https://astro.theoj.org/article/141682-on-inertial-forces-indirect-terms-in-problems-with-a-central-body

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Earth and Planetary Astrophysics
Vol. 8, 2025July 01, 2025 IST

On inertial forces (indirect terms) in problems with a central body

Aurelien Crida

      + Lagrange, Universite Cote d'Azur
      + Lagrange, Observatoire de la Cote d'Azur
  * ORCID iD: 0000-0002-1293-9782

Clement Baruteau

      + IRAP, Universite de Toulouse

Philippine Griveaud

      + Lagrange, Universite Cote d'Azur
      + Lagrange, Observatoire de la Cote d'Azur
      + Max-Planck-Institut fur Astronomie

Elena Lega

      + Lagrange, Universite Cote d'Azur
      + Lagrange, Observatoire de la Cote d'Azur

Frederic Masset

      + Instituto de Ciencas Fisicas, Universidad Nacional Autonoma
        de Mexico

William Bethune

      + University of Tubingen
      + DAAA, Office National d'Etudes et de Recherches Aerospatiales

David Fang

      + IRAP, Universite de Toulouse
      + Departement de Physique, Ecole Normale Superieure de Lyon

Jean-Francois Gonzalez

      + CRAL, Universite Claude Bernard Lyon 1

Heloise Meheut

      + Lagrange, Universite Cote d'Azur
      + Lagrange, Observatoire de la Cote d'Azur

Alessandro Morbidelli

      + Lagrange, Universite Cote d'Azur
      + Lagrange, Observatoire de la Cote d'Azur
      + College de France

Fabiola Gerosa

      + Lagrange, Universite Cote d'Azur
      + Lagrange, Observatoire de la Cote d'Azur

Dylan Kloster

      + Lagrange, Universite Cote d'Azur
      + Lagrange, Observatoire de la Cote d'Azur

Lea Marques

      + MAUCA - Master track in Astrophysics at Universite Cote
        d'Azur, Universite Cote d'Azur
      + Leibniz Institute for Astrophysics Potsdam
      + Institut fur Physik und Astronomie, University of Potsdam

Alain Miniussi

      + Galilee, Universite Cote d'Azur
      + Galilee, Observatoire de la Cote d'Azur

Kate Minker

      + MAUCA - Master track in Astrophysics at Universite Cote
        d'Azur, Universite Cote d'Azur
      + Lagrange, Universite Cote d'Azur
      + Lagrange, Observatoire de la Cote d'Azur

Gabriele Pichierri

      + Division of Geological and Planetary Sciences, California
        Institute of Technology
      + Dipartimento di Fisica, University of Milan

Paul Segretain

      + Lagrange, Universite Cote d'Azur
      + Lagrange, Observatoire de la Cote d'Azur

https://doi.org/10.33232/001c.141682
accretion discshydrodynamicsmethods: numericalplanetary systems:
formationplanetary systems: protoplanetary discs
ccby-4.0
Crida, Aurelien, Clement Baruteau, Philippine Griveaud, Elena Lega,
Frederic Masset, William Bethune, David Fang, et al. 2025. "On
Inertial Forces  (Indirect Terms) in Problems with a Central Body."
The Open Journal of Astrophysics 8 (July). https:/ / doi.org/
 10.33232/ 001c.141682.
Download... V

  * Citation (BibTeX)

Abstract

Read article at ArXiv

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.

Read article at ArXiv
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