proceeded to the requirement for high accuracy ephemerides, and the progression of accuracy improvement has led to the discoveries of the variable rotation of the Earth, several planets, and a satellite. By means of mapping techniques, it is now possible to integrate a model of the motion of the entire solar system back for the history of the solar system. The challenges for the future are: Can general planetary and lunar theories with an acceptable number of terms achieve the accuracies of observations? How can numerical integrations more accurately represent the true motions of the solar system? Can regularly available observations be improved in accuracy? What are the meanings and interpretations of stability and chaos with respect to the motions of the bodies of our solar system? There has been a parallel progress and development of problems in dealing with the motions of artificial satellites. The large number of bodies of various sizes in the limited space around the Earth, subject to the additional forces of drag, radiation pressure, and Earth zonal and tesseral forces, require more accurate theories, improved observational accuracies, and improved prediction capabilities, so that potential collisions may be avoided. This must be accomplished by efficient use of computer capabilities.     

A tidal theory for the origin of the solar nebula

There are two angular momentum (AM) problems associated with the formation of stars in general and the solar system in particular. The first is how to dispose of the AM possessed by turbulent protostellar clouds. Two-dimensional calculations of the gravitational infall of rotating gas clouds by several authors now indicate that stars are formed in groups or clusters rather than as single entities. Added evidence comes from observation of probable regions of star formation and young clusters, plus the fact that most stars are presently members of binaries or other multiples. Thus the first problem is solved by postulating the fragmentation of massive clouds with most of the AM ending up in the relative orbits. These clusters are notoriously unstable and evolve with the ejection of single stars like the Sun.The second problem is the uneven distribution of AM with mass in the solar system. It turns out that the collapse time for the majority of the infalling material is comparable to the time necessary for significant dynamical interaction of the protostellar fragment with its neighbors. It is found here through calculations utilizing very simplified numerical models that the last few tens of percent of infalling material can easily have sufficient AM transferred to it by the tidal action of passing protostars to form a solar nebula and ensure alignment of the solar spin. The most important parameter is the degree of central condensation: fragments without several tenthsM in a central core tend to be torn apart by encounters, or at least stimulated into binary fission. A stabilizing central mass maintains its identity and acquires a rotating envelope of material.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.     

动力天文中常用多步方法的比较（Ⅱ）

本文从几个方面给出了动力天文中三种常用的多步积分方法的比较结果,为积分器的选择提供了依据。     

The coupling of solar convection and rotation – (Invited Review)

In recent years, helioseismology has provided an unprecedented look at the dynamics of the solar interior. These new insights have been accompanied by tremendous advances in high-performance computing technology, prompting increasingly sophisticated and realistic numerical models of solar convection. Among the most important helioseismic constraints on global-scale convection models is the mean differential rotation profile of the solar envelope, which is established by convection under the influence of rotation. The highly turbulent nature of solar convection makes this rotational influence difficult to determine and model. I will begin this review by discussing the solar rotation profile inferred from helioseismic measurements and various theoretical and numerical approaches to account for it. Computational constraints limited early numerical models to relatively laminar flow regimes but more recent investigations have begun to explore the distinct nature of turbulent convection. After a brief overview of empirical and numerical results on the related Rayleigh-Bernard system, I will outline the current state of numerical modeling of turbulent convection in rotating, stratified fluids, first in Cartesian and then in spherical geometries. The emphasis throughout will be on how rotation influences the structure, evolution, and transport processes of turbulent convection and what type of differential rotation can result.     

Solar irradiance below 120 nm and its variations

The solar irradiance below 120 nm was first predicted by astronomers. Since its accurate measurement required the solution of a variety of technological problems, little is known about the variability before 1972, though for more than two decades data have been collected. Therefore, on a quantitative basis only a very rough picture can be given for the solar cycle 19. Also, not enough data with sufficient absolute accuracy are available to describe the solar EUV flux variations of the solar cycle 20, especially during the period of solar maximum. However, due to technological improvements of space and laboratory instrumentations, an almost complete set of data has been obtained from 1972 to date. These observations exhibit strong differences of the flux variations from solar cycle 20 to 21. - For the theoretical and for semi-empirical treatments of many aeronomic processes controlled by the solar EUV radiation, its adequate representation e.g. as indices is required. The problems involved and possible solutions are discussed. Results from some relevant aeronomically oriented computations based on variable solar EUV fluxes are presented.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

On solar system nomenclature

Arguments are presented for naming topographic features on other solar system objects after human beings other than astronomers; and to institute a more consistent scheme for Jovian satellite nomenclature.     

Career situation of female astronomers in Germany

We survey the job situation of women in astronomy in Germany and of German women abroad and review indicators for their career development. Our sample includes women astronomers from all academic levels from doctoral students to professors, as well as female astronomers who have left the field. We find that networking and human support are among the most important factors for success. Experience shows that students should carefully choose their supervisor and collect practical knowledge abroad. We reflect the private situation of female German astronomers and find that prejudices are abundant, and are perceived as discriminating. We identify reasons why women are more likely than men to quit astronomy after they obtain their PhD degree. We give recommendations to young students on what to pay attention to in order tobe on the successful path in astronomy (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

太阳系动力学中当前的重要课题

以当前太阳系动力学中的重要课题以及研究方法进行讨论，并提出一些看法，课题中主要讨论动力学模型，轨道共振，行星环，混沌和长期演化，近地天体运动，Kupiper带，太阳系中的引力理论，以及其他有关问题。     

The nekhoroshev theorem and the asteroid belt dynamical system

The present paper reviews the Nekhoroshev theorem from the point of view of physicists and astronomers. We point out that Nekhoroshev result is strictly connected with the existence of a specific structure of the phase space, the existence of which can be checked with several numerical tools. This is true also for a degenerate system such as the one describing the motion of an asteroid in the so called main belt. The main difference is that in some parts of the belt, the Nekhoroshev result cannot apply a priori. Mean motion resonances of order smaller than the logarithm of the mass of Jupiter and first order secular resonances must be excluded. In the remaining parts, conversely, the Nekhoroshev theorem can be proved, provided someparameters, such as the masses, the eccentricities and the inclinations of the planets are small enough. At the light of this result, a massive campaign of numerical integrations of real and fictitious asteroids should allow to understand which is the real dynamical structure of the asteroid belt.     

Variational and symplectic integrators for satellite relative orbit propagation including drag

Orbit propagation algorithms for satellite relative motion relying on Runge–Kutta integrators are non-symplectic—a situation that leads to incorrect global behavior and degraded accuracy. Thus, attempts have been made to apply symplectic methods to integrate satellite relative motion. However, so far all these symplectic propagation schemes have not taken into account the effect of atmospheric drag. In this paper, drag-generalized symplectic and variational algorithms for satellite relative orbit propagation are developed in different reference frames, and numerical simulations with and without the effect of atmospheric drag are presented. It is also shown that high-order versions of the newly-developed variational and symplectic propagators are more accurate and are significantly faster than Runge–Kutta-based integrators, even in the presence of atmospheric drag.     

Existence of formal integrals of symplectic integrators

A recurrent method of solving the formal integrals of symplectic integrators is given. The special examples show that there are no long-term variations in all integrals of the Hamiltonian system in addition to the energy one when symplectic integrators are used in the numerical studies of the system. As an application of the formal integrals, the relation between them and the linear stability of symplectic integrators is discussed.     

Chaos in N-body systems

Here is a selection of applications of what is now called theory of dynamical systems in galactic dynamics and N-body systems. The study of chaotic motions in potentials used as a model for elliptical galaxies is a first example of these applications. The interest in this problem stems from the fact that there are now many theoretical and observational evidences that the overall potentials of galaxies are indeed non-integrable. There are classes of objects, for example small and intermediate luminosity elliptical galaxies, for which the presence of the famous third integral is not necessary or others in which we observe peculiarities in their photometry or kinematics. We address here some of these issues and their implications in modifying our current understanding of the structure and evolution of galaxies.More in general, there is the natural question of how the systems we see have settled to their present status and what would happen if some external cause perturbs it. This issue is related to the question of the stochasticity involved in the general N-body dynamics, especially when N is very large. An N-body dynamical system is definitely chaotic, as shown by several numerical investigations, at least for N not very large. However, this statement must be reconciled with the picture of non-collisional equilibrium of big systems. The second part of this review presents a survey of numerical experiments and an interpretation of the results obtained using standard chaoticity indicators.     

国内太阳数据VO化初步方案

随着太阳物理研究的深入、观测仪器的发展、观测数据的积累，促使人们去思考这样的问题：利用全世界不同时间、地点、波段的太阳相关数据、历史数据去对很多悬而未解的科学问题寻求答案，同时使研究者容易的去检索这些数据，进行分析，这就是虚拟太阳天文台要解决的问题，也是为什么虚拟太阳天文台项目得到了全世界有关天文台、研究所和大学的积极响应和运作。本文介绍了国内应如何面对虚拟天文台的发展及国内太阳数据VO化初步方案。     

Vesta fragments from v6 and 3:1 resonances: Implications for V-type near-Earth asteroids and howardite,eucrite and diogenite meteorites

Abstract— A large body of evidence, including the presence of a dynamical family associated with 4 Vesta, suggests that this asteroid might be the ultimate source of both the V-type near-Earth asteroids (NEAs) and howardite, eucrite and diogenite (HED) meteorites. Dynamical routes from Vesta to the inner regions of the solar system are provided by both the 3:1 mean-motion resonance with Jupiter and the V₆, secular resonance. For this reason, numerical integrations of the orbits of fictitious Vesta fragments injected in both of these resonances have been performed. At the same time, the orbital evolution of the known V-type NEAs has been investigated. The results indicate that the dynamical half lifetimes of Vesta fragments injected in both the 3:1 and the V₆, resonances are rather short ('2 Ma). The present location of the seven known V-type NEAs is better explained by orbital evolutions starting from the v₆ secular resonance. The most important result of the present investigation, however, is that we now face what we call the “Vesta paradox.” Roughly speaking, the paradox consists of the fact that the present V-type NEAs appear to be too dynamically young to have originated in the event that produced the family, but they are too big to be plausible second-generation fragments from the family members. The cosmic-ray exposure (CRE) age distribution of HED meteorites also raises a puzzle, since we would expect an overabundance of meteorites with short CRE ages. We propose different scenarios to explain these paradoxes.     

太阳射电日像仪的进步与发展

叙述了太阳射电天文和太阳物理上作出过杰出贡献的几个射电日像仪的概况及其进步与发展,并简述了未来射电日像仪可以完成的科学目标以及应具有的特点,以期为在２１世纪我国实现“一颗空间Ｘ射线卫星、一座红外太阳塔和一台射电像仪”的宏伟构想提供研制依据。     

Synthetic secular theories of the planetary orbits: Regular and chaotic behavior

Modern computer technology allows dynamical astronomers to investigate the long term stability of real systems as thoroughly as ever. However, the process is not straightforward and new problems need to be solved. This work deals with only one such problem: the construction-from the numerical integration- of a secular perturbation theory that is able to describe the dynamical behavior of the system. The discussion refers to the outer planets and is based on the knowledge acquired by the author during her participation in project LONGSTOP. A digital filter is used in order to reduce the output and eliminate short periodic terms. Filtering uncovers long term variations in the semimajor axes. From the filtered output a secular perturbation theory is constructed in the assumption that the solution is regular, as secular perturbation theories can only be constructed for regular solutions. If we succeed, this means that the solution is indeed regular for the computed span of time; if not-and this can be established in a rigorous way-it has to be concluded a posteriori that the solution is not regular. The LONGSTOP 1A and 1B integrations show well that as the timespan of the integration increases it is possible to detect the non-regular behavior of the solution. This happens in the eccentricity of Saturn at the 10^–4 level.     

主带小行星的动力学模拟

采用接近真实太阳系的动力学模型,对主带小行星的动力学演化进行了数值模拟。计算的起始时间是儒略日JD=2.4540005×10~6,计算的时间长度为100万年。力学模型采用n+m体模型,计算程序基于小行星轨道演化的软件Orbit9。对演化结果进行分析可以发现测试粒子与木星的平运动共振对测试粒子稳定性的不同作用,以及在2:3、3:4共振处不同初始ω值对测试粒子演化结果的影响。     

几类辛方法的数值稳定性研究

主要对一阶隐式Euler辛方法M1、二阶隐式Euler中点辛方法M2、一阶显辛Euler方法M3和二阶leapfrog显辛积分器M4共4种辛方法及一些组合算法进行了通常意义下的线性稳定性分析．针对线性哈密顿系统,理论上找到每个数值方法的稳定区,然后用数值方法检验其正确性．对于哈密顿函数为实对称二次型的情况,为了理论推导便利,特推荐采用相似变换将二次型的矩阵对角化来研究辛方法的线性稳定性．当哈密顿分解为一个主要部分和一个小摄动次要部分且二者皆可积时,无论是线性系统还是非线性系统,这种主次分解与哈密顿具有动势能分解相比,明显扩大了辛方法的稳定步长范围．