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 micrometers. 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 10^5 to 2 x 10^6 years, approximately.Comment: 22 pages, 3 figures; Accepted for publication in Celestial Mechanics
and Dynamical Astronom