New Nondeterministic Celestial Mechanics

Abstract

The current status of analytical celestial mechanics (CM) is surveyed, with a focus on the role and/or lack of determinism, defined as the predictability of the state variables of a system at any time from their values at the initial time. The causes of indeterminism in practically all realistic CM problems are identified as uncertainty in the initial conditions, unknown dynamical effects, the nonintegrability of system equations, and the inherent instability of dynamical systems; these factors are shown to make reliable long-term predictions difficult or impossible. Examples considered include the emergence of nondeterministic behavior in an extremely simple linear system (as described by Born, 1969), the nonlinear pendulum problem near the separatrix, the integrable nonlinear two-body problem of CM, and the circular restricted three-body problem.