Orbital evolution under the action of fast interstellar gas flow with a non-constant drag coefficient

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).