Abstract:
N body gravitational simulations are widely used to model the evolution of the celestial bodies in the Solar System. The simulations vary from two bodies over short intervals of time to a large number of bodies over long intervals. We use N body gravitational simulations to study the long-term evolution of the major Uranian satellites. We also study the probable capture of the two major satellites into a mean-motion resonance. We develop a coupled orbital-thermal model of Uranus and its major satellites. The orbital part models the evolution of the satellites' orbital elements with the help of detailed equations of motion and associated perturbing terms. The thermal part models the evolution of the satellites' interior using the heat equation. The model exchanges the feedback between the two parts during the entire simulation and so is coupled. The implementation of our model is based on the numerical integration of developed equations of motion and the heat equation. We test the performance of two integrators on representative test problems. We run simulations of our model to investigate an increase in the orbital elements of the two major satellites during the resonance process. We also analyse our results for the uncertainty in the initial input parameters, and for the number of satellites and perturbing terms in the equations of motion.