{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:58:01Z","timestamp":1760057881134,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,28]],"date-time":"2025-02-28T00:00:00Z","timestamp":1740700800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union\u2014NextGenerationEU and Romanian Government","award":["760071"],"award-info":[{"award-number":["760071"]}]},{"name":"Romanian Ministry of Research, Innovation and Digitalization","award":["760071"],"award-info":[{"award-number":["760071"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper offers new insights into gravitational interactions within a general non-inertial reference frame. By utilizing symbolic tensor calculus, the study establishes a unified framework that connects time derivatives in non-inertial frames to those in inertial frames. The research introduces new first integrals of motion for a system of many particles in arbitrary non-inertial and barycentric rotating reference frames. These first integrals provide a kinematic and geometric visualization of motion in non-inertial frames. Additionally, a generalized potential energy function is presented for broader applicability. For the gravitational two-body problem, the paper delivers a closed-form, coordinate-free solution for the motion of each body relative to the original frame. Consequently, sufficient conditions for stability against collisions are established within the context of the two-body problem in a non-inertial reference frame. Furthermore, the paper examines the relative orbital motion of spacecraft, presenting a closed-form and coordinate-free solution in the local vertical local horizontal (LVLH) non-inertial frame, which is centered on the center of mass of the main spacecraft.<\/jats:p>","DOI":"10.3390\/sym17030368","type":"journal-article","created":{"date-parts":[[2025,2,28]],"date-time":"2025-02-28T10:12:33Z","timestamp":1740737553000},"page":"368","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["About a Classical Gravitational Interaction in a General Non-Inertial Reference Frame: Applications on Celestial Mechanics and Astrodynamics"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9287-8387","authenticated-orcid":false,"given":"Daniel","family":"Condurache","sequence":"first","affiliation":[{"name":"Department of Theoretical Mechanics, \u201cGheorghe Asachi\u201d Technical University of Iasi, D. Mangeron 59, 700050 Iasi, Romania"},{"name":"Research Center for Industrial Robots Simulation and Testing, Technical University of Cluj-Napoca, Memorandumului 14, 400114 Cluj-Napoca, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-1443-9050","authenticated-orcid":false,"given":"Mihail","family":"Cojocari","sequence":"additional","affiliation":[{"name":"Department of Theoretical Mechanics, \u201cGheorghe Asachi\u201d Technical University of Iasi, D. Mangeron 59, 700050 Iasi, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-9954-8048","authenticated-orcid":false,"given":"Ionu\u021b","family":"Popa","sequence":"additional","affiliation":[{"name":"Department of Theoretical Mechanics, \u201cGheorghe Asachi\u201d Technical University of Iasi, D. Mangeron 59, 700050 Iasi, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,28]]},"reference":[{"key":"ref_1","unstructured":"Goroff, D.L. (1993). 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