SIMBAD references

We investigate the orbital evolution of particles in a planet's chaotic zone to determine their final destinations and their timescales of clearing. There are four possible final states of chaotic particles: collision with the planet, collision with the star, escape, or bounded but non-collision orbits. In our investigations, within the framework of the planar circular restricted three body problem for planet-star mass ratio µ in the range 10^–9 to 10^–1.5, we find no particles hitting the star. The relative frequencies of escape and collision with the planet are not scale-free, as they depend upon the size of the planet. For planet radius R_p ≥ 0.001 R_H where R_His the planet's Hill radius, we find that most chaotic zone particles collide with the planet for µ ≲ 10^–5; particle scattering to large distances is significant only for higher mass planets. For fixed ratio R_p/R_H, the particle clearing timescale, T_cl, has a broken power-law dependence on µ. A shallower power law, T_cl∼ µ^–1/3, prevails at small µ where particles are cleared primarily by collisions with the planet; a steeper power law, T_cl∼ µ^–3/2, prevails at larger µ where scattering dominates the particle loss. In the limit of vanishing planet radius, we find T_cl~ 0.024 µ^–3/2. The interior and exterior boundaries of the annular zone in which chaotic particles are cleared are increasingly asymmetric about the planet's orbit for larger planet masses; the inner boundary coincides well with the classical first order resonance overlap zone, Δa_cl, int_≃ 1.2 µ^0.28 a_p; the outer boundary is better described by Δa_cl, ext_≃ 1.7 µ^0.31 a_p, where a_p is the planet-star separation.