On a question of A. Wintner about Jacobi coordinates in the three-body problem

In his work on the elimination of the nodes in the Three-Body Problem, Jacobi considered a certain straight line (defined below, in the Introduction) which lies always within the invariable plane. Here we settle the question of Wintner on the classification of all motions for which this line fails to exist.     

Jacobi Dynamics And The N-Body Problem With Variable Masses

An appropriate generalization of the Jacobi equation of motion for the polar moment of inertia I is considered in order to study the N-body problem with variable masses. Two coupled ordinary differential equations governing the evolution of I and the total energy E are obtained. A regularization scheme for this system of differential equations is provided. We compute some illustrative numerical examples, and discuss an average method for obtaining approximate analytical solutions to this pair of equations. For a particular law of mass loss we also obtain exact analytical solutions. The application of these ideas to other kind of perturbed gravitational N-body systems involving drag forces or a different type of mass variation is also considered. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Spin-Orbit Resonant Rotation of Mercury: A Two Degree of Freedom Hamiltonian Model

The paper develops a hamiltonian formulation describing the coupled orbital and spin motions of a rigid Mercury rotation about its axis of maximum moment of inertia in the frame of a 3:2 spin orbit resonance; the (ecliptic) obliquity is not constant, the gravitational potential of mercury is developed up to the second degree terms (the only ones for which an approximate numerical value can be given) and is reduced to a two degree of freedom model in the absence of planetary perturbations. Four equilibria can be calculated, corresponding to four different values of the (ecliptic) obliquity. The present situation of Mercury corresponds to one of them, which is proved to be stable. We introduce action-angle variables in the neighborhood of this stable equilibrium, by several successive canonical transformations, so to get two constant frequencies, the first one for the free spin-orbit libration, the other one for the 1:1 resonant precession of both nodes (orbital and rotational) on the ecliptic plane. The numerical values obtained by this simplified model are in perfect agreement with those obtained by Rambaux and Bois [Astron. Astrophys. 413, 381–393]. This revised version was published online in July 2006 with corrections to the Cover Date.     

HD 12661行星系统构形的形成与稳定性

最近的多普勒观测表明恒星HD 12661周围存在两颗中等偏心率轨道上运行的行星,内行星的最小质量为2．3木星质量,轨道周期为263．6天;外行星的最小质量为1．57木星质量,轨道周期为1444．5天．该系统的稳定性要求两颗行星处在平运动轨道共振．用数值方法研究了该系统形成初期在恒星气体盘作用下的轨道迁移与稳定性,计算了行星在迁移中被平运动共振俘获的概率．发现这两颗行星目前很可能正处在11:2平运动共振边缘,且运动是混沌的,从而澄清了关于系统目前构形的不同说法,并且很可能在系统形成后行星迁移到目前构形时,气体盘几乎消失了．     

The Development of the Spanish Fireball Network Using a New All-Sky CCD System

We have developed an all-sky charge coupled devices (CCD) automatic system for detecting meteors and fireballs that will be operative in four stations in Spain during 2005. The cameras were developed following the BOOTES-1 prototype installed at the El Arenosillo Observatory in 2002, which is based on a CCD detector of 4096 × 4096 pixels with a fish-eye lens that provides an all-sky image with enough resolution to make accurate astrometric measurements. Since late 2004, a couple of cameras at two of the four stations operate for 30 s in alternate exposures, allowing 100% time coverage. The stellar limiting magnitude of the images is +10 in the zenith, and +8 below ~ 65° of zenithal angle. As a result, the images provide enough comparison stars to make astrometric measurements of faint meteors and fireballs with an accuracy of ~ 2°arcminutes. Using this prototype, four automatic all-sky CCD stations have been developed, two in Andalusia and two in the Valencian Community, to start full operation of the Spanish Fireball Network. In addition to all-sky coverage, we are developing a fireball spectroscopy program using medium field lenses with additional CCD cameras. Here we present the first images obtained from the El Arenosillo and La Mayora stations in Andalusia during their first months of activity. The detection of the Jan 27, 2003 superbolide of ± 17 ± 1 absolute magnitude that overflew Algeria and Morocco is an example of the detection capability of our prototype.     

Approximate General Solution Of The Two-Dimensional Duffing Dynamical System

This paper presents the approximate general solution of the triple well, double oscillator non-linear dynamical system. This system is non-integrable and the approximate general solution is calculated by application of the Last Geometric Theorem of Poincaré (Birkhoff, 1913, 1925). The original problem, known as the Duffing one, is a 1 degree of freedom system that, besides the conservative force component, includes dumping and external forcing terms (see details in the web site: http://www.uncwil.edu/people/hermanr/chaos/ted/chaos.html). The problem considered here is a 2 degree of freedom, autonomous and conservative one, without dumping, and of axisymmetric potential. The space of permissible motions is scanned for identification of all solutions re-entering after from one to nine oscillations and the precise families of periodic solutions are computed, including their stability parameter, covering all cases with periods T corresponding to 4osc/T. Seven sub-domains of the space of solutions were investigated in detail by zooming, an operation that proved the possibility to advance the accuracy of the approximate general solution to the level permitted by the integration routine. The approximation of the general solution, although impressive, provides clear evidence of the complexity of the problem and the need to proceed to larger period families. Nevertheless, it allows prediction of the areas where chaos and order regions in the Poincaré surfaces of section are to be expected. Examples of such surfaces of sections, as well as of types of closed solutions, are given. Two peculiar points of the space of solutions were identified as crossing, or source points from which infinite families of periodic solutions emanate. The morphology and stability of solutions of the problem are studied and discussed.     

Limitations Of The Tangent Plane Approximation For Wide-field Imaging Using The Mauritius Radio Telescope

The Mauritius Radio Telescope (MRT) is a Fourier synthesis, non-coplanar T array. The primary objective of the telescope is to survey the southern sky at 151.5 MHz in the declination range -70^° to -10^°. Due to non-coplanarity, wide-field imaging and deconvolution of wide field images made using MRT are challenging problems in applications of radio interferometric techniques. This paper discusses the usefulness and limitations of the tangent plane approximation in transforming the measured visibilities to wide field images and in estimating the point spread function (PSF) required for the deconvolution. This revised version was published online in July 2006 with corrections to the Cover Date.     

大气反常折射对星表和参考系的影响

在过去的时间纬度工作中,对大气反常折射的研究证明,大气反常折射给时问纬度测量带来了严重的影响。而当时大多数星表的编制都是时间纬度测量的副产品,无疑大气反常折射也给这些星表带来严重的误差影响。过去我国的经典天体测量工作以测时、测纬为主,这一问题并没有得到重视。在星表和参考系工作已成为我国基本天休测量工作的一项主要内容的今天,对大气反常折射的测量与研究,尤其对有效的测量应得到足够的重视。作者根据自己的实际测量和研究指出,大气反常折射主要由观测室周围不良小气候的造成,其中以具有周年变化和周日变化的大气反常折射对初始星表系统的影响最为严重。并分别讨论了这种反常折射对子午星表、等高星表和参考系的影响,提出了今后开展这方面工作的建议。     

Neutrino Tomography – Learning About The Earth’s Interior Using The Propagation Of Neutrinos

Because the propagation of neutrinos is affected by the presence of Earth matter, it opens new possibilities to probe the Earth’s interior. Different approaches range from techniques based upon the interaction of high energy (above TeV) neutrinos with Earth matter, to methods using the MSW effect on the oscillations of low energy (MeV to GeV) neutrinos. In principle, neutrinos from many different sources (sun, atmosphere, supernovae, beams etc.) can be used. In this talk, we summarize and compare different approaches with an emphasis on more recent developments. In addition, we point out other geophysical aspects relevant for neutrino oscillations.     

The Homoclinic Tangle of A 1:2 Resonance in a 2-D Hamiltonian System

We study in great detail the geometry of the homoclinic tangle, with respect to the energy, corresponding to an unstable periodic orbit of type 1:2, on a surface of section representing a 2-D Hamiltonian system. The tangle consists of two resonance areas, in contrast with the tangles of type-l or -{l, m, k, x = 0} considered in previous studies, that consist of only one resonance area. We study the intersections of the inner and outer lobes of the same resonance area and of the two resonance areas. The intersections of the lobes follow certain rules. The detailed study of these rules allows us to derive quantitative relations about the number of intersections and to understand the complex behavior of the higher order lobes by studying the lower order lobes. We find 1st, 2nd, 3rd, etc. order intersections formed by lobes making 1, 2, 3, etc. turns around an island. After a sufficiently high order of iterations a lobe may intersect its image and thus produce a Poincaré recurrence. Numerical results for a wide interval of energies are presented. The number of intersections changes through tangencies. In any finite interval of the energy between two tangencies of 1st order, an infinite number of higher order tangencies occur and thus, according to the Newhouse theorem, there exist nearby islands of stability.     

GJ 876行星系统中潜在类地行星研究

用数值积分方法模拟探讨了GJ876行星系统中存在潜在类地行星的可能性．结果表明分别产生于内外两颗巨行星的长期共振v_1和v_2可激发类地行星(其轨道半长轴分布在0．21AU≤a＜0．50AU之间)的偏心率,并使它们在极短时间内被抛射出系统．然而,从动力学角度而言,类地行星潜在存在区域可分布在0．50 AU≤a≤1．00 AU之间,其能在系统中10~5年时间尺度上稳定地存在．     

The Apsidal Antialignment of the HD 82943 System

We perform numerical simulations to explore the dynamical evolution of the HD 82943 planetary system. By simulating diverse planetary configurations, we find two mechanisms of stabilizing the system: the 2:1 mean motion resonance (MMR) between the two planets can act as the first mechanism for all stable orbits. The second mechanism is a dynamical antialignment of the apsidal lines of the orbiting planets, which implies that the difference of the periastron longitudes ₃ librates about 180° in the simulations. We also use a semi-analytical model to explain the numerical results for the system under study.     

1.2m地平式望远镜伺服控制和传动系统的特性研究--伺服系统校正网络在控制系统中的作用(二)

根据云南天文台1.2m地平式望远镜对近地卫星激光测距要求,以及对串联校正网络在控制系统中的作用分析和实际观测的结果,详细讨论了1.2m望远镜伺服系统校正网络以及经其补偿作用后系统的控制性能。得到在两点摩擦传动时,使用超前校正网络后,望远镜的快速跟踪性能得到了大大提高,能够达到的方位最大角加速度为10°/s2,方位最大角速度5°/s,满足跟踪近地卫星的要求。