In Memory of Alexey V. Borisov. On His 60th Birthday

Some Central Configurations of the Newtonian $n$-Body Problem

H. E. Cabral

Universidade Federal de Pernambuco Cidade Universitária, Recife, 50670-420 Brasil

Abstract: In this work we construct symmetric central configurations for the $n$-body problem, for $n = 4, 5, 6, 7, 8$. Geometric arguments are used in the proof of existence of these configurations. We observe that these examples of central configurations can be proved by other means, for instance, using arguments for the existence of symmetric solutions to variational problems as is done by J. Montaldi in [10]. However, we believe that our geometrical approach will be useful in tackling other questions of central configurations of the Newtonian $n$-body problem.

Keywords: celestial mechanics, Newtonian $n$-body problem, central configurations

Received: 01.08.2025
Accepted: 15.12.2025

Language: English

DOI: 10.20537/nd251206