Evolution of extended clouds of particles near the sun and stars

The evolution of the trajectories of small objects not entirely ejected from the solar system and subject to significant perturbations owing to the regular galactic field is studied. These objects may be individual dust particles, comets, or, in the case of other stars, large dust clouds and stellar satellites. The possibility of averaging their motion over the period of the galactic rotation is examined. The averaged equations are solved in terms of elliptic functions. The eccentricity of the orbit also evolves, but returns periodically to its original value, ~1, corresponding to ejection if the interaction with individual stars is neglected. The slope of the line of apsides with respect to the galactic plane evolves in two ways: with time it either passes through 90° or through 0°.