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Context. Due to our increasing knowledge on the Galactic and stellar neighborhood of the Solar System, modern long-period comet motion studies have to take into account both stellar perturbations and the overall Galactic potential. Aims. Our aim is to propose algorithms and methods to perform numerical integration of a Solar System small body equations of motion much faster and at the same time with greater precision. Methods. We propose a new formulation of the equations of motion formulated in the Solar System barycentric frame but accurately accounting for the differential perturbations caused by the Galactic potential. To use these equations effectively we provide numerical ephemerides of the Galactic positions of the Sun and a set of potential stellar perturbers. Results. The proposed methods offer the precision higher 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.
The long-term dynamics of Oort cloud comets are studied under the influence of both the radial and the vertical components of the Galactic tidal field. Sporadic dynamical perturbation processes are ignored, such as passing stars, since we aim to stud
We report the discovery of TOI-561, a multi-planet system in the galactic thick disk that contains a rocky, ultra-short period planet (USP). This bright ($V=10.2$) star hosts three small transiting planets identified in photometry from the NASA TESS
There remain significant uncertainties in the origin and evolution of black holes in binary systems, in particular regarding their birth sites and the influence of natal kicks. These are long-standing issues, but their debate has been reinvigorated i
The textit{Nancy Grace Roman Space Telescope} (textit{ Roman}) will provide an enormous number of microlensing light curves with much better photometric precisions than ongoing ground-based observations. Such light curves will enable us to observe hi
The discovery of the second interstellar object 2I/Borisov on 2019 August 30 raises the question of whether it was ejected recently from a nearby stellar system. Here we compute the asymptotic incoming trajectory of 2I/Borisov, based on both recent a