Galactic and stellar perturbations of long-period comet motion Practical considerations

Context. Thanks to our expanding knowledge of the Galactic and stellar neighborhood of the Solar System, modern long-period comet motion studies must take into account both stellar perturbations and the overall Galactic potential. Aims. Our aim is to propose algorithms and methods that aid in performing numerical integrations of equations of motion for a small body of the Solar System that are much faster and with greater precision. Methods. We propose a new formulation of the equations of motion formulated in the Solar System barycentric frame, but one that accurately accounts for the differential perturbations caused by the Galactic potential. To make certain these equations are applied effectively, we provide numerical ephemerides of the Galactic positions of the Sun and a set of potential stellar perturbers. Results. The proposed methods raise the precision by several orders of magnitude and, simultaneously, greatly reduce the necessary CPU time. The application of this approach is presented with the example of a detailed dynamical study of the past motion of comet C/2015 XY1.