Dynamical Symmetry,by Carl E. Wulfman

The contemporary view of stellar movements is that the motion is orbital motion in the attracting field of the galaxy as a whole. The orbits can be classified according to their eccentricity and inclination to the plane of the galaxy. Orbits of low eccentricity and inclination are characteristic of very young stars. Most stars describe orbits of moderate eccentricity and moderate inclination, but some orbits are known to occur with very high eccentricity and high inclination to the plane of the galaxy, these orbits being characteristic of very old stars, and in particular RR Lyrae Variable stars. The article sketches the technique by which velocities relative to the Sun are found and gives a brief account of the mathematics by means of which these velocities are shown to correspond to galactic orbits, and the article concludes with a sketch of the interpretation of the statistics of galactic orbits in terms of the history of the galaxy.     

On the Tidally Induced Gravitational Collapse of a Particle Cluster

An important issue in the dynamics of neutron star binaries is whether tidal interaction can cause the individual stars to collapse into black holes during inspiral. To understand this issue better, we study the dynamics of a cluster of collisionless particles orbiting a non-rotating black hole, which is part of a widely separated circular binary. The companion body's electric- and magnetic-type tidal fields distort the black hole and perturb the cluster, eventually causing the cluster to collapse into the hole as the companion spirals in under the influence of gravitational radiation reaction. We find that magnetic-type tidal forces do not significantly influence the evolution of the cluster as a whole. However, individual orbits can be strongly affected by these forces. For example, some orbits are destabilized due to the addition of magnetic-type tidal forces. We find that the most stable orbits are close to the companion's orbital plane and retrograde with respect to the companion's orbit.     

转动双星同步和轨道圆化的物理过程研究

潮汐效应是影响恒星结构和演化非常重要的物理因素.本文研究了影响潮汐同步和轨道圆化的物理因素,如恒星质量、初始转速、轨道周期、金属丰度、对流超射等,并根据转动恒星的角动量转移和元素扩散方程,给出了这些因素对转动双星演化和元素混合的影响.结果表明：具有大质量子星、初始转速慢、对流超射小、轨道周期短的双星系统,能更早地达到平衡速度和轨道圆化;初始转速快的恒星,由于潮汐同步过程减速,双星系统中氮元素增丰没有单星的氮元素增丰显著;大质量星、高金属丰度、超射大和短周期的双星系统,氮增丰相对显著;质量小、金属丰度低、转速慢、超射大的恒星具有较小的恒星半径,而低金属丰度恒星表面却具有较高的有效温度,快速转动单星向低温和低光度端演化.     

Geodesic Structure of a Non-linear Magnetic Charged Black Hole Surrounded by Quintessence

This paper aims to investigate the geodesic motion in the spacetime of a non-linear magnetic charged black hole surrounded by quintessence. By varying the Lagrangian corresponding to the metric, the orbital motion equation has been obtained. The effects of the magnetic charge $Q$, positive normalization factor $C$, angular momentum $b$, and energy $E$ on time-like and null geodesic motion are discussed from three aspects: orbital stability, orbital types, and circular orbits. By comparing the effects of the above parameters $C$, $b$ on the effective potential, it is found that quintessence has an impact on the types and stability of orbits. In addition, for time-like orbital motion, when $3.443113\leq b\leq6.392\,578$ (for fixed $C=0.0002$, $M = 1$, $Q=0.7$), there are bound orbits, and within this range, the stable circular orbits exist, and the radii of the innermost and outermost stable circular orbit are $r=5.912\,654$ and $r=56.745\,933$, respectively. For null orbital motion, the orbital types have only unstable circular orbit which occur at $r=2.951\,072$ ($E^{2}=E_{2}^{2}=0.4$), absorb orbits and escape orbits, but no stable circular orbits, and bound orbits.     

A simple method to design non-collision relative orbits for close spacecraft formation flying

A set of linearized relative motion equations of spacecraft flying on unperturbed elliptical orbits are specialized for particular cases, where the leader orbit is circular or equatorial. Based on these extended equations, we are able to analyze the relative motion regulation between a pair of spacecraft flying on arbitrary unperturbed orbits with the same semi-major axis in close formation. Given the initial orbital elements of the leader, this paper presents a simple way to design initial relative orbital elements of close spacecraft with the same semi-major axis, thus preventing collision under non-perturbed conditions. Considering the mean influence of J₂ perturbation, namely secular J₂ perturbation, we derive the mean derivatives of orbital element differences, and then expand them to first order. Thus the first order expansion of orbital element differences can be added to the relative motion equations for further analysis. For a pair of spacecraft that will never collide under non-perturbed situations, we present a simple method to determine whether a collision will occur when J₂ perturbation is considered. Examples are given to prove the validity of the extended relative motion equations and to illustrate how the methods presented can be used. The simple method for designing initial relative orbital elements proposed here could be helpful to the preliminary design of the relative orbital elements between spacecraft in a close formation, when collision avoidance is necessary.     

The Euler-Poincaré equations and double bracket dissipation

This paper studies the perturbation of a Lie-Poisson (or, equivalently an Euler-Poincaré) system by a special dissipation term that has Brockett's double bracket form. We show that a formally unstable equilibrium of the unperturbed system becomes a spectrally and hence nonlinearly unstable equilibrium after the perturbation is added. We also investigate the geometry of this dissipation mechanism and its relation to Rayleigh dissipation functions. This work complements our earlier work (Bloch, Krishnaprasad, Marsden and Ratiu [1991, 1994]) in which we studied the corresponding problem for systems with symmetry with the dissipation added to the internal variables; here it is added directly to the group or Lie algebra variables. The mechanisms discussed here include a number of interesting examples of physical interest such as the Landau-Lifschitz equations for ferromagnetism, certain models for dissipative rigid body dynamics and geophysical fluids, and certain relative equilibria in plasma physics and stellar dynamics.Research partially supported by the National Science Foundation PYI grant DMS-91-57556, and AFOSR grant F49620-93-1-0037.Research partially supported by the AFOSR University Research Initiative Program under grants AFOSR-87-0073 and AFOSR-90-0105 and by the National Science Foundation's Engineering Research Centers Program NSFD CDR 8803012.Research partially supported by, DOE contract DE-FG03-92ER-25129, a Fairchild Fellowship at Caltech, and the Fields Institute for Research in the Mathematical Sciences.Research partially supported by NSF Grant DMS 91-42613, DOE contract DE-FG03-92ER-25129, the Fields Institute, the Erwin Schrödinger Institute, and the Miller Institute of the University of California.     

Measurement of gravitational spin-orbit coupling in a binary-pulsar system

In relativistic gravity, a spinning pulsar will precess as it orbits a compact companion star. We have measured the effect of such precession on the average shape and polarization of the radiation from PSR B1534+12. We have also detected, with limited precision, special-relativistic aberration of the revolving pulsar beam due to orbital motion. Our observations fix the system geometry, including the misalignment between the spin and orbital angular momenta, and yield a measurement of the precession time scale consistent with the predictions of general relativity.     

在有心力场中行星运行轨道稳定性的证明

从粒子的基本运动方程出发,利用非线性动力学的方法证明了行星在有心力场中运行轨道的稳定性,得到结论:粒子在有心力F=-k2m2r-n的作用下运行时,轨道稳定的条件是n<3.     

Motion and gravitational radiation of a binary system consisting of an oscillating and rotating coplanar dusty disk and a point-like object

A binary system composed of an oscillating and rotating coplanar dusty disk and a point mass is considered. The conservative dynamics is treated on the Newtonian level. The effects of gravitational radiation reaction and wave emission are studied to leading quadrupole order. The related waveforms are given. The dynamical evolution of the system is determined semi-analytically exploiting the Hamiltonian equations of motion which comprise the effects both of the Newtonian tidal interaction and the radiation reaction on the motion of the binary system in elliptic orbits. Tidal resonance effects between orbital and oscillatory motions are considered in the presence of radiation damping.     

Relativistic orbital perturbations in a weak gravitational field

With the general third-order equations of motion for a test particle, Synge's third-order orbital equations at great distance in the weak gravitational field generated by a massive body are derived. The body has an axis of symmetry around which is rotating steadily. The results found for the advance of perihelion using first integrals of motion for the general equations show that the effect due to the inner stress of the body can be derived for orbits with inclination with respect to the equator of the body. Then, by means of the variation of the parameters method, we obtain with the equations at great distance the corresponding perturbations on the elements of such orbits in the field considered. These perturbations result to be of second order with regard to the mass of the body (the basis of the approximation).     

Orbital and epicyclic motion of charged test particles around non-rotating Einstein-Æther black holes

The study of charged test particle dynamics in the combined black hole gravitational field and magnetic field around it could provide important theoretical insight into astrophysical processes around such compact object. We have explored the orbital and epicyclic motion of charged test particles in the background of non-rotating Einstein-Æther black holes in the presence of external uniform magnetic field. We numerically integrate the equations of motion and analyze the trajectories of the charged test particles. We examined the stability of circular orbits using effective potential technique and study the characteristics of innermost stable circular orbits. We analyze the key features of quasi-harmonic oscillations of charged test particles nearby the stable circular orbits in an equatorial plane of the black hole, and investigate the radial profiles of the frequencies of latitudinal as well as radial harmonic oscillations in dependence on the strength of magnetic field, mass of the black hole and dimensionless coupling constants of the theory. We demonstrate that the magnetic field and dimensionless parameters of the theory have strong influence on charged particle motion around Einstein-Æther black holes.     

Simulations for terrestrial planets formation

In this paper, the formation of terrestrial planets in the late stage of planetary formation is investigated using the two-planet model. At that time, the protostar formed for about 3 Ma and the gas disk dissipated. In the model, the perturbations from Jupiter and Saturn are considered. Variations of the mass of outer planet, and the initial eccentricities and inclinations of embryos and planetesimals are also considered. Our results show that, terrestrial planets are formed in 50 Ma, and the accretion rate is about 60%–80%. In each simulation, 3–4 terrestrial planets are formed inside “Jupiter” with masses of 0.15–3.6 M _⊕. In the 0.5–4 AU, when the eccentricities of planetesimals are excited, planetesimals are able to accrete material from wide radial direction. The plenty of water material of the terrestrial planet in the Habitable Zone may be transferred from the farther places by this mechanism. Accretion could also happen a few times between two major planets only if the outer planet has a moderate mass and the small terrestrial planet could survive at some resonances over time scale of 10⁸ a. In one of our simulations, commensurability of the orbital periods of planets is very common. Moreover, a librating-circulating 3:2 configuration of mean motion resonance is found. Supported by the National Natural Science Foundation of China (Grant Nos. 10573040, 10673006, 10833001, and 10233020) and the Foundation of Minor Planets of Purple Mountain Observatory     

Analysis on motion of Earth’s center of mass observed with CHAMP mission

Geocenter motion (GCM) is one important topic for constructing and maintaining the terrestrial reference frame and its applications. GCM is studied from CHAMP with the multi-step approach in this paper. Geometric orbits of CHAMP in 2001–2006 are precisely determined with the kinematic method only from the satellite-borne GPS zero-difference data. Then a GCM time series is estimated from the precise kinematic orbits based on the theory of satellite dynamics to fit the CHAMP’s real geometric orbits. We compare the series with the geocenter series used in ITRF2005. Then the GCM series are analyzed with Fourier transform and wavelet transformation. The mean motions within 6 years in TX, TY and TZ directions are respectively 0.8 mm, 2.2 mm, and 7.9 mm. The trends of GCM in the three directions are 0.495 mm/a, −0.004 mm/a, and 1.309 mm/a, respectively. The long-term movement (2001–2006) indicates that the crustal figure is changing. The seasonal variations are the main component which may be excitated by the mass redistribution of Earth’s fluid layer, e.g. ocean, atmosphere and continental water. The inter-annual variations are also found in the GCM series measured with CHAMP. Supported by the International S&T Cooperation Program of China (Grant No. 2006DFA21980), the National Hi-tech R&D Program of China (Grant No. 2006AA12z303), the National Natural Science Foundation of China (Grant No. 40774009), and the Natural Science Foundation of Shandong Province, China (Grant No. Y2003E01)     

The two-dimensional,N=2 Wess-Zumino model on a cylinder

We construct a family of supersymmetric, two-dimensional quantum field models. We establish the existence of the HamiltonianH and the superchargeQ as self-adjoint operators. We establish the ultraviolet finiteness of the model, independent of perturbation theory. We develop functional integral representations of the heat kernel which are useful for proving estimates in these models. In a companion paper [1] we establish an index theorem forQ, an infinite dimensional Dirac operator on loop space. This paper and, another related one [2], provide the technical justification for our claim thatQ is Fredholm, and for our computation of its index by a homotopy onto quantum mechanics.Supported in part by the National Science Foundation under Grant DMS/PHY 86-45122Hertz Foundation Graduate Fellow     

On a possible dust-plasma interaction at Mars

According to present theoretical models, material ejected from the Martian satellite Phobos due to meteoroid bombardment and tidal coupling can stay for a long time in circular orbits near the planet, forming a dust belt. The dust particles are moving through various plasma domains of the Martian magnetosphere and may undergo electrostatic disruption there, producing very fine motes in the range 0.005-0.1 μm which can stay positively charged for a time comparable with the orbital period. A negatively charged spacecraft will attract such particles and an ion spectrometer with wide enough mass range (1-10⁸ amu/Q, where Q is the particle charge) may detect these grains. The model can explain observations made by the ASPERA mass spectrometer during the PHOBOS mission when signals in the mass channels 10³-10⁷ amu were detected inside the Martian magnetosphere. The evolution of a grain orbiting Mars is shown in a diagram of the particle size-particle potential. Such a diagram gives a qualitative picture of the grain interaction with the Martian plasma environment     

Annihilation luminosity of a neutrino-cooled accretion disk in a gamma-ray burst

We discuss how the annihilation luminosity of a neutrino-cooled accretion disk in a gamma-ray burst, Lν ν, is determined by the disk’s fundamental parameters, namely, the mass of the central black hole M, the mass accretion rate M, and the viscosity parameter α. It is shown that Lν ν depends mainly on M in evidence, and decreases with increasing M, but is almost independent of α. This result argues additionally that the central black hole in a gamma-ray burst must be with a stellar mass.     

Structure of geodesics in the regular Hayward black hole space-time

The regular Hayward model describes a non-singular black hole space-time. By analyzing the behaviors of effective potential and solving the equation of orbital motion, we investigate the time-like and null geodesics in the regular Hayward black hole space-time. Through detailed analyses of corresponding effective potentials for massive particles and photons, all possible orbits are numerically simulated. The results show that there may exist four orbital types in the time-like geodesics structure: planetary orbits, circular orbits, escape orbits and absorbing orbits. In addition, when \(\ell \), a convenient encoding of the central energy density \(3/8\pi \ell ^{2}\), is 0.6M, and b is 3.9512M as a specific value of angular momentum, escape orbits exist only under \(b>3.9512M\). The precession direction is also associated with values of b. With \(b=3.70M\) the bound orbits shift clockwise but counter-clockwise with \(b=5.00M\) in the regular Hayward black hole space-time. We also find that the structure of null geodesics is simpler than that of time-like geodesics. There only exist three kinds of orbits (unstable circle orbits, escape orbits and absorbing orbits).     

The identification of comets in Chinese historical records

The historical records of astronomical phenomena may play a significant role in comet identification.Getting an accurate result is based on many factors,of which the calculation of orbital elements is the most important.This paper presents a Cross Reference method in which the perturbation of Jupiter is the only considered factor used to attempt an efficient way of comet identification with ancient Chinese historical records.In this method,the records before and after the calculated result from orbital dete...     

Influence of Orbital Motion of Inner Cylinder on Eccentric Taylor Vortex Flow of Newtonian and Power-Law Fluids

The effects of inner cylinder orbital motion on Taylor vortex flow of Newtonian and power-law fluid are studied numerically. The results demonstrate that when the eccentricity is not small, the orbital motion influences the stability of the flow in a non-monotonic manner. The variations of the flow-induced forces on the inner cylinder versus orbital motion are also different from the cases in which the flow is two-dimensional and laminar.