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 primordial cosmological scenario with two scalar fields and matter

The presence of matter in its different forms in a hexadimensional space-time, where gravitation is coupled to a conformal field, generates a class of cosmological solutions with very peculiar features: the initial proper distance between any two points of the space-time is infinite, following successive contraction and expansion phases in the evolution of the Universe. This behaviour defines a Anti-Big Bang Singular Cosmology. In this article we analyze this primordial cosmological scenario considering different matter forms and the effects of a Conformal Transformation on the metric.     

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.     

Numerical evaluation of the dilogarithm of complex argument

A numerical algorithm to evaluate the dilogarithmic function of a complex argument is proposed. The use of the dilogarithm in celestial mechanics appears in the exact Delaunay normalization of some functions involving the equation of the centre.     

Transversal ejection-collision orbits in Hill's problem forC≫1

In a recent paper [3], Lacomba and Llibre showed numerically the existence of two transversal ejection-collision orbits in Hill's problem for a valueC=5 of the Jacobian constant. This result can be used to prove the non-existence ofC ¹-extendable regular integrals for Hill's problem. Here we give an analytic proof of the existence of four ejection-collision orbits which are transversal for large enough values ofC.