Overview: Regularization and Numerical methods in Celestial Mechanics and Dynamical Astronomy

Abstract

"The relevant study of the n-body problem (predicting individual motions of a group of celestial objects interacting with each other gravitational) is substantial in space dynamics. Further, the various perturbations effects, the collisions or the close encounters between celestial bodies are trajectory modifiers. In the digital age, the behaviour of non-integrable systems is usually and primarily studied with restricted models or coupled with the help of numerical integrators. Over time, these numerical integrators progressed, and the numerical challenge led to the introduction of many new techniques. The question is, which numerical algorithm to choose for the correct research? Is what we get through numerical integration close to the proper orbit? In other words, how can one be sure that the obtained trajectories reflect reality and that their prediction can be taken into account for a long time? This paper presents some analytical and numerical methods with highly accurate computations, such as regularization methods and symplectic integrators, which can be useful in obtaining the corresponding more accurate results."