In this paper, we investigate the action of solar wind on an arbitrarily shaped interplanetary dust particle. The final relativistically covariant equation of motion of the particle also contains the change of the particle’s mass. The non‐radial solar wind velocity vector is also included. The covariant equation of motion reduces to the Poynting–Robertson effect in the limiting case when a spherical particle is treated, when the speed of the incident solar wind corpuscles tends to the speed of light and when the corpuscles spread radially from the Sun. The results of quantum mechanics have to be incorporated into the physical considerations, in order to obtain the limiting case. If the solar wind affects the motion of a spherical interplanetary dust particle, then . Here, p′in and p′out are the incoming and outgoing radiation momenta (per unit time), respectively, measured in the proper frame of reference of the particle, and and are the solar wind pressure and the total scattering cross‐sections, respectively. An analytical solution of the derived equation of motion yields a qualitative behaviour consistent with numerical calculations. This also holds if we consider a decrease of the particle’s mass. Using numerical integration of the derived equation of motion, we confirm our analytical result that the non‐radial solar wind (with a constant value of angle between the radial direction and the direction of the solar wind velocity) causes outspiralling of the dust particle from the Sun for large values of the particle’s semimajor axis. The non‐radial solar wind also increases the time the particle spirals towards the Sun. If we consider the periodical variability of the solar wind with the solar cycle, then there are resonances between the particle’s orbital period and the period of the solar cycle.

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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.

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.

Abstract. Effect of stellar electromagnetic radiation on 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 monotonous secular evolution of eccentricity when the particle is trapped in the resonance. Elliptically 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 longitude of pericenter in the planar circular and elliptical restricted three-body problems are shown. Our numerical integrations suggest that any analytic expression for secular time derivative of the particle's longitude of pericenter does not exist, if a dependence on semi-major axis, eccentricity and longitude of pericenter is considered (the P-R effect and mean-motion resonance with the planet in circular orbit is taken into account).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 secular evolution of eccentricity, ii) causes that the shift of pericenter is mainly in the same direction/orientation as the particle motion around the Sun. The statements hold both for circular and noncircular planetary orbits.