The eccentric frame decomposition of central force fields

The rosette-shaped motion of a particle in a central force field is known to be classically solvable by quadratures. We present a new approach of describing and characterizing such motion based on the eccentricity vector of the two body problem. In general, this vector is not an integral of motion. However, the orbital motion, when viewed from the nonuniformly rotating frame defined by the orientation of the eccentricity vector, can be solved analytically and will either be a closed periodic circulation or libration. The motion with respect to inertial space is then given by integrating the argument of periapsis with respect to time. Finally we will apply the decomposition to a modern central potential, the spherical Hernquist–Newton potential, which models dark matter halos of galaxies with central black holes.     

Standard and Non-Standard Solar Models

We summarize the physical input and assumptions commonly adopted in modern standard solar models that also produce good agreement with solar oscillation frequencies. We discuss two motivations for considering non-standard models: the solar neutrino problem and surface lithium abundance problem. We begin to explore the potential for mixed core models to solve the neutrino problem, and compare the structure, neutrino flux, and oscillation frequency predictions for several models in which the inner 25% of the radius is homogenized, taking into account the effects of non-local equilibrium abundances of ³He. The results for the neutrino flux and helioseismic predictions are far from satisfactory, but such models have the potential to reduce the predicted ⁷Be/⁸B neutrino flux ratio, and further studies are warranted. Finally, we discuss how much the neutrino problem can be alleviated in the framework of the standard solar model by using reaction rates, abundances and neutrino capture cross-sections at the limits of their uncertainties, while still satisfying the constraints of helioseismology.     

50 m 射电望远镜的时间标准问题的讨论

定量分析了原子钟的时间频率特性产生的守时时差,估算了原子时频标准的守时时差对有关物理量测量所产生的影响．给出了现代实用型原子钟的性能指标比较表,和用现代无线电手段传递、比对时频标准信号达到的指标．论述了高精度时间频率标准在大地、深空间探测、VLBI及毫秒脉冲星计时应用测量中的重要地位、作用．阐述了50 m射电望远镜的科学目标、“嫦娥”1号探月卫星任务对时间标准提出的高精度要求和选用原则．为了实现其科学目标和任务,必须建设与其研究目标相适宜的、标准尽可能高的原子时频标准,才能获得高质量的数据信息和高效能的研究成果．并对建设怎样的时间标准等问题进行讨论和提出具体建议．     

Nonlinear diffuse reflection and transmission of radiative energy by a layer of finite thickness

The major results for the linear problem of diffuse reflection and transmission of radiation by a layer of finite thickness are carried over to the nonlinear case by successive application of Ambartsumyan’s approach for a one dimensional anisotropic medium. Formulas are given for nonlinear addition of layers which can be used to construct recurrence calculation procedures for uniform, periodic, and arbitrary stratified media. A complete set of differential equations for invariant imbedding is derived with the aid of these formulas. These equations are used to obtain a system of total invariance equations, which, in turn, offer the possibility of reducing the nonlinear problem of diffuse reflection and transmission during irradiation of a layer from both sides to the simpler problem of illuminating this medium from only one side, with the thickness of the layer remaining only as a fixed parameter. Finally, it is shown that the results obtained for the single frequency case (two-level atom) remain valid in the polychromatic case (multilevel atom), which is important for interpreting astrophysical data.     

Artificial satellites and the three-body problem: A general case

The three-body problem is the most celebrated problem of classical celestial mechanics that is not soluble in finite terms by means of any of the functions at present known to mathematical analysis.In the modern celestial mechanics is known as the main problem of the theory of the satellites and it too is not soluble in finite terms.The low-altitude satellites, which move along close orbits, are encountered. They may be done case in which the centers of masses of the bodies form an isosceles or nearly equilaterial triangle with the center of the oblate planet, and another one in which they are always located in the straight line.We study the planar problem, in which the satellites move along close orbits in a plane which forms an angle with the equatorial plane of the planet; the oblateness of which exercises a great effect. The practical importance of this problem arises from its applications.Differential equations of motion are given and particular solutions are shown to exist when the centers of masses are at the vertices of a nearly equilateral triangle or are collinear. Of course, if we take the first two terms of the Legendre series with =0, we shall obtain the same results as Aksenov (1988).     

CCD star images: On the determination of Moffat’s PSF shape parameters

Among the variety of empirical models of optical Point Spread Function used in the astronomical environment, only the Moffat’s (1969) one is able to describe by means of two parameters (in the circular case) both the inner and the outer star image regions. In view of this very important feature, the problem of the simultaneous estimates of Moffat’s PSF shape parameters, off-centring, and the background level in CCD star images has been investigated. The problem does not seem to be rigorously resolvable, but an approximate way to calculate all the parameters except off-centring is shown. It must be stressed that, the Moffat’s PSF model being a softened power law belonging to the family of modified King and Hubble models, the present discussion can be of aid in many other research fields. Also, the integral equation enabling us to convolve a spherical source with Moffat’s PSF is given and applied for comparison to Multi-Gaussian convolution.     

Horizon synthesis for archaeo‐astronomical purposes

In this paper I describe a simple numerical procedure to compute synthetic horizon altitude profiles for any given site. The method makes use of a simplified model of local Earth's curvature, and it is based on the availability of digital elevation models describing the topography of the area surrounding the site under study. Examples constructed using the Shuttle Radar Topographic Mission (SRTM) data (with 90 m horizontal resolution) are illustrated, and compared to direct theodolite measurements. The proposed method appears to be reliable and applicable in all cases when the distance to the local horizon is larger than ∼10 km, yielding a rms accuracy of ∼0.1 degrees (both in azimuth and elevation). Higher accuracies can be achieved with higher resolution digital elevation models, like those produced by many modern national geodetic surveys (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Astronomical Data Archives and the Next Ground Based Telescopes

Next generation telescopes will be all digital instruments. This fact will allow the full integration of archives into telescopes operation. This is a main step if one wants to fulfill the requirement of usefulness of both scientific and technical data contained in the archives. A great change with respect to the past is required involving the modes of scheduling, observing, calibrating etc. New models of approaching the whole scientific data flow starting from the archiving problem are studied in several Institutions. These new models of observation, whose consequences in terms of human factor seem to be as important as the technological implications, promise to ensure a high and constant quality level of the data to be archived. The current status of this topic is reviewed. Some thoughts on the data model presently used in astronomy are also briefly given.     

The radiation force on small particles

A more complete expression for the radiation force on a small particle in the solar system is given which includes the effect of asymmetry of the thermal reradiation and also of inelastic scattering such as fluorescence. Both the Poynting-Robertson drag and the Yarkovsky effect are affected by such asymmetries and are incorporated into the formalism. For non-spherical particles the direction of the radiation force will no longer coincide with the solar irradiation.     

Robe's restricted three-body problem revisited

Robe's restricted three-body problem is reanalyzed with a view to incorporate a new assumption, namely that the configuration of the fluid body is that described by an hydrostatic equilibrium figure (Roche's ellipsoid). In the concomitant gravitational field a full treatment of the buoyancy force is given. The pertinent equations of motion are derived, the linear stability of the equilibrium solution is studied and the connection between the effect of the buoyancy forces and a perturbation of the Coriolis force is pointed out.     

A statistical comparison of Antarctic finds and modern falls: Mass frequency distributions and relative abundance by type

Abstract— The relative abundance of different compositional types and mass frequency distributions are presented for four meteorite samples (the modern falls, Antarctic finds, Yamato finds and Allan Hills Main Icefield finds). The modern falls sample represents continuous collection of a known number of falls over a short timespan, while the Antarctic samples represent a longer timespan and an unknown number of falls. The Allan Hills Main Icefield sample has many desirable collection characteristics indicating it best represents Antarctic meteorites. By retabulating the modern falls to create a sample with characteristics similar to those of the Allan Hills Main Icefield finds, we can directly compare the two. The mass frequency distributions of Antarctic samples exhibit a tail toward the larger sizes and thus differ from that of the modern falls (which approximates a normal curve). In general, normal and power law models prove to be inadequate to explain the observed mass frequency distributions, possibly because they fail to correctly account for atmospheric and collection effects. Non-parametric statistics show that it is unlikely that the two are good samples of a single steady-state meteoritic complex. In addition, there is an excess in numbers of small H chondrites in Allan Hills Main Icefield finds relative to modern falls which is not easy to explain given modern showerfall rates of occurrence. This supports the view that the delivery of meteoritic material to Earth might be variable over the short timescale represented by these samples.     

The Ashima/MIT Mars GCM and argon in the martian atmosphere

We investigate the ability of modern general circulation models (GCMs) to simulate transport in the martian atmosphere using measurements of argon as a proxy for the transport processes. Argon provides the simplest measure of transport as it is a noble gas with no sinks or sources on seasonal timescales. Variations in argon result solely from ‘freeze distillation’, as the atmosphere condenses at the winter poles, and from atmospheric transport. Comparison of all previously published models when rescaled to a common definition of the argon enhancement factor (EF) suggest that models generally do a poor job in predicting the peak enhancement in southern winter over the winter pole – the time when the capability of the model transport approaches are most severely tested. Despite observed peak EF values of ～6, previously published model predictions peaked at EF values of only 2–3. We introduce a new GCM that provides a better treatment of mass conservation within the dynamical core, includes more sophisticated tracer transport approaches, and utilizes a cube–sphere grid structure thus avoiding the grid-point convergence problem at the pole that exists for most current Mars GCMs. We describe this model – the Ashima Research/Massachusetts Institute of Technology Mars General Circulation Model (Ashima/MIT Mars GCM) and use it to demonstrate the significant sensitivity of peak EF to the choices of transport approach for both tracers and heat. We obtain a peak EF of 4.75 which, while over 50% higher than any prior model, remains well short of the observed value. We show that the polar EF value in winter is primarily determined by the competition between two processes: (1) mean meridional import of lower-latitude air not enriched in argon and (2) the leakage of enriched argon out of the polar column by eddies in the lowest atmospheric levels. We suggest possibilities for improving GCM representation of the CO₂ cycle and the general circulation that may further improve the simulation of the argon cycle. We conclude that current GCMs may be insufficient for detailed simulation of transport-sensitive problems like the water cycle and potentially also the dust cycle.     

An analysis of the radial velocity curves of close binary systems,I

The aim of the present paper will be to develop a theory of the radial-velocity changes of the components of close binary systems, with special attention to phenomena arising from finite dimensions of such components and their mutual distortion as well as irradiation. It is particularly stressed that the deformability of fluid stars and gas motions in their atmospheres can give rise to systematic differences between the observed radial velocities of such stars and those of their mass centres.In Section 2 (which follows a brief statement of the problem outlined in Section 1) we shall introduce the coordinate systems subsequently employed to treat various aspects of our problem: Section 3 will be concerned with an extraction of information from the radial-velocity component of absolute motions of the mass-centres of such stars; and in Section 4 we shall generalize the classical work by an investigation of radial velocities at any point of the apparent disks of distorted components, and their relation to the motion of their centres of mass. Section 5 will contain an evaluation of the effects of distortion, on radial velocity, averaged over the entire visible disk of the respective star at different phases; and in Section 6 we shall extend the same treatment to stars undergoing eclipses.An investigation of the effects, on the observed radial velocities, of atmospheric streaming caused by mutual irradiation of the two stars is being postponed for a subsequent communication.     

On magnetostatic equilibrium in a stratified atmosphere

This is a study of the relationship between a magnetic field and its embedding plasma in static equilibrium in a uniform gravity. The ideal gas law is assumed. A system invariant in a given direction is treated first. We show that an exact integral of the equation for force balance across field lines can be derived in a closed form. Using this integral, exact solutions can be generated freely by integrating directly for the distributions of pressure, density and temperature necessary to keep a given magnetic field in equilibrium. Particular solutions are presented for illustration with the solar atmosphere in mind. Extending the treatment to the general system depending on all three spatial coordinates, we arrive at the general form of a theorem of Parker that a magnetic field in static equilibrium must possess certain symmetries. We derive an equation involving the Euler potentials of the magnetic field stipulating these necessary symmetries. Only those magnetic fields satisfying this equation can be in static equilibrium and for these fields, the endowed symmetries make the construction of exact solutions an essentially two dimensional problem as exemplified by the special case of invariance in a given direction.     

Stability of particle orbits

The correspondence between the stability of particle orbits in synchrotrons and storage rings and the standard maps of modern nonlinear dynamics is discussed. The problem is exposed in the language of particle accelerator physics. Examples are given how the equations for synchrotron and betatron oscillations can be brought into the form of standard maps.     

Heavy-element abundances from a neutron burst that produces Xe-H

Abstract— We examine quantitatively the suggestion that the heavy anomalous isotopes of Xe-HL found in meteoritic diamonds were produced by a short intense neutron burst and then implanted into the diamonds. Using a large nuclear reaction network we establish one (out of many) neutron irradiation histories that successfully reproduces the heavy isotopes of Xe-HL, and then evaluate what that same history would produce in every heavy element. This has become more relevant following recent measurement of anomalous Ba and Sr in those same diamond samples. Therefore we offer these calculations as a guide to the anomalies to be expected in all elements if this scenario is correct. We also discuss several other aspects of the problem, especially the established contradictions for Ba, the observed Kr pattern, the near normalcy of ¹²⁹Xe, and some related astrophysical ideas. In particular we argue from p-process theory that the observed deficit of ⁷⁸Kr in correlation with ^124–126Xe excess implicates Type II supernovae as the diamond sources. However, our more complete astrophysical conclusions will be published elsewhere. This present work is offered as computational expectation for this class of models and as a guide to considerations that may accelerate the digestion of new experimental results in the diamonds.     

Spectra of radioactivity induced in caesium iodide scintillator crystals by 155 MeV protons

Previous work has shown the importance of induced radioactivity as a source of background counts in X- and -ray astronomy experiments which use scintillation detectors. Comprehensive data on the decay spectra observed in Caesium Iodide crystals following irradiation by 155 MeV protons has been obtained by the Imperial College group and is presented here. The spectra cover the energy loss range from 20 keV to 3.4 MeV and were collected at times after irradiation ranging from 1 min until 200 d. A sufficient selection of spectra is given to enable calculations to be made of the time variations in radioactivity which would be observed in similar space-borne detectors subjected to irradiation by inner belt and cosmic ray protons. Examples of such calculations are given.     

On the non-adiabatic particle scattering in the earth''s magnetotail current sheet

The empirical model of disturbed magnetosphere of Tsyganenko and Usmanov (1982) and the semi-empirical model of the storm-time magnetospheric configuration of Tsyganenko (1981) are used to find the critical energy for non-adiabatic particle scattering in the midnight sector. Computed values of E_crit vs L are compared with the appropriate experimental data of Imhof et al. (1977). It is found that none of the considered models is able to reproduce the observed steep decrease of E_crit with L. The steepest slope is given by the Tsyganenko model which includes a current sheet with the finite thickness. The current sheet thickness is a crucial parameter in the non-adiabatic scattering problem. In discussion we point to natural limitations of an empirical model as far as the current sheet thickness is to be determined. Imhof et al.'s data as well as some magnetic field data sets seem to indicate that magnetosphere models incorporating a thin current sheet and allowing for the thickness dependence on the geocentric distance would probably be closer to reality than the considered models, at least during higher levels of magnetic activity.     

Least squares parameter estimation in chaotic differential equations

A recent least squares algorithm, which is designed to adapt implicit models to given sets of data, especially models given by differential equations or dynamical systems, is reviewed and used to fit the Hénon-Heiles differential equations to chaotic data sets.This numerical approach for estimating parameters in differential equation models, called theboundary value problem approach, is based on discretizing the differential equations like a boundary value problem,e.g. by a multiple shooting or collocation method, and solving the resulting constrained least squares problem with a structure exploiting generalized Gauss-Newton-Method (Bock, 1981).Dynamical systems like the Hénon-Heiles system which can have initial values and parameters that lead to positive Lyapunov exponents or phase space filling Poincaré maps give rise to chaotic time series. Various scenarios representing ideal and noisy data generated from the Hénon-Heiles system in the chaotic region are analyzedw.r.t. initial conditions, parameters and Lyapunov exponents. The original initial conditions and parameters are recovered with a given accuracy. The Lyapunov spectrum is then computed directly from the identified differential equations and compared to the spectrum of the true dynamics.presently at IWR, Universität Heidelberg, Im Neuenheimer Feld 368, D-6900 Heidelberg, Germany