Nonlocal Instabilities for the Restricted Planar Circular 3 Body

The Restricted Planar Circular 3 Body Problem (RPC3BP) is the
simplest nonintegrable 3 body problem. Usually it is viewed as a model for
planar either Sun-Jupiter-Asteriod or Sun-Earth-Earth Satellite system.
Stability v.s. instability of such a system is one of long standing
problems. We consider the first model. Using Aubry-Mather theory, Mather
variational method, and numerical analysis, we managed to prove existence
of rich variety of unstable motions. For example, an Asteriod could have a
nearly elliptic orbit of say eccenticity 0.76 in the past and escape to
infinity along nearly parabolic orbit of eccentricity more than 1 in the
future. These motions could be interpreted as Arnold diffusion for this
system. This is a joint work with T. Nguyen and D. Pavlov.