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Pastor P.,Tekov Observatory
Celestial Mechanics and Dynamical Astronomy | Year: 2014

Circumstellar dust particles can be captured in a mean-motion resonance (MMR) with a planet and simultaneously be affected by non-gravitational effects. It is possible to describe the secular variations of a particle orbit in the MMR analytically using averaged resonant equations. We derive the averaged resonant equations from the equations of motion in near-canonical form. The secular variations of the particle orbit depending on the orientation of the orbit in space are taken into account. The averaged resonant equations can be derived/confirmed also from Lagrange's planetary equations. We apply the derived theory to the case when the non-gravitational effects are the Poynting-Robertson effect, the radial stellar wind, and an interstellar wind. The analytical and numerical results obtained are in excellent agreement. We found that the types of orbits correspond to libration centers of the conservative problem. The averaged resonant equations can lead to a system of equations which holds for stationary points in a subset of resonant variables. Using this system we show analytically that for the considered non-gravitational effects, all stationary points should correspond to orbits which are stationary in interplanetary space after an averaging over a synodic period. In an exact resonance, the stationary orbits are stable. The stability is achieved by a periodic repetition of the evolution during the synodic period. Numerical solutions of this system show that there are no stationary orbits for either the exact or non-exact resonances. © 2014 Springer Science+Business Media Dordrecht. Source


Pastor P.,Tekov Observatory
Celestial Mechanics and Dynamical Astronomy | Year: 2012

The orbital evolution of a dust particle under the action of a fast interstellar gas flow is investigated. The secular time derivatives of Keplerian orbital elements and the radial, transversal, and normal components of the gas flow velocity vector at the pericentre of the particle's orbit are derived. The secular time derivatives of the semi-major axis, eccentricity, and of the radial, transversal, and normal components of the gas flow velocity vector at the pericentre of the particle's orbit constitute a system of equations that determines the evolution of the particle's orbit in space with respect to the gas flow velocity vector. This system of differential equations can be easily solved analytically. From the solution of the system we found the evolution of the Keplerian orbital elements in the special case when the orbital elements are determined with respect to a plane perpendicular to the gas flow velocity vector. Transformation of the Keplerian orbital elements determined for this special case into orbital elements determined with respect to an arbitrary oriented plane is presented. The orbital elements of the dust particle change periodically with a constant oscillation period or remain constant. Planar, perpendicular and stationary solutions are discussed. The applicability of this solution in the Solar System is also investigated. We consider icy particles with radii from 1 to 10 μm. The presented solution is valid for these particles in orbits with semi-major axes from 200 to 3000 AU and eccentricities smaller than 0.8, approximately. The oscillation periods for these orbits range from 105 to 2 × 106 years, approximately. © 2011 Springer Science+Business Media B.V. Source


Pastor P.,Tekov Observatory
Monthly Notices of the Royal Astronomical Society | Year: 2016

The equations of secular evolution for dust grains in mean motion resonances with a planet are solved for stationary points. Non-gravitational effects caused by stellar radiation (the Poynting- Robertson effect and the stellar wind) are taken into account. The solutions are stationary in the semimajor axis, eccentricity and resonant angle, but allow the pericentre to advance. The semimajor axis of stationary solutions can be slightly shifted from the exact resonant value. The periodicity of the stationary solutions in a reference frame orbiting with the planet is proved analytically. The existence of periodic solutions in mean motion resonances means that analytical theory enables infinitely long capture times for dust particles. The stationary solutions are periodic motions to which the eccentricity asymptotically approaches and around which the libration occurs. Initial conditions corresponding to the stationary solutions are successfully found by numerically integrating the equation of motion. Numerically and analytically determined shifts of the semimajor axis from the exact resonance for the stationary solutions are in excellent agreement. The stationary solutions can be plotted by the locations of pericentres in the reference frame orbiting with the planet. The pericentres are distributed in space according to the properties of the dust particles. © 2016 The Author. Published by Oxford University Press on behalf of The Royal Astronomical Society. Source


Pastor P.,Tekov Observatory
Monthly Notices of the Royal Astronomical Society | Year: 2012

The acceleration of a spherical dust particle as a result of interstellar gas flow depends on the drag coefficient, which is, for a given particle and flow of interstellar gas, a specific function of the relative speed of the dust particle with respect to the interstellar gas. We investigate the motion of a dust particle in the case when the acceleration caused by the interstellar gas flow (with the variability of the drag coefficient taken into account) represents a small perturbation to the gravity of a central star. We present the secular time derivatives of the Keplerian orbital elements of the dust particle under the action of the acceleration from the interstellar gas flow, with linear variability of the drag coefficient taken into account, for arbitrary orbit orientations. The semimajor axis of the dust particle is a decreasing function of time for an interstellar gas flow acceleration with constant drag coefficient, and also for such an acceleration with a linearly variable drag coefficient. The decrease of the semimajor axis is slower for the interstellar gas flow acceleration with the variable drag coefficient. The minimal and maximal values of the decrease of the semimajor axis are determined. In the planar case, when the interstellar gas flow velocity lies in the orbital plane of the particle, the orbit always approaches the position with the maximal value of the transversal component of the interstellar gas flow velocity vector measured at perihelion. The properties of the orbital evolution derived from the secular time derivatives are consistent with numerical integrations of the equation of motion. The main difference between the orbital evolutions with constant and variable drag coefficients lies in the evolution of the semimajor axis. The evolution of the semimajor axis decreases more slowly for the variable drag coefficient. This is in agreement with the analytical results. If the interstellar gas flow speed is much larger than the speed of the dust particle, then the linear approximation of the dependence of the drag coefficient on the relative speed of the dust particle with respect to the interstellar gas is usable for most (not too close to zero) values of the molecular speed ratios (Mach numbers). © 2012 The Author Monthly Notices of the Royal Astronomical Society © 2012 RAS. Source


Pastor P.,Tekov Observatory | Pastor P.,Comenius University | Klacka J.,Comenius University | Komar L.,Comenius University
Monthly Notices of the Royal Astronomical Society | Year: 2011

We investigate the orbital evolution of an interplanetary dust particle under the action of an interstellar gas flow. We present the secular time derivatives of the particle's orbital elements, for arbitrary orbit orientation. An important result concerns the secular evolution of the semimajor axis. The secular semimajor axis of the particle on a bound orbit decreases under the action of fast interstellar gas flow. In this paper, we discuss the possible types of evolution of other Keplerian orbital elements. Also, we compare the influences of the Poynting-Robertson effect, the radial solar wind and the interstellar gas flow on the dynamics of the dust particle in the outer planetary region of the Solar system and beyond, up to 100 au. We study the evolution of a putative dust ring in the zone of the Edgeworth-Kuiper belt. The non-radial solar wind and the gravitational effect of the major planets might have an important role in this zone. We take into account both these effects. The low-inclination orbits of micrometre-sized dust particles in the belt are not stable, because of the fast increase of eccentricity caused by the long-term monodirectional interstellar gas flow and subsequent planetary perturbations - the increase of eccentricity leads to the planet-crossing orbits of the particles. Gravitational and non-gravitational effects are treated in a way that fully respects physics. As a consequence, some of the published results have turned out to be incorrect. Moreover, in this paper we treat the problem in a more general way than it has been presented up to now. The influence of the fast interstellar neutral gas flow should not be ignored in the modelling of the evolution of dust particles beyond planets. © 2011 The Authors Monthly Notices of the Royal Astronomical Society © 2011 RAS. Source

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