Timescale vs. particle count N. The horizontal lines are the orbital periods T_j and the precession periods T_precj. of the Solar System planets (gray, brown, blue, red, coral, golden, turquoise, azure are Mercury through Neptune) from Murray & Dermott (2009). The black curve shows the collision time T_coll estimated for a disk with a = 4au, I = .1, and a mass of three Earths containing N particles of Earth density. For N < 10, the collision time is comparable to the precession time (10⁵yr). The radius of gravitational influence is roughly 10³ times the planet radius s; this determines T_scatt, the dashed curve.