Temporary orbital capture of ejecta from comets and asteroids: Application to the Deep Impact experiment

The trajectories of dust particles ejected from the surface of a comet or asteroid after a cratering impact are influenced by the interplay of solar radiation pressure, solar tide, cometary outgassing (for comets) and the body's irregular gravity field. In this paper we evaluate the ability of these forces to cause ejecta to become captured in temporary orbits about the parent body. We concentrate on the effect of solar radiation pressure and compute conditions in which particles can be caught in temporary orbits. The first order effects of the solar tide, comet outgassing, and body gravity field are also discussed. Our analysis uses the approximation introduced by Richter & Keller (1995) which gives an analytical solution of the averaged equations of motion under the assumption that the radiation pressure is the dominant perturbative force. We validate that this approximation works properly under the special orbital conditions which ejecta have - characterized by high eccentricities and large semimajor axes. As a specific example, we use the theory to analyze the trapping of particles following the Deep Impact experiment, which will send a man-made impactor into the comet Tempel 1. The theory can be extended to other small solar system bodies as well.