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.     

Low velocity shock-cloud encounters I.

Shocks propagating in the interstellar medium (ISM) play an important role in the life of molecular clouds. Through a theoretical study of interaction between clouds and shocks we can understand, for example, the density distribution of observed molecular clouds and the first steps of star formation. The only way to study of interaction in detail is via a numerical hydrodynamical simulation. In this paper we present the first results of a hydrocode which is able to follow the processes after the collision between the cloud and shock front.Our main theoretical result is that the chemical processes (e.g. H₂ dissociation) can affect the dynamical processes significantly. Global parameters of the cloud are calculated for the comparision of the simulation and the observations.     

Twenty years of evolution for the DORIS permanent network: from its initial deployment to its renovation

The ground network is one of the major components of the DORIS system. Its deployment, managed by the French national mapping agency [Institut Géographique National, (IGN)], started in 1986 at a sustained pace that allowed it to reach 32 stations upon the launch of the first DORIS-equipped satellite (SPOT-2) in 1990. For the first generation of transmitting antennas, the installation procedures were adapted to the decimetre performance objective for the DORIS system. During the second era of the deployment of an even denser network, the antenna support layouts gradually evolved towards a better quality, thus improving the long-term stability of the antenna reference point, and a new antenna model allowed a more accurate survey. As the positioning accuracy of the DORIS system improved, it was necessary to review the antenna stability for the whole network. A first stability estimation, using criteria like antenna model and support design, was followed by a major renovation effort which started in 2000 and is now almost complete. In 6 years, through the renovation or installation of 43 stations and the implementation of new installation procedures to meet more stringent stability requirements, significant improvement in network quality was achieved. Later a more analytical approach, taking into account the characteristics of each element that support the antenna, has been taken to assess the potential stability of all DORIS occupations. IGN is also in charge of its operational maintenance, an intensive activity on account of the significant failure rate of the successive generations of equipment. Nevertheless, thanks to its unique density and homogeneity, DORIS has maintained a very good coverage rate of the satellite orbits. Through 38 well-distributed current co-locations with the Global Positioning System, Satellite Laser Ranging and Very Long Baseline Interferometry techniques in its current 56-station network, DORIS contributes significantly to the realisation of the International Terrestrial Reference System. DORIS stations in areas where no other space geodesy technique is available provide a significant contribution to the study of plate tectonics. Many stations co-located with tide gauges contribute to the monitoring of sea level changes. Although it has several advantages over similar techniques, there is still room for improvement in the DORIS network.     

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.     

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.     

Analytical derivation of the probability for the escape of stars from colliding galaxies

We use the impulse approximation to derive analytical formulae for the escape probability from a simple binary system that interacts with a third body. The binary system is made up of a mass-less body in circular orbit around a massive object, and we assume that the two massive bodies follow a Schuster (or Plummer) distribution. Within the ranges imposed by the impulsive approximation to the parameters of the encounter, we find good agreement between our results and those obtained from numerical experiments.     

A New Symbolic Processor for the Earth Rotation Theory

In this paper we present a new symbolic processor specially suited for the Earth rotation theory. This processor works with a more general kind of Poisson series called Kinoshita series, which has resulted to be very useful in the Earth rotation theory. Its structure is adapted for dealing with the more general analytical expressions that appear in the Earth rotation theory. This new algebraic processor has been successfully used for computing different contributions to the nutation series of the rigid Earth.This revised version was published online in October 2005 with corrections to the Cover Date.     

Orbital Elements of 2004 Perseid Meteoroids Perturbed by Jupiter

Jupiter and Saturn produce important gravitational impulses on meteoroids released by comet 109P/Swift-Tuttle. The meteoroids from this comet once released follow retrograde orbits that during their periodic approaches to these planets (within 1.6 and 0.9 A.U., respectively) are impulsed gaining orbital energy. This perturbation effect is translated into a net inward shift in the node of the perturbed meteoroids. Such geometry with Jupiter occurred in 2004 over a meteoroid trail ejected by this comet during the 1862 A.D. return of the comet to perihelion. In order to study the predicted outburst produced by one-revolution meteoroids, the Spanish Photographic Meteor Network (SPMN) performed an extensive campaign. As a part of this observational effort here are presented 10 accurate meteoroid orbits. We discuss their origin by comparing them with the theoretical orbital elements of the dust trails intercepting the Earth during the 2004 Perseid return.