Limits of predictability of gravitational systems

The concept of finite predictability of gravitational many-body systems is related to the non-deterministic nature of celestial mechanics and of dynamics, in general. The basic, fundamental reasons for the uncertainty of predictions are as follows: (1) the initial conditions are known only approximately since they are obtained either from observations or from approximate computations; (2) the equations of motion given by a selected model describe the actual system only approximately; (3) the physical constants of the dynamical system have error limits; (4) the differential equations of motion are non-integrable and numerical integration methods must be used for solution, generating errors in the final result at every integration step.In addition to these reasons, mostly depending on our techniques, there are some more fundamental reasons depending on the nature of the dynamical system investigated. These are the appearance of regions of instability, non-integrability and chaotic motion.Details, effects and controls of these regions for finite predictability are discussed for various dynamical systems of importance in celestial mechanics with special emphasis on planetary systems.