J. Klačka

Electromagnetic Radiation and Motion of a Particle

We consider the motion of uncharged dust grains of arbitrary shape including the effects of electromagnetic radiation and thermal emission. The resulting relativistically covariant equation of motion is expressed in terms of standard optical parameters. Explicit expressions for secular changes of osculating orbital elements are derived in detail for the special case of the Poynting-Robertson effect. Two subcases are considered: (i) central acceleration due to gravity and the radial component of radiation pressure independent of the particle velocity, (ii) central acceleration given by gravity and the radiation force as the disturbing force. The latter case yields results which may be compared with secular orbital evolution in terms of orbital elements for an arbitrarily shaped dust particle. The effects of solar wind are also presented.

Poynting-Robertson effect I. Equation of motion

Derivations of the Poynting-Robertson effect are presented. They are based on the corpuscular nature of light (unlike Robertsons 1937 derivation). It is justified why currently presented derivations are incorrect and why classical (nonrelativistic) physics is not able to understand this effect. Relativistically covariant derivations not only for perfectly absorbing (spherical) dust particles are presented. Fundamental feature of the interaction between the dust particle and the electromagnetic radiation is the conservation of the (proper) mass of the particle.

Motion of nonspherical dust particle under the action of electromagnetic radiation

Abstract Equation of motion of realistically shaped particle in the circumstellar dust shell is derived under the action of electromagnetic radiation including the gravity of central body. The effect is considered to the accuracy v → /c , where v → is particles velocity in a given inertial frame of reference and c is the speed of light. Equation of motion is expressed in terms of particles optical properties, standardly used in optics for stationary particles. Application to nonspherical dust particle in the Solar System with initial orbital elements identical to those of comet Encke is presented as an example. It is shown that the motion of nonspherical submicron- and small micron-sized particle may significantly differ from the motion for spherical particle of an identical volume.

Interplanetary dust particles and solar radiation

The problem of the action of the solar radiation on the motion of interplanetary dust particle is discussed. Differences between the action of electromagnetic solar radiation and that of the solar wind are explained not only from the point of view of the physical nature of these phenomena but also from the point of view of dust particles orbital evolution. As for the electromagnetic solar radiation, general equation of motion for the particle is written and the most important consequences are: (i) the process of inspiralling toward the Sun is not the only possible motion - even spiralling from the Sun is also possible, and, (ii) the orbital plane of the particle (its inclination) may change in time. As for the solar wind, the effect corresponding to the fact that solar wind particles spread out from the Sun in nonradial direction causes that the process of inspiralling toward the Sun is in more than 50% less effective than for radial spread out; in the region of the asteroid belt (long period orbits) the process of inspiralling is changed into offspiralling. Also shift in the perihelion of dust particles orbit exists.

Interplanetary dust particles and solar wind

An effect of the solar wind on the motion of interplanetary dust particles is investigated. An equation of motion is derived. It is pointed out that the ‘Pseudo-Poynting-Robertson effect’ (and its special case — a ‘corpuscular drag’) and the ‘corpuscular sputtering’ represent in reality one and the same effect within the framework of special relativity. In this context perturbation equations of celestial mechanics are also discussed.

Scattering of electromagnetic waves by charged spheres: near-field external intensity distribution

This Letter treats the scattering of electromagnetic waves by an electrically charged spherical particle in near-field approximation. Particular attention is paid to the external intensity distribution at the outer edges of the particle. The difference between scattering by a charged sphere and an electrically neutral sphere is significant only when size parameters exceed unity.

Motion of dust in mean motion resonances with planets

Effect of stellar electromagnetic radiation on the motion of spherical dust particle in mean motion orbital resonances with a planet is investigated. Planar circular restricted three-body problem with the Poynting–Robertson (P–R) effect yields monotonic secular evolution of eccentricity when the particle is trapped in the resonance. Planar elliptic restricted three-body problem with the P–R effect enables nonmonotonous secular evolution of eccentricity and the evolution of eccentricity is qualitatively consistent with the published results for the complicated case of interaction of electromagnetic radiation with nonspherical dust grain. Thus, it is sufficient to allow either nonzero eccentricity of the planet or nonsphericity of the grain and the orbital evolutions in the resonances are qualitatively equal for the two cases. This holds both for exterior and interior mean motion orbital resonances. Evolutions of argument of perihelion in the planar circular and elliptical restricted three-body problems are shown. Numerical integrations show that an analytic expression for the secular time derivative of the particle’s argument of perihelion does not exist, if only dependence on semimajor axis, eccentricity and argument of perihelion is admitted. Connection between the shift of perihelion and oscillations in secular eccentricity is presented for the planar elliptic restricted three-body problem with the P–R effect. Period of the oscillations corresponds to the period of one revolution of perihelion. Change of optical properties of the spherical grain with the heliocentric distance is also considered. The change of the optical properties: (i) does not have any significant influence on the secular evolution of eccentricity, (ii) causes that the shift of perihelion is mainly in the same direction/orientation as the particle motion around the Sun. The statements hold both for circular and noncircular planetary orbits.

The non-radial component of the solar wind and motion of dust near mean motion resonances with planets

We investigate the effect of solar wind and solar electromagnetic radiation on the dynamics of spherical cosmic dust particles. We also consider the non-radial component of the solar wind velocity, in the reference frame of the Sun. We apply the equation of motion to the motion of dust grains near commensurability resonances with a planet – mean motion orbital resonance (MMR; a particle is in resonance with a planet when the ratio of their mean motions is approximately the ratio of two small integers) – and possible capture of the grains in the resonances. Up to now, only nonspherical grains, under action of the electromagnetic radiation of the central star, were known to exhibit an increase of semimajor axis before capture into the MMR. This paper shows that the same result can be generated by the non-radial component of the solar wind even for spherical dust particles. Spherical dust grains enable the treatment of the problem in an analytic way (at least partially), which is not the case for the effect of electromagnetic radiation on nonspherical dust grains. The situation treated in the paper presents the second known case when resonant trapping of a cosmic body occurs for diverging orbits. The paper presents the first case of secular evolution of the eccentricity of a body captured in the resonance derived in an analytic way for a body characterized by a diverging orbit.

Poynting-Robertson effect : circular' orbit

Time evolution of the interplanetary dust particle under the action of the solar electromagnetic radiation (Poynting-Robertson effect) is investigated. Evolution of the initially circular orbit in terms of the orbital elements present in the standard equations for their secular changes is considered. It is pointed out that the osculating eccentricity is practically constant during the motion in spite of generally accepted opinion that the standard equations for the secular changes of orbital elements represent time evolution of the osculating elements.

Orbital evolution under the action of fast interstellar gas flow

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 particles 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.