Using the quasar VLBI network for the fundamental time—positioning service of the GLONASS space system

Regular high-precision determinations of the Earth’s orientation parameters (EOPs) on the Quasar VLBI Network were begun in August 2006. The observations are performed within the framework of two national programs: daily sessions at three observatories of the Network to determine all five EOPs (the RU-E program) and 8-h sessions on the Zelenchukskaya-Badary and Svetloe-Badary baselines to determine the Universal Time (the RU-U program). The observations from August 2006 through May 2007 are analyzed. The rms deviations of the EOP values obtained in the RU-E program from the IERS C04 series are 1.1 mas for X _p and Y _p, 37 μs for UT1-UTC, and 0.7 and 0.6 mas for X _c and Y _c, respectively. These results closely match the prospective requirements of GLONASS. The rms deviations of the Universal Times obtained in the RU-U program from the IERS C04 series are 146 μs. We consider the immediate prospects for improving the accuracy of EOP determinations in daily sessions and for implementing the e-VLBI mode for an online determination of the Universal Time. Original Russian Text ? A.M. Finkelstein, E.A. Skurikhina, I.F. Surkis, A.V. Ipatov, I.A. Rakhimov, S.G. Smolentsev, 2008, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2008, Vol. 34, No. 1, pp. 66–76.     

Multiple solutions in preliminary orbit determination from three observations

Charlier’s theory (1910) provides a geometric interpretation of the occurrence of multiple solutions in Laplace’s method of preliminary orbit determination, assuming geocentric observations. We introduce a generalization of this theory allowing to take into account topocentric observations, that is observations made from the surface of the rotating Earth. The generalized theory works for both Laplace’s and Gauss’ methods. We also provide a geometric definition of a curve that generalizes Charlier’s limiting curve, separating regions with a different number of solutions. The results are generically different from Charlier’s: they may change according to the value of a parameter that depends on the observations.     

Baily’s Beads Atlas in 2005 – 2008 Eclipses

In the annular or total eclipses of 3 October 2005, 29 March 2006, 22 September 2006, and 1 August 2008, observational campaigns were organized to record the phenomenon of Baily’s beads. These campaigns were internationally coordinated through the International Occultation Timing Association (IOTA) at both its American and European sections. From the stations in the northern and southern zones of grazing eclipse, the eclipses have been recorded on video. Afterward, as many beads as possible have been identified by analyzing the video data of each observing station. The atlas presented in this paper includes 598 data points, obtained by 23 observers operating at 28 different observing stations. The atlas lists the geographic positions of the observing stations and the observed time instants of disappearance or reappearance of beads, identified by an angle measured relative to the Moon’s axis of rotation. The atlas will serve as a basis for determining the solar diameter. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

A method for averaging the perturbing function in Hill’s problem

A modified method for averaging the perturbing function in Hill’s problem is suggested. The averaging is performed in the revolution period of the satellite over the mean anomaly of its motion with a full allowance for a variation in the position of the perturbing body. At its fixed position, the semimajor axis of the satellite orbit during the revolution of the satellite is constant in view of the evolution equations, while the remaining orbital elements undergo secular and long-period perturbations. Therefore, when the motion of the perturbing body is taken into account, the semimajor axis of the satellite orbit undergoes the strongest perturbations. The suggested approach generalizes the averaging method in which only the linear (in time) term is included in the perturbing function. This method requires no expansion in powers of time. The described method is illustrated by calculating the perturbations of the semimajor axes for two distant satellites of Saturn, S/2000 S 1 and S/2000 S5. An approximate analytic solution is compared with the results of numerical integration of the averaged system of equations of motion for these satellites.     

Irregular Satellites of Jupiter: a study of the capture direction

The irregular satellites of Jupiter are believed to be captured asteroids or planetesimals. In the present work is studied the direction of capture of these objects as a function of their orbital inclination. We performed numerical simulations of the restricted three-body problem, Sun-Jupiter-particle, taking into account the growth of Jupiter. The integration was made backward in time. Initially, the particles have orbits as satellites of Jupiter, which has its present mass. Then, the system evolved with Jupiter losing mass and the satellites escaping from the planet. The reverse of the escape direction corresponds to the capture direction. The results show that the Lagrangian points L1 and L2 mainly guide the direction of capture. Prograde satellites are captured through these two gates with very narrow amplitude angles. In the case of retrograde satellites, these two gates are wider. The capture region increases as the orbital inclination increases. In the case of planar retrograde satellites the directions of capture cover the whole 360° around Jupiter. We also verified that prograde satellites are captured earlier in actual time than retrograde ones. This paper was presented at the Asteriods, Comets and Meteors meeting held at Búzios, Rio de Janeiro, Brazil in August 2005 and could not be included in the special issue related to that conference.     

Ion acceleration and Alfvén wave generation at the Earth’s bow shock

The processes of ion acceleration and Alfvén wave generation by accelerated particles at the Earth’s bow shock are studied within a quasi-linear approach. Steady-state ion and wave spectra are shown to be established in a time of 0.3–4 h, depending on the background level of Alfvénic turbulence in the solar wind. The Alfvén waves produced by accelerated ions are confined within the frequency range 10^?2–1 Hz and their spectral peak with a wave amplitude βB ～ B comparable to the interplanetary magnetic field strength B corresponds to the frequency v = (2–3) × 10^?2 Hz. The high-frequency part of the wave spectrum (v > 0.2 Hz) undergoes damping by thermal ions. The calculated spectra of the accelerated ions and the Alfvén waves generated by them reproduce the main features observed in experiments.     

Celestial-mechanical peculiarities of Uranus’s satellite system

We consider the structural peculiarities of Uranus’s satellite system associated with its separation into two groups: inner equatorial satellites moving in nearly circular orbits and distant irregular satellites with retrograde motion in highly elliptical orbits. The intermediate region is free from satellites in a wide range of semimajor axes. By analyzing the evolution of satellite orbits under the combined effect of solar attraction and Uranus’s oblateness, we offer a celestial-mechanical explanation for the absence of equatorial satellites in this region. M.L. Lidov’s studies during 1961–1963 have served as a basis for our analysis.     

Orbital evolution of Uranus’s new outer satellites

Data on three recently discovered satellites of Uranus are used to determine basic evolutional parameters of their orbits: the extreme eccentricities and inclinations, as well as the circulation periods of the pericenter arguments and of the longitudes of the ascending nodes. The evolution is mainly investigated by analytically solving Hill’s double-averaged problem for the Uranus-Sun-satellite system, in which Uranus’s orbital eccentricity e _U and inclination i _U to the ecliptic are assumed to be zero. For the real model of Uranus’s evolving orbit with e _U≠0 and i _U≠0, we refine the evolutional parameters of the satellite orbits by numerically integrating the averaged system. Having analyzed the configuration and dynamics of the orbits of Uranus’s five outer satellites, we have revealed the possibility of their mutual crossings and obtained approximate temporal estimates.     

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INFLUENCE OF SERIES OF SQUARE GRIDS ON FRACTAL DIMENSIONS—A Case Study of Mountains of China＇s Mainland

MANDELBROT enunciated the uncertainty of the length of a coastline in his paper “How long is the coastline of Britain?” published in Science in 1967. The fractal concept was presented for the first time in that paper and has been applied to many fields ever since. Although fractal dimensions of lots of phenomena were calculated by the box-counting method, the quantitative influence of series of square grids on them is ignored. The issue is systematically discussed as a case study of the mountains of China‘s Mainland in this paper. And some significant conclusions are drawn as follows: 1) Although the fractal character objectively exists in the mountains of China‘s Mainland, and it does not vary with the changes of series of square grids, the fractal dimensions of the mountains of China‘s Mainland are different with these changes. 2) The fractal dimensions of the mountains of China‘s Mainlandvary with the average lengths of sides of series of square grids. The fractal dimension of the mountains of China‘s Mainland is the function of the average length of side of square grid. They conform to the formula D=f(r) (where D is the fractal dimension, and r is the average length of side of square grid). 3) Different dots of data collection can affect the fractal dimension of the mountains of China‘s Mainland. 4) The same range of length of side of square grid and dots of data collection can ensure the comparison of fractal dimensions of the mountains of China‘ s Mainland. The research is helpful to get the more understanding of fractal and fractal dimension, and ensure that the fractal studies would be scientific.