N -body Models of Aggregation and Disruption. Derek C. Richardson University of Maryland. Overview. Introduction/the N -body problem. Numerical method ( pkdgrav ). Application: binary asteroids. Non-idealized & strength models.
Derek C. Richardson
University of Maryland
The orbit of any one planet depends on the combined motion of all the planets, not to mention the actions of all these on each other. To consider simultaneously all these causes of motion and to define these motions by exact laws allowing of convenient calculation exceeds, unless I am mistaken, the forces of the entire human intellect.
— Isaac Newton, 1687.
Cost = N (N – 1) / 2 = O(N2)
Replace many summations with single multipole expansion around center of mass.
Use multipole expansion if opening angle < crit.
E.g. Barnes & Hut (1986) two-dimensional tree.
Cost = O(N log N)
Michel et al. 2001
Recoil: new mobility mechanism?
For a demo of the new strength model in action, see Patrick’s presentation!
Work in progress!
Close approach distance q
Encounter speed v∞
Spin period P
Semimajor axis a (50% > 10 Rp)
Eccentricity e (97% > 0.1)
For 2000 asteroids:
Richardson et al. 2003
Stress response may be predicted by plotting tensile strength (resistance to stretching) vs. porosity.
Asphaug et al. 2003
Asphaug et al. 1998