Why do asteroids leave the asteroid belt in the first place?
Any multibody gravitational system is a chaotic system; the non-linear dynamics
involved in the motions of the bodies causes there to be multiple stable, repeating
states (i.e. orbits). Gravitational interactions between the bodies can induce a
transition from one stable state to another- in other words, the gravitational pulls
of neighbors can sometimes slingshot asteroids out of stable, near circular orbits
near the ecliptic plane and into erratic, eccentric orbits at various angles around
the sun. The large number of objects in the solar system makes the number of
possible minute fluctuations in position and velocity innumerable, and the
interactions between bodies allow even small initial differences to quickly lead to
drastic changes in orbit.
Rob Landolfi, Science Teacher, Washington, DC
'There is no inductive method which could lead to the fundamental concepts of physics. Failure to understand this fact constituted the basic philosophical error of so many investigators of the nineteenth century.'