On the central configurations of the planar 1 + 3 body problem

We consider the Newtonian four-body problem in the plane with a dominat mass M . We study the planar central configurations of this problem when the remaining masses are infinitesimal. We obtain two different classes of central configurations depending on the mutual distances between the infinitesim...

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Bibliographic Details
Published in:Celestial mechanics and dynamical astronomy Vol. 109; no. 1; pp. 27 - 43
Main Authors: Corbera, Montserrat, Cors, Josep Maria, Llibre, Jaume
Format: Journal Article Publication
Language:English
Published: Dordrecht Springer Netherlands 01.01.2011
Springer Nature B.V
Springer Verlag
Subjects:
70 Mechanics of particles and systems
70F Dynamics of a system of particles, including celestial mechanics
Aerospace Technology and Astronautics
Astrophysics
Astrophysics and Astroparticles
Celestial mechanics
Classical Mechanics
Classificació AMS
Dynamical Systems and Ergodic Theory
Enginyeria mecànica
Geophysics/Geodesy
Many-body problem
Matemàtiques i estadística
Mathematics
Mecànica celest
Orbits
Original Article
Physics
Physics and Astronomy
Problema dels cossos múltiples
Àrees temàtiques de la UPC
Central configurations
1 + 3 body problem
Coorbital satellites
ISSN:0923-2958, 1572-9478
Online Access:Get full text
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Summary:We consider the Newtonian four-body problem in the plane with a dominat mass M . We study the planar central configurations of this problem when the remaining masses are infinitesimal. We obtain two different classes of central configurations depending on the mutual distances between the infinitesimal masses. Both classes exhibit symmetric and non-symmetric configurations. And when two infinitesimal masses are equal, with the help of extended precision arithmetics, we provide evidence that the number of central configurations varies from five to seven.
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ISSN:0923-2958
1572-9478
DOI:10.1007/s10569-010-9316-0