Light curves of the eclipsing systems of RS CVn-type

This work presents the light curves for rotating spotted stars generated by a computational code developed by us. This code is based in a model of the system and its analytical solution. The work also present an analysis of the photometric curve variations with the changes in the model's parameters.As a first result we have simulated a temporal evolution of the light curve when the photospheric spot varies its size and position and we reproduced some observational light curves of the II Peg star.Work supported by Dirección de Investigación, Universidad de La Serena, Chile.     

Origin and evolution of the earth-moon system

The origin and evolution of the Earth-Moon system is studied by comparing it to the satellite systems of other planets. The normal structure of a system of secondary bodies orbiting around a central body depends essentially on the mass of the central body. The Earth with a mass intermediate between Uranus and Mars should have a normal satellite system that consists of about half a dozen satellites each with a mass of a fraction of a percent of the lunar mass. Hence, the Moon is not likely to have been generated in the environment of the Earth by a normal accretion process as is claimed by some authors.Capture of satellites is quite a common process as shown by the fact that there are six satellites in the solar system which, because they are retrograde, must have been captured. There is little doubt that the Moon is also a captured satellite, but its capture orbit and tidal evolution are still incompletely understood.The Earth and the Moon are likely to have been formed from planetesimals accreting in particle swarms in Kepler orbits (jet streams). This process leads to the formation of a cool lunar interior with an outer layer accreted at increasingly higher temperatures. The primeval Earth should similarly have formed with a cool inner core surrounded in this case by a very strongly heated outer core and with a mantle accreted slowly and with a low average temperature but with intense transient heating at each individual impact site.     

A study of apparently nearby stars with coinciding spectral type and apparent magnitude

At visual inspection of objective-prism plates one frequently detects a pair or higher multiple of apparently identical stellar spectra so close together that they form a conspicuous configuration for the eye. An attempt to analyse this type of objects has given no positive indication that it should be identified with any unique physical phenomenon. A series of explanations is presented. A minor fraction of the objects may constitute widely separated binary components, the identity of which is physically conditioned by the process of formation. For the majority, however, it seems more probable that they form parts of cluster remnants or very small clusters, and that the coincidence of the spectral types is in the first instance to consider as a fortunate random effect that facilitates the detection of the hidden cluster. Although there are several interpretations of the appearance of such ‘miniclusters’, I find it particularly important to take the possibility into consideration that the number of open clusters (and associations) may be considerably greater than one has hitherto assumed—from observational as well as from theoretical point of view.     

Intercomparisons of earth gravity models by means of lumped coefficients: Terms for eccentricity and longitude

The comparisons of the Earth gravity field models by the order of their harmonic coefficients, performed with the basic lumped coefficients (Planet. Space Sci.29, 653, 1981, Paper I) are here extended to cover all harmonic coefficients (both odd and even degree). The lumped coefficients (the “e-terms” and “longitudinal” terms), corresponding to 18 Earth models, are compared mutually (Figs. 2–15). The large differences, observed for various models and orders, are of particular interest: they are gathered into Table 1. The result of Paper I was a little pessimistic. The same is true here: various inhomogeneities, sometimes very large, in the accuracy of the harmonic coefficients must exist—even for low orders. Most of our comments and objections, however, relate to the older Earth models, which have only a historical value now. Our comparisons are only relative ones; an actual test of the accuracy of the models (their calibration) is possible via data with independent status (Kloko?ník, 1982, 1983).     

Approximating constant‐Q seismic propagation in the time domain

In this study, we investigate the accuracy of approximating constant‐Q wave propagation by series of Zener or standard linear solid (SLS) mechanisms. Modelling in viscoacoustic and viscoelastic media is implemented in the time domain using the finite‐difference (FD) method. The accuracy of numerical solutions is evaluated by comparison with the analytical solution in homogeneous media. We found that the FD solutions using three SLS relaxation mechanisms as well as a single SLS mechanism, with properly chosen relaxation times, are quite accurate for both weak and strong attenuation. Although the RMS errors of FD simulations using a single relaxation mechanism increase with increasing offset, especially for strong attenuation (Q = 20), the results are still acceptable for practical applications. The synthetic data of the Marmousi‐II model further illustrate that the single SLS mechanism, to model constant Q, is efficient and sufficiently accurate. Moreover, it benefits from less computational costs in computer time and memory.     

Study of bi-orthogonal modes in magnetic butterflies

We present a bi-orthogonal decomposition of the temporal and latitudinal distribution of solar magnetic fields from synoptic magnetograms. Results are compared with a similar decomposition of the distribution of sunspots since 1874. We show that the butterfly diagrams can be interpreted as the result of approximately constant amplitudes and phases of two oscillations with periods close to 22 years. A clear periodicity of 7 years can also be identified in the most energetic modes of both spatio-temporal series. These results can be used to obtain relevant information concerning the physics of the solar dynamo.     

Repeat Ground Track Orbits of the Earth Tesseral Problem as Bifurcations of the Equatorial Family of Periodic Orbits

Orbits repeating their ground track on the surface of the earth are found to be members of periodic-orbit families (in a synodic frame) of the tesseral problem of the Earth artificial satellite. Families of repeat ground track orbits appear as vertical bifurcations of the equatorial family of periodic orbits, and they evolve from retrograde to direct motion throughout the 180 degrees of inclination. These bifurcations are always close to the resonances of the Earth's rotation rate and the mean motion of the orbiter.     

Dynamics of a satellite orbiting a planet with an inhomogeneous gravitational field

We study the dynamics of a satellite (artificial or natural) orbiting an Earth-like planet at low altitude from an analytical point of view. The perturbation considered takes into account the gravity attraction of the planet and in particular it is caused by its inhomogeneous potential. We begin by truncating the equations of motion at second order, that is, incorporating the zonal and the tesseral harmonics up to order two. The system is formulated as an autonomous Hamiltonian and has three degrees of freedom. After three successive Lie transformations, the system is normalised with respect to two angular co-ordinates up to order five in a suitable small parameter given by the quotient between the angular velocity of the planet and the mean motion of the satellite. Our treatment is free of power expansions of the eccentricity and of truncated Fourier series in the anomalies. Once these transformations are performed, the truncated Hamiltonian defines a system of one degree of freedom which is rewritten as a function of two variables which generate a phase space which takes into account all of the symmetries of the problem. Next an analysis of the system is achieved obtaining up to six relative equilibria and three types of bifurcations. The connection with the original system is established concluding the existence of various families of invariant 3-tori of it, as well as quasiperiodic and periodic trajectories. This is achieved by using KAM theory techniques.