Behaviour of the SMF method for the numerical integration of satellite orbits

The SMF algorithms were recently developed by the authors as a multistep generalization of the ScheifeleG-functions one-step method. Like the last, the proposed codes integrate harmonic oscillations without truncation error and the perturbing parameter appears as a factor of that error when integrating perturbed oscillations. Therefore they seemed to be convenient for the accurate integration of orbital problems after the application of linearizing transformations, such as KS or BF. In this paper we present several numerical experiments concerning the propagation of Earth satellite orbits, that illustrate the performance of the the SMF method. In general, it provides greater accuracy than the usual standard algorithms for similar computational cost.     

Long-Term Photometry of RT Lacertae: 1. Light and Colour Variation

The peculiar chromospherically active binary system RT Lac was observed in B and V bands between 1989 and 1992. The four-year photoelectric B and V light curves are presented. The light and colour variations in the four special regions of the light curve between 1978 and 1992 are discussed. The available photometry obtained by the present authors defines at least three consecutive maxima in the variation of the brightness of the system at second maximum and in mid-primary eclipse. The behaviour of the light and colour changes in mid-primary and at second maximum harmonizes with the common property of the RS CVn-type binaries. However, the light changes at first maximum do not resemble either at second maximum or in mid-primary minimum. Therefore, we conclude that the observed features cannot be attributed to the spottedness of the more massive component alone. The signs of the starspots are masked by the matter in front of the more massive component at the first maximum. The present data indicate that the magnetic cycle in RT Lac is about 12 years, which is analogous to the Sun's 11-year sunspot cycle.     

Comments on the Magnetic Alternative to Missing Mass

The arguments against the magnetic alternative given by Katz (1994) are discussed. Our conclusion is that the major problem regarding this alternative to dark matter is the flaring of the disk as suggested by Cuddeford and Binney (1993). We propose that the study of the equilibrium in the vertical direction should be carried out in dwarf spirals. Magnetic tension could alter the rotation curve of spiral galaxies but is not able to eliminate the necessity of dark matter. This revised version was published online in July 2006 with corrections to the Cover Date.     

Book Review : Global Change and History of Geophysics. Edited by W. Schröder and M. Colacino. Interdivisional Commission on History of IAGA and History Commission of the German Geophysical Society,Bremen - Roennebeck 1996, 293 pp.

Studia Geophysica et Geodaetica -     

On The Origin of The High-Perihelion Scattered Disk: The Role of The Kozai Mechanism And Mean Motion Resonances

We study the transfer process from the scattered disk (SD) to the high-perihelion scattered disk (HPSD) (defined as the population with perihelion distances q > 40 AU and semimajor axes a>50 AU) by means of two different models. One model (Model 1) assumes that SD objects (SDOs) were formed closer to the Sun and driven outwards by resonant coupling with the accreting Neptune during the stage of outward migration (Gomes 2003b, Earth, Moon, Planets 92, 29–42.). The other model (Model 2) considers the observed population of SDOs plus clones that try to compensate for observational discovery bias (Fernández et al. 2004, Icarus , in press). We find that the Kozai mechanism (coupling between the argument of perihelion, eccentricity, and inclination), associated with a mean motion resonance (MMR), is the main responsible for raising both the perihelion distance and the inclination of SDOs. The highest perihelion distance for a body of our samples was found to be q = 69.2 AU. This shows that bodies can be temporarily detached from the planetary region by dynamical interactions with the planets. This phenomenon is temporary since the same coupling of Kozai with a MMR will at some point bring the bodies back to states of lower-q values. However, the dynamical time scale in high-q states may be very long, up to several Gyr. For Model 1, about 10% of the bodies driven away by Neptune get trapped into the HPSD when the resonant coupling Kozai-MMR is disrupted by Neptune’s migration. Therefore, Model 1 also supplies a fossil HPSD, whose bodies remain in non-resonant orbits and thus stable for the age of the solar system, in addition to the HPSD formed by temporary captures of SDOs after the giant planets reached their current orbits. We find that about 12 – 15% of the surviving bodies of our samples are incorporated into the HPSD after about 4 – 5 Gyr, and that a large fraction of the captures occur for up to the 1:8 MMR (a ⋍ 120 AU), although we record captures up to the 1:24 MMR (a ≃ 260 AU). Because of the Kozai mechanism, HPSD objects have on average inclinations about 25°–50°, which are higher than those of the classical Edgeworth–Kuiper (EK) belt or the SD. Our results suggest that Sedna belongs to a dynamically distinct population from the HPSD, possibly being a member of the inner core of the Oort cloud. As regards to 2000 CR₁₀₅ , it is marginally within the region occupied by HPSD objects in the parametric planes (q,a) and (a,i), so it is not ruled out that it might be a member of the HPSD, though it might as well belong to the inner core.     

Improved Approximated Solutions to the Nonlinear Debye Potential

The shielding effect of plasma on the electrostatic potential due to a central nucleus is studied. The potential is determined by the Poisson equation with Boltzmann factor for the charge density of ions. The aim of this work is to find approximated analytical solutions, without the usual linearization hypothesis, by means of the technique of quasifractional approximants in two points. In a previous work (Martín and Pérez, 1994) a quasifractional fractional approximation was obtained, but the coefficients were found by means of the numerical solution of the differential equation. Now we find a complete analytical expression. The approximant found is highly precise in the range of validity of the physical model used.