Chaotic Asteroidal Dynamics and Maximum Lyapunov Exponents

This paper describes the results of studies of dynamical chaos in the problem of the orbital dynamics of asteroids near the 3 : 1 mean-motion resonance with Jupiter. Maximum Lyapunov characteristic exponents (MLCEs) are used as an indicator and a measure of the chaoticity of motion. MLCE values are determined for trajectories calculated by the numerical integration of equations of motion in the planar elliptical restricted three-body problem. The dependence of the MLCE on the problem parameters and on the initial data is analyzed. The inference is made that the domain of chaos in the phase space of the problem considered consists of two components of different nature. The values of the MLCEs observed for one of the components (namely, for the component corresponding to low-eccentricity asteroidal orbits) are compared to the theoretical estimates obtained within the framework of model of the resonance as a perturbed nonlinear pendulum.     

月球卫星轨道力学综述

月球探测器的运动通常可分为3个阶段，这3个阶段分别对应3种不同类型的轨道：近地停泊轨道、向月飞行的过渡轨道与环月飞行的月球卫星轨道。近地停泊轨道实为一种地球卫星轨道；过渡轨道则涉及不同的过渡方式(大推力或小推力等)；环月飞行的月球卫星轨道则与地球卫星轨道有很多不同之处，它决不是地球卫星轨道的简单克隆。针对这一点，全面阐述月球卫星的轨道力学问题，特别是环月飞行中的一些热点问题，如轨道摄动解的构造、近月点高度的下降及其涉及的卫星轨道寿命、各种特殊卫星(如太阳同步卫星和冻结轨道卫星等)的轨道特征、月球卫星定轨等。     

The Dynamics of Ejecting Stellar Systems

We consider the ejection of one stellar system from the centre of another stellar system, representing both by Plummer models. Using the impulsive appoximation, we derive analytically the overall and differential energy changes and also the mass escape from the systems. We compare the results with those obtained for colliding systems.We find that the disruptive effects are considerably less in the case of ejection. If the ejected system is compact, it escapes with negligible disruptive effects.In the case of ejections, stars are also accelerated in the direction of motion of the system. Using a dimensionless parameter λ defined as the ratio of the squares of the stellar velocity perturbations in the direction of motion of the system and perpendicular to it, we find a significant difference between ejecting systems and colliding systems. In fast head-on collisions of spherical stellar systems, the systems become elongated in the direction perpendicular to the direction of motion whereas in the case of ejecting systems, they also become elongated in the direction of motion. These effects are more pronounced in the outer regions of the smaller system and the innner regions of the bigger system. These effects are enhanced if the ejected system is compact.     

Status of Satellite Orbit Determination and Time Synchronization Technology for Global Navigation Satellite Systems

In the form of satellite ephemerides and clock parameters, the space datum and system time information of one global navigation satellite system (GNSS) is transferred to users. With the continuous updating in the satellite payload such as the high-precision atomic clock, the monitoring and tracking technique such as the inter-satellite link, and in the data processing technique, the accuracy and real-time performance of the satellite ephemeris and clock error products are steadily improved. Starting from December 27th, 2018, the BeiDou Navigation System 3, or BDS-3, has provided the accurate and reliable basic positioning, navigation, and timing (PNT) service for the users in the countries within the “one belt and one road”. This paper has summarized the faced challenges of the precise orbit determination and time synchronization from the regional BDS-2 system to the BDS-3 global system, and the specific solutions at the control segment. In addition, this paper has compared the BDS with other GNSS systems in terms of technical characteristics. Finally, aiming at a higher accuracy and more reliable PNT service, the road map of precise orbit determination and time synchronization technique for the next generation navigation systems is discussed, which will provide a reference for developing the global navigation satellite systems with an even higher accuracy.     

太阳系外行星系统构型的形成与动力学

自从Maryor和Queloz于1995年在51Pegb周围发现了第1颗主序恒星系统内的行星以来,人类已经利用越来越精密的探测方法获得了更多的太阳系外行星系统的信息.截至2010年3月,人类已经探测到了431颗太阳系外行星,其中包含了45个多行星系统.从统计结果来看,系外行星系统的构型以及行星的特点与太阳系存在很多差异.研究这些系统的形成过程可以对太阳系的形成有更深刻的理解,并将推进行星系统形成理论的发展.     

Ice Mass Balance and Ice Dynamics from Satellite Gravity Missions

An overview of advances in ice research which can be expected from future satellite gravity missions is given. We compare present and expected future accuracies of the ice mass balance of Antarctica which might be constrained to 0.1–0.3 mm/year of sea level equivalent by satellite gravity data. A key issue for the understanding of ice mass balance is the separation of secular and interannual variations. For this aim, one would strongly benefit from longer uninterrupted time series of gravity field variations (10 years or more). An accuracy of 0.01 mm/year for geoid time variability with a spatial resolution of 100 km would improve the separability of ice mass balance from mass change due to glacial isostatic adjustment and enable the determination of regional variations in ice mass balance within the ice sheets. Thereby the determination of ice compaction is critical for the exploitation of such high accuracy data. A further benefit of improved gravity field models from future satellite missions would be the improvement of the height reference in the polar areas, which is important for the study of coastal ice processes. Sea ice thickness determination and modelling of ice bottom topography could be improved as well.     

双星系统中行星的形成及动力学

自1995年在类太阳恒星周围发现第1颗太阳系外行星(简称系外行星)以来,到目前为止发现的系外行星数目已达500多个.恒星一般诞生在双星系统中,因此在双星系统中发现行星是很自然的.目前的观测统计显示,双星系统中具有行星的恒星比例大概为17％.显然这个比例应该看成一个下限,因为很强的观测选择效应使很多行星观测计划避开了双星系统.目前发现的有行星的双星系统大都为S型,即一颗伴星围绕着里面的恒星-行星系统公转.一般S型的双星轨道间距在100 AU以上,不过目前也发现了4个S型双星轨道间距在20 AU左右.这些系统包括Gamma Cephei、GJ 86、HD41004和HD 196885.除了以上介绍的S型双星,还有一类叫P型,即行星围绕两个恒星公转.P型的双星到目前为止只发现并确认了两例.本论文将主要研究S型双星系统中的行星形成. 在第1章,我们首先概括了到目前为止有关单星和双星系统中行星的观测特征.然后,我们系统地介绍了有关行星形成的理论模型,特别是这些理论模型应用到双星系统中时需要考虑的情况变化.双星系统中,由于伴星的引力扰动,行星形成与之在单星系统中相比变得更加复杂.伴星的引力可以激发起星子的轨道,从而使得它们的碰撞速度增大到大于星子的表面逃逸速度,甚至大于使星子碎裂的极限速度.行星形成的中间(第2)阶段—从星子到行星胚胎,因此变得问题重重和扑朔迷离.我们接下来的内容将主要集中在这个问题很多的中间阶段,看星子能否以及如何顺利通过这个阶段.     

Comparison of Numerical Methods for the Integration of Natural Satellite Systems

We present a new implementation of the recurrent power series (RPS) method which we have developed for the integration of the system of N satellites orbiting a point-mass planet. This implementation is proved to be more efficient than previously developed implementations of the same method. Furthermore, its comparison with two of the most popular numerical integration methods: the 10th-order Gauss–Jackson backward difference method and the Runge–Kutta–NystrRKN12(10)17M shows that the RPS method is more than one order of magnitude better in accuracy than the other two. Various test problems with one up to four satellites are used, with initial conditions obtained from ephemerides of the saturnian satellite system. For each of the three methods we find the values of the user-specified parameters (such as the method's step-size (h or tolerance (TOL)) that minimize the global error in the satellites' coordinates while keeping the computer time within reasonable limits. While the optimal values of the step-sizes for the methods GJ and RKN are all very small (less than T/100, the ones that are suitable for the RPS method are within the range: T/13<h<T/6 (T being the period of the innermost satellite of the problem). Comparing the results obtained by the three methods for these step-sizes and for the various test problems we observe the superiority of the RPS method over GJ in terms of accuracy and over RKN both in accuracy and in speed. This revised version was published online in July 2006 with corrections to the Cover Date.     

卫星导航定位系统中伪随机码的研究

伪随机码在扩频通信中得到广泛应用。目前的卫星导航定位系统大多采用扩频通信技术来传输导航信息 ,常用的伪随机码是平衡Gold码。对平衡Gold码的特性和产生方法作了研究 ,对全球定位系统 (GPS)粗码的平衡性作了分析 ,最后给出了在SystemView平台上相应的仿真结果。此研究对开展相关领域的研究工作具有借鉴意义     

The Inverse Problem of Dynamics for Systems with Non-Stationary Lagrangian

We construct a non-stationary form of the Lagrangian of a material point with a known integral of motion and given monoparametric family of evolving orbits. An equation for non-stationary space symmetrical ‘potential’ function of such Lagrangian is given and this stands for the analog of Szebehely's (1974) equation. As an application of the problem, an integrable equation from celestial mechanics of variable mass with use of non-perturbed orbits of evolving type is constructed. On its basis adiabatic invariants of non-stationary two-body problem containing a tangential force are found. This revised version was published online in July 2006 with corrections to the Cover Date.     

Numerical Instruments for the Analysis of Secular Dynamics of Exoplanetary Systems

A review is given of modern numerical methods for the analysis of resonant and chaotic dynamics: calculation of the Lyapunov characteristic exponents, the MEGNO method, and the maximum eccentricity method. These methods are used to construct stability diagrams for the planetary systems γ Cep, HD 196885, and HD 41004. The diagrams are analyzed to determine the most probable values taken by the orbital parameters of the exoplanets and obtain estimates for the Lyapunov time of their orbital dynamics. The stability diagrams constructed using the different methods are compared to analyze their effectiveness in the study of secular dynamics of exoplanetary systems.     

Relativistic Motor Dynamics of Systems of Mass Points and Rigid Bodies

A relativistic motor model for the dynamics of systems of mass points and rigid bodies, partly satisfying the program of KUSTAANHEIMO (1971) for a relativistic motor mechanics, is given. The conservation laws are valid independently of the type of dependence between mass and velocity.     

Challenges From Solid Earth Dynamics for Satellite Gravity Field Missions in the Post-Goce Era

Examples from four main categories of solid-earth deformation processes are discussed for which the GOCE and GRACE satellite gravity missions will not provide a high enough spatial or temporal resolution or a sufficient accuracy. Quasi-static and episodic solid-earth deformation would benefit from a new satellite gravity mission that would provide a higher combined spatial and temporal resolution. Seismic and core periodic motions would benefit from a new satellite mission that would be able to detect gravity variations with a higher temporal resolution combined with very high accuracies.     

On the Dynamics of a Deformable Satellite in the Gravitational Field of a Spherical Rigid Body

In this paper, a model is developed for the dynamics of a system of two bodies whose material points are under the influence of a central gravitational force. One of the bodies is assumed to be rigid and spherically symmetric, while the other is assumed to be deformable. To develop a tractable model for the system, the deformable body is modeled using Cohen and Muncaster's theory of a pseudo-rigid body. The resulting model of the system has several of the features, such as angular momentum conservation, exhibited by more restrictive models. We also show how the self-gravitation of the deformable body can be accommodated using appropriate constitutive equations for a force tensor. This enables our model to subsume many existing models of ellipsoidal figures of equilibrium. After the model and its conservations have been discussed, attention is restricted to steady motions of the system. Several results, which generalize recent works on rigid satellites, are established for these motions. For a specific choice of constitutive equations for the pseudo-rigid body, we determine the steady motions with the aid of a numerical continuation method. These results can also be considered as generalizations of earlier works on Roche's ellipsoids of equilibrium.     

Rotational Dynamics and Evolution of Planetary Satellites in the Solar and Exoplanetary Systems

Solar System Research - In this review we consider the main rotation regimes that are inherent for planetary satellites of the Solar System, satellites of trans-Neptunian objects, and potential...     

Symmetric and Asymmetric Librations in Planetary and Satellite Systems at the 2/1 Resonance

Families of asymmetric periodic orbits at the 2/1 resonance are computed for different mass ratios. The existence of the asymmetric families depends on the ratio of the planetary (or satellite) masses. As models we used the Io-Europa system of the satellites of Jupiter for the case m₁>m₂, the system HD82943 for the new masses, for the case m₁=m₂ and the same system HD82943 for the values of the masses m₁<m₂ given in previous work. In the case m₁≥ m₂ there is a family of asymmetric orbits that bifurcates from a family of symmetric periodic orbits, but there exist also an asymmetric family that is independent of the symmetric families. In the case m₁<m₂ all the asymmetric families are independent from the symmetric families. In many cases the asymmetry, as measured by and by the mean anomaly M of the outer planet when the inner planet is at perihelion, is very large. The stability of these asymmetric families has been studied and it is found that there exist large regions in phase space where we have stable asymmetric librations. It is also shown that the asymmetry is a stabilizing factor. A shift from asymmetry to symmetry, other elements being the same, may destabilize the system.     

Chaotic spiral galaxies

We study the role of asymptotic curves in supporting the spiral structure of a N-body model simulating a barred spiral galaxy. Chaotic orbits with initial conditions on the unstable asymptotic manifolds of the main unstable periodic orbits follow the shape of the periodic orbits for an initial interval of time and then they are diffused outwards along the spiral structure of the galaxy. Chaotic orbits having small deviations from the unstable periodic orbits, stay close and along the corresponding unstable asymptotic manifolds, supporting the spiral structure for more than 10 rotations of the bar. Chaotic orbits of different Jacobi constants support different parts of the spiral structure. We also study the diffusion rate of chaotic orbits outwards and find that the orbits that support the outer parts of the galaxy are diffused outwards more slowly than the orbits supporting the inner parts of the spiral structure.     

Jerk in Planetary Systems and Rotational Dynamics,Nonlocal Motion Relative to Earth and Nonlocal Fluid Dynamics in Rotating Earth Frame

Some results following from the implications of nonlocal-in-time kinetic energy approach introduced recently by Suykens in the framework of rotational dynamics and motion in a non-inertial frame are discussed. Their roles in treating aspects concerning the nonlocal motion relative to Earth, the free-fall problem, the Foucault pendulum and the motion of a massive body in a rotating tube are analyzed. Governing nonlocal equations of fluid dynamics in particular the nonlocal-in-time Navier–Stokes equations are constructed under the influence of Earth rotation. Their properties are analyzed and a number of features were revealed and discussed accordingly.     

Dynamics Of 2/1 Resonant Extrasolar Systems Application to HD82943 and GLIESE876

A complete study is made of the resonant motion of two planets revolving around a star, in the model of the general planar three body problem. The resonant motion corresponds to periodic motion of the two planets, in a rotating frame, and the position and stability properties of the periodic orbits determine the topology of the phase space and consequently play an important role in the evolution of the system. Several families of symmetric periodic orbits are computed numerically, for the 2/1 resonance, and for the masses of some observed extrasolar planetary systems. In this way we obtain a global view of all the possible stable configurations of a system of two planets. These define the regions of the phase space where a resonant extrasolar system could be trapped, if it had followed in the past a migration process.The factors that affect the stability of a resonant system are studied. For the same resonance and the same planetary masses, a large value of the eccentricities may stabilize the system, even in the case where the two planetary orbits intersect. The phase of the two planets (position at perihelion or aphelion when the star and the two planets are aligned) plays an important role, and the change of the phase, other things being the same, may destabilize the system. Also, the ratio of the planetary masses, for the same total mass of the two planets, plays an important role and the system, at some resonances and some phases, is destabilized when this ratio changes.The above results are applied to the observed extrasolar planetary systems HD 82943, Gliese 876 and also to some preliminary results of HD 160691. It is shown that the observed configurations are close to stable periodic motion.