On inertial forces (indirect terms) in problems with a central body
Gravitational systems in astrophysics often comprise a body – the primary – that far outweights the others, and which is taken as the centre of the reference frame. A fictitious acceleration, also known as the indirect term, must therefore be added to all other bodies in the system to compensate for the absence of motion of the primary. In this Research Note, we first stress that there is not one indirect term but as many indirect terms as there are bodies in the system that exert a gravitational pull on the primary. For instance, in the case of a protoplanetary disc with two planets, there are three indirect terms: one arising from the whole disc, and one per planet. We also highlight that the direct and indirect gravitational accelerations should be treated in a balanced way: the indirect term from one body should be applied to the other bodies in the system that feel its direct gravitational acceleration, and only to them. We point to situations where one of those terms is usually neglected however, which may lead to spurious results. These ideas are developed here for star-disc-planets interactions, for which we propose a recipe for the force to be applied onto a migrating planet, but they can easily be generalized to other astrophysical systems.
Authors
- Dylan Kloster
- Jean-François Gonzalez (ORCID: https://orcid.org/0000-0001-9423-6062)
- F. Masset (ORCID: https://orcid.org/0000-0002-9626-2210)
- A. Crida (ORCID: https://orcid.org/0000-0002-1293-9782)
- H. Méheut
- Alessandro Morbidelli (ORCID: https://orcid.org/0000-0001-8476-7687)
- Gabriele Pichierri (ORCID: https://orcid.org/0000-0003-3622-8712)
- L. Marques (ORCID: https://orcid.org/0000-0001-6809-3811)
- Philippine Griveaud
- Kate Minker (ORCID: https://orcid.org/0009-0002-6435-9453)
- Elena Lega (ORCID: https://orcid.org/0000-0001-6086-0545)
- William Béthune (ORCID: https://orcid.org/0009-0001-2471-0336)
- Fabiola Antonietta Gerosa (ORCID: https://orcid.org/0000-0002-9821-2903)
- Alain Miniussi
- Clément Baruteau (ORCID: https://orcid.org/0000-0002-2672-3456)
- Paul Segretain
- D. J. Fang (ORCID: https://orcid.org/0009-0000-6424-300X)
Institutions
- Université Claude Bernard Lyon 1 (FR)
- École Normale Supérieure de Lyon (FR)
- California Institute of Technology (US)
- University of Potsdam (DE)
- Université Fédérale de Toulouse Midi-Pyrénées (FR)
- Collège de France (FR)
- University of Milan (IT)
- Université Côte d'Azur (FR)
- Leibniz Institute for Astrophysics Potsdam (DE)
- Office National d'Études et de Recherches Aérospatiales (FR)
- Max Planck Institute for Astronomy (DE)
- Observatoire de la Côte d’Azur (FR)
- East China Normal University (CN)
- University of Tübingen (DE)
- Universidad Nacional Autónoma de México (MX)
Publication Details
- Journal
- The Open Journal of Astrophysics
- Published
- 2025-07-01
- DOI
- https://doi.org/10.33232/001c.141682
- Citations
- 1
- Primary Topic
- Elasticity and Wave Propagation
- Type
- article
- Field-Weighted Citation Impact
- 0.86
Funders
- Institut des Origines de Lyon
- Agence Nationale de la Recherche
- Centre National d’Etudes Spatiales
- Centre National de la Recherche Scientifique
- Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México