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Dust particles in mean motion resonances influenced by an interstellar gas flow

The orbital evolution of a dust particle captured in a mean motion resonance with a planet in circular orbit under the action of the Poynting-Robertson effect, radial stellar wind and an interstellar gas flow of is investigated. The secular time derivative of Tisserand parameter is analytically derived for arbitrary orbit orientation. From the secular time derivative of Tisserand parameter a general relation between the secular time derivatives of eccentricity and inclination is obtained. In the planar case (the case when the initial dust particle position vector, initial dust particle velocity vector and interstellar gas velocity vector lie in the planet orbital plane) is possible to calculate directly the secular time derivative of eccentricity. Using numerical integration of equation of motion we confirmed our analytical results in the three-dimensional case and also in the planar case. Evolutions of eccentricity of the dust particle captured in an exterior mean motion resonance under the action of the Poynting-Robertson effect, radial stellar wind for the cases with and without the interstellar gas flow are compared. Qualitative properties of the orbital evolution in the planar case are determined. Two main groups of the secular orbital evolutions exist. In the first group the eccentricity and argument of perihelion approach to some values. In the second group the eccentricity oscillates and argument of perihelion rapidly shifts.