Central configurations of the planar coorbital satellite problem
The planar Newtonian \((n+1)\)-body problem where one of the masses is large and the other n masses are infinitesimal and equal is considered. The so-called central configurations are studied. One of the reasons why central configurations are interesting (since Laplace times) is that they allow to obtain explicit homographic solutions of the \(n\)-body problem. Here, the all known central configurations for the cases \(2 \leq n \leq 4 \) are found analytically. The known central configurations for \(n=2,\dots, 9\) are checked numerically and then the investigations are continued to the values of \(n\) up to 15. A short review of the papers (since \textit{F. R. Moulton}, Ann. Math. (2) 12, 1--17 (1910; JFM 41.0794.02)]) on the subject is given. There are 41 references.
scientific article; zbMATH DE number 2140058