Orbital variation of the rotating non-spherical dust grains due to change of the solar radiation forces by shape effect

Abstract

We present the values of a ratio β of the solar radiation pressure force to the solar gravity on the finite circular cylindrical grains, as functions of an aspect ratio of the cylinder and an incident angle Θ of the solar radiation. By using the resulting formula of β(Θ), the trajectory of the Kepler orbit for the rotating silicate cylinder is computed associated with a spin motion under the assumption that the spin axis is along the shortest axis of the cylinder and points to the direction perpendicular to the solar radiation. We found for the silicate cylinder grain with a mass equivalent to a sphere with a radius of 0.15 μm, and the aspect ratio of 2.0 that a heliocentric distance of the grain varies periodically with a time, having an amplitude of the fluctuation in the heliocentric distance of about 0.02 AU, where the spin velocity is 0.25 rotation/day and the initial orbit has a semi-major axis 3.0 AU and an eccentricity 0. In addition, during such a fluctuation of the heliocentric distance, the instantaneous eccentricity of the orbit also varies simultaneously from 0 to 1.6 with the rotation of the grain. This implies that the in-situ measurements of orbital elements of impact grains on the dust detector may record those instantaneous orbital elements related to the phase of the grain’s rotation.