Numerical continuation of families of frozen orbits in the zonal problem of artificial satellite theory

In the zonal problem of a satellite around the Earth, we continue numerically natural families of periodic orbits with the polar component of the angular momentum as the parameter. We found three families; two of them are made of orbits with linear stability while the third one is made of unstable orbits. Except in a neighborhood of the critical inclination, the stable periodic (or frozen) orbits have very small eccentricities even for large inclinations.     

Classical T Tauri Stars and Substellar Analogs

We propose a spectroscopic criterion based on Hα equivalent width and spectral type to classify classical T Tauri stars and substellar analogs. We argue that accreting objects can be identified from low-resolution optical spectroscopy, when their Hα flux is stronger than the saturation limit at Log {Lum(Hα)/Lum(bol)} = ?3.3. Additional criteria, such as the relation between HeI5876 or HeI6678 and Hα, or the ratios between the components of the CaII infrared triplet, are also discussed. We have tested the reliability of these criteria by applying them to several objects with masses in the range 0.11–0.025 M_⊙, which belong to nearby star forming regions and the TW Hya association.     

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.     

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.     

Space Charge Potentials in Cylindrical Geometries Including Temperature Effects

The analysis of space-charge in cylindrical geometries has been performed using kinetic theory. The current collected by central electrodes inmersed in plasmas with a discriminant grid has been determined through the Poisson equation and truncated Maxwellian distribution functions for the ions. The electrons are assumed to be repelled by the entrance grid. The non-linear adimensional equations have been solved approximately using linear expansion around the point with zero potential.     

Invariant rotational curves in Sitnikov's Problem

The Sitnikov's Problem is a Restricted Three-Body Problem of Celestial Mechanics depending on a parameter, the eccentricity,e. The Hamiltonian,H(z, v, t, e), does not depend ont ife=0 and we have an integrable system; ife is small the KAM Theory proves the existence of invariant rotational curves, IRC. For larger eccentricities, we show that there exist two complementary sequences of intervals of values ofe that accumulate to the maximum admissible value of the eccentricity, 1, and such that, for one of the sequences IRC around a fixed point persist. Moreover, they shrink to the planez=0 ase tends to 1.     

On the Centre Manifold of Collinear Points in the Planar Three-Body Problem

We study the existence of invariant tori in a neighbourhood of the collinear equilibrium points of the planar three-body problem. To this end some properties of the normal form of the Hamiltonian reduced to the 4D central manifold are proved. Using this normal form, we show that the nondegeneracy conditions of KAM theorem are satisfied for all positive masses, including the 2:1 resonance case. The evaluation of the conditions is done numerically.     

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.