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

Abstract

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.

On the stability of dust orbits in mean-motion resonances perturbed by from an interstellar wind

“…Eq. ( 18) is consistent with the same result obtained from an averaging of the time derivative of the Tisserand parameter over the resonant libration period of the semimajor axis (see Gomes 1997;Pástor 2013) and with the same result obtained from a near-canonical approach Gomes (1995Gomes ( , 1997. We can rewrite Eq.…”

“…The two groups with the largest maximal capture times (libration in the region beyond the collision curve and libration around the bottom center) were already identified in Pástor (2013). For a planet initially located on the positive x-axis and a particle with initial conditions a in = a 2/1 , e in arbitrary,ω in arbitrary, and f in = 0 • , we obtain, in theω in e in plane, the collision line depicted in Fig.…”

“…5. This curve divides the evolutions in Pástor (2013) into two groups (in the present paper, we refer to these two groups as the region below the collision curve and the region beyond the collision curve).…”

“…In Pástor (2013), the results of Pástor (2012b) were used in order to obtain the secular time derivative of the orbit eccentricity for a dust particle captured in an MMR within the framework of the planar CR3BP with the PR effect, a radial stellar wind, and an IGF. The agreement between the analytical and numerical results in Pástor (2013) was excellent for the IGF in the Solar system. The results show that two sets of orbital evolutions divided by a strong boundary in the initial conditions exist for the exterior 2/1 resonance.…”

Positions of equilibrium points for dust particles in the circular restricted three-body problem with radiation

“…7 represents one possible behavior of the dust particles captured into the 1/1 resonance with the Earth. The spherical dust particles captured in the 1/1 resonance in the planar CR3BP under the action of the PR effect and the radial stellar wind have an evolution of eccentricity which asymptotically decreases to a zero eccentricity (Pástor et al 2009;Pástor 2013). This feature enables using an application of adiabatic invariant theory presented in Gomes (1995) to prove that during the libration around an equilibrium point on the stable part of an equilibrium branch the libration amplitude must always increase.…”