Inverse problem with two-parametric families of planar orbits

As a possible extension of recent work we study the following version of the inverse problem in dynamics: Given a two-parametric familyf(x, y, b)=c of plane curves, find an autonomous dynamical system for which these curves are orbits.We derive a new linear partial differential equation of the first order for the force componentsX(x, y) andY(x, y) corresponding to the given family. With the aid of this equation we find that, depending on the given functionf, the problem may or may not have a solution. Based on given criteria, we present a full classification of the various cases which may arise.     

Exact Brans-Dicke-Bianchi type-VIIh solutions

We discuss the Brans-Dicke-Bianchi type-VII_h field equations. Exact solutions are given for the vacuum case as well as for the stiff matter case. The derived solutions are the generalizations of the GRT-solutions first given by Doroshkevichet al. (1973) and Lukash (1974a). In addition we present a new BDT-stiff matter solution which has no analogy in the GRT.     

On the detectability of distant clusters of galaxies

J-magnitude limits (KRON'S J) which have to be reached to detect a cluster of galaxies of given redshift (up to z ≊ 1) and richness class against the background of field galaxies are given.     

On the potential–density relation for Stäckel discs

The general form of the surface density of an infinitely thin disc is given that generates a Sta¨ckel potential in the disc only, using formulae for the potential of elliptic and hyperbolic strings. This is useful for problems in which a simple form for the potential is important, while the corresponding surface density need only be known to check (numerically) that it is positive. A simple potential with a positive surface density is given. Also, formulae are given to calculate the surface density of such a Sta¨ckel disc, in the case in which the rotation curve is given and all the mass is concentrated in the disc.     

Period study of IT Persei

A new period (P=1 _. ^d 533731) of the eclipsing binary system IT Persei has been given, which is based on all available times of minima. O-C diagrams of IT Persei, based on the period given in PPEN (1980) and based on the new period, have been given.Long-term period changes are not present in the system, however, some period fluctuations of the order of 10^–5d are seen around the years 1907, 1921, and 1933.     

基于历史TLE的空间目标轨道预报误差演化规律研究

北美防空司令部(North American Aerospace Defense Command, NORAD)发布的双行根数(Two Line Element, TLE)是广大航天工作者最常用的轨道根数,与其对应的轨道模型是SGP4/SDP4 (Simplified General Perturbation Version 4/Simplified Deep-space Perturbation Version 4)解析模型.由于TLE中并没有包含相应的轨道精度信息,编目轨道的应用范围受到很大的限制.基于Space-Track网站发布的历史TLE数据和配套的SGP4/SDP4动力学模型,采用定轨标预报的方法统计并生成了大量目标轨道的预报误差,通过对预报轨道的时间区间划分给出了每个目标的预报误差随预报时间变化的拟合系数,并进一步对不同类型轨道预报误差的演化规律和特征进行了分类讨论,给出了4种轨道类型目标的轨道预报误差随时间演化的平均解析模型,为拓展双行根数的应用提供有价值的参考.     

A unified presentation of the Voigt functions

In the present paper, we have given a generalization of a unified study of the Voigt functionsK(x, y) andL(x, y) obtained by Srivastava and Miller (1987; Vol. 135, pp. 111–118) which play an important role in several diverse fields of physics-such as astrophysical spectroscopy and the theory of neutron reactions. Explicit expressions for these functions are given in terms of relatively more familiar special functions of one and two variables; indeed, each of these representations will naturally lead to various other needed properties of the Voigt functions.     

Radio emission of fast cosmic ions

It is usually assumed that the ions of cosmic rays contribute nothing to the observable electromagnetic radiation. However, this is true only when these ions are moving in a vacuum or a quiet (nonturbulent) plasma. In the case of fast ions in a turbulent plasma, there is an effective nonlinear mechanism of radiation which is discussed in this paper. The fast ion (relativistic or nonrelativistic) moving in the plasma creates a polarization cloud around itself which also moves with the particles. The turbulent plasma waves may scatter on the moving electric field of this polarization cloud. In the process of this scattering an electromagnetic wave with frequency (2.7) is generated. Let ₁ and k₁ be the frequency and wave vector of turbulent plasma waves,V is the velocity of the ion, and is the angle between the wave vector of electromagnetic radiation and the direction of the ion velocity. The method of calculating the probability of the conversion of plasma waves (k₁) into electromagnetic waves (k) by scattering on an ion with velocityV is described in detal in Section 2 (Equation (2.14)).The spectral coefficients of spontaneous radiation in the case of scattering of plasma waves on polarization clouds created by fast nonrelativistic ions are given in (3.6) for an ion energy distribution function (3.4) and in (3.8) for more general evaluations. The Equations (3.9)–(3.13) describe the spectral coefficients of spontaneous emission for different modes of plasma turbulence (Langmuir (3.9), electron cyclotron in a weak (3.10) or strong (3.11) magnetic field and ion acoustic (3.12)–(3.13) waves). The coefficients of reabsorption or induced emission are given by Equations (3.14) and (3.16)–(3.19). There is a maser effect in the case of scattering of plasma waves on a stream of ions. The effective temperature of the spontaneous emission is given by Equation (3.15). The spectral coefficients of radiation due to scattering of plasma waves on relativistic ions are calculated in the same manner (Equations (4.14)–(4.15)). The total energy loss due to this radiation is given in Equations (4.23)–(4.25). The coefficients of induced emission are given in (4.26)–(4.28).The results are discussed in Section 5. It is shown that the loss of energy by nonlinear plasma radiation is much smaller than the ionization loss. However, the coefficients of synchrotron radiation of electrons and nonlinear radiation of ions under cosmic conditions may be comparable in the case of a weak magnetic field and fairly low frequencies (5.5)–(5.6). Usually the spectrum of nonlinear plasma radiation is steeper than in the case of synchroton radiation. Equation (5.10) gives the condition for nonlinear radiation to prevail over thermal radiation.Translated by D. F. Smith.     

Rotation axes of asteroids: Results for 14 objects

In this paper results of determinations of the rotation axis direction (as given by ecliptic coordinates of its intersection with geocentric celestial sphere) for 14 asteroids are presented for which a sufficient number of good observations are available. The calculation is performed by using the improved amplitude-magnitude method developed by V. Zappalà, M. Di Martino, P. Farinella, and P. Paolicchi (1983, In Asteroids, Comets, Meteors, pp. 73–76). Additionally, an improvement of the method is described regarding a weighting procedure. Whenever possible, the results are compared with already existing data, coming from other methods (mainly from photometric astrometry). In general, very good agreement was found, which can be considered as strongly encouraging for further application of the adopted procedure. Some preliminary approaches for a statistical investigation are given.     

Radial,transverse and normal satellite position perturbations due to the geopotential

Perturbations in the position of a satellite due to the Earth's gravitational effects are presented. The perturbations are given in the radial, transverse (or alongtrack) and normal (or cross-track) components. The solution is obtained by projecting the Kepler element perturbations obtained by Kaula [Kaula, 1966] into each of the three components. The resulting perturbations are presented in a form analogous to the form of Kaula's solution which facilitates implementation and interpretation.     

Perturbation theory for stellar interior problems

A rather general first order linearized perturbation theory is derived with which one can calculate a quasi-static equilibrium stellar interior model if given an initial approximation thereto. The process developed is applicable to both static and evolutionary models, wherein slightly different physical assumptions (e.g. gas characteristics) or physical conditions (e.g. matter composition) are imposed. The correction to the given model is obtained through bi-directional quadrature with fitting at an intermediate position; however, no trial integrations are necessary.     

The significance of electrostatic accretion forces between dust grains

A brief review of electrostatic image forces between dust grains is given. Some comments are then made as to where these forces are significant and where they are not significant. Their significant roles are: (i) in aiding accretion where there is amixed population of charged and uncharged grains; (ii) in providing a fractionation mechanism for metals and silicates where all the grains are charged with thesame sign; (iii) in assuring that two grains which come into contact stick to each other. Some shortcomings in recent articles are pointed out.     

Period changes in EI Cephei

A new period (P=8^d.439422) of the eclipsing binary system EI Cephei has been given, which is based on all available times of minima. Periods using Strohmeier's (1958) epoch have also been presented for the observations given by other investigators. Period based on only photoelectric minima comes out to be 8^d.439336, which is lesser than the earlier periods given in the literature. O-C diagrams of EI Cephei have been presented for the first time, and period variations have been estimated in different portions of the O-C diagram (Figure 2) of EI Cephei. Strong period changes have occurred around the years 1959 and 1965. The total change in period (P/P) ranges from 6.7×10^–5 to 4.3×10^–4. Thus, P of the order of 10^–3 d are present, which fact suggests that strong period variations are present in EI Cephei. However, periods given by various investigators show no systematic trend of period variations. The existence of a third body in the system could not be confirmed.     

Effects On the Nutation of the Non-Zonal Harmonics of Third Degree

In this paper, we calculate the coefficients of the nutation for a rigid Earth model due to the C _3m and S _3m (m ≠ 0) harmonics of the geopotential, starting from the Hamiltonian theory as developped by Kinoshita (1977). We show that these coefficients are far from being negligible as given the level of truncation of 0.1 μas which is necessary in the reconstruction of the tables of nutation, and also that their value is very close to that given by Bretagnon et al. (1997). This revised version was published online in July 2006 with corrections to the Cover Date.     

Zur Metallhäufigkeit in offenen Sternhaufen

The noteworthy deviations and differences given in the individual values of the metal abundance of open clusters were studied. It could be shown that the metal abundance of open clusters, which are situated in or near the galactic plane (|z| ≦ 0.3 Kpc) are not only correlated wiht the galactocentric distance (RGC ) but also with the galactic longitude l of the clusters. This correlation is not given in the open clusters of high |z|-distances. There, the metal abundance is connected as well with the galactocentric radius (RGC ) as with the distances of the objects form the galactic plane.     

Numerical methods of star formation history measurement and applications to seven dwarf spheroidals

A comprehensive study of the measurement of star formation histories from colour–magnitude diagrams (CMDs) is presented, with an emphasis on a variety of subtle issues involved in the generation of model CMDs and maximum likelihood solution. Among these are the need for a complete sampling of the synthetic CMD, the use of proper statistics for dealing with Poisson-distributed data (and a demonstration of why χ ² must not be used), measuring full uncertainties in all reported parameters, quantifying the goodness-of-fit, and questions of binning the CMD and incorporating outside information. Several example star formation history measurements are given. Two examples involve synthetic data, in which the input and recovered parameters can be compared to locate possible flaws in the methodology (none were apparent) and measure the accuracy with which ages, metallicities and star formation rates can be recovered. Solutions of the histories of seven Galactic dwarf spheroidal companions (Carina, Draco, Leo I, Leo II, Sagittarius, Sculptor and Ursa Minor) illustrate the ability to measure star formation histories given a variety of conditions – numbers of stars, complexity of star formation history and amount of foreground contamination. Significant measurements of ancient >8 Gyr star formation are made in all seven galaxies. Sculptor, Draco and Ursa Minor appear entirely ancient, while the other systems show varying amounts of younger stars.     

Necessary condition for the existence of algebraic first integrals

Existence of algebraic first integrals for a class of dynamical systems is discussed in connection with the nature of the singularities of solutions. It is shown that under some conditions, the existence of algebraic first integrals controls a quantity characterising a singularity (Kowalevski's exponent) which can be calculated in a finite procedure. Two simple examples are given, which illustrate how main theorems work.     

The magneto-optical filter

In this paper we describe a filter which utilizes magneto-optical effects for velocity fields measurements. The working principle of the instrument is described and its transmission profiles are given. Velocitygrams are shown of the five minutes oscillations (FMO) and the results compared with the expected (theoretical) signal from the instrument. We found a V _rms of 400 m s^–1 for the FMO.     

A unified presentation of the Voigt functions

This paper aims at presenting a unified study of the Voigt functionsK(x,y) andL(x,y) which play a rather important role in several diverse fields of physics such as astrophysical spectroscopy and the theory of neutron reactions. Explicit expressions for these functions are given in terms of relatively more familiar special functions of one and two variables; indeed, each of these representations will naturally lead to various other needed properties of the Voigt functions.