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 \mu 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 } \geq 0.001 R _ { H } where R _ { H } is the planet ’ s Hill radius , we find that most chaotic zone particles collide with the planet for \mu \lesssim 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 \mu .
A shallower power-law , T _ { cl } \sim \mu ^ { - { 1 / 3 } } , prevails at small \mu where particles are cleared primarily by collisions with the planet ; a steeper power law , T _ { cl } \sim \mu ^ { - { 3 / 2 } } , prevails at larger \mu where scattering dominates the particle loss .
In the limit of vanishing planet radius , we find T _ { cl } \approx 0.024 \mu ^ { - { 3 \over 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 , \Delta a _ { cl,int } \simeq 1.2 \mu ^ { 0.28 } a _ { p } ; the outer boundary is better described by \Delta a _ { cl,ext } \simeq 1.7 \mu ^ { 0.31 } a _ { p } , where a _ { p } is the planet-star separation .