https://doi.org/10.1140/epjp/s13360-023-04729-0
Regular Article
Celestial mechanics in Newtonian-like gravity with variable G
1
Departamento de Física, Universidade Federal de Ouro Preto (UFOP), Campus Universitário Morro do Cruzeiro, 35.400-000, Ouro Preto, Brazil
2
Núcleo Cosmo-ufes & Departamento de Física, Universidade Federal do Espírito Santo (UFES), Av. Fernando Ferrari, 540, CEP 29.075-910, Vitória, ES, Brazil
3
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe Shosse 31, 115409, Moscow, Russia
4
Núcleo Cosmo-ufes & Departamento de Química e Física, Universidade Federal do Espírito Santo, Alto Universitário s/n, 29500-000, Alegre, ES, Brazil
Received:
15
September
2023
Accepted:
21
November
2023
Published online:
6
December
2023
A Newtonian-like theory inspired by the Brans–Dicke gravitational Lagrangian has been recently proposed in Fabris (Eur Phys J Plus 136:143, 2021). This work demonstrates that the modified gravitational force acting on a test particle is analogous to that derived from the Manev potential. Specifically, an additional term 
emerges alongside the conventional Newtonian component. We analyze the predicted expression for the pericenter advance and the Roche limit and use them to constraint the theory’s single free parameter 
which is analogous to the Brans–Dicke parameter. At the same time this theory is able to solve the advance of Mercury’s perihelion, we also show that there is no relevant impact on the Roche limit in comparison with the well-known Newtonian results.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
