Stabilitätsuntersuchungen an Asteroidenbahnen in ausgewählten Bahnresonanzen des Edgeworth-Kuiper-Gürtels

Abstract

This dissertation presents a comprehensive description of the stability of asteroid orbits in the Edgeworth-Kuiper belt taking the 3:5, 4:7 and 1:2 mean motion resonance with Neptune as example. Further emphasis is given to the numerical computability of the Lyapunov time of asteroids. Starting with a general description of rounding and approximation errors in numerical computations, the growth of these errors within numerical integrations is estimated. These, partly machine-dependent errors influence the calculated trajectory of the asteroid as well as the derived Lyapunov time. Different hardware architectures and integration methods were used to investigate the influence on the computed Lyapunov time. As a measure of this dependence a computability index ê is defined. Furthermore it is shown, that the general structure of phase space is robust against these changes...