We strengthen a generic finiteness result due to Moeckel by showing that the number of spatial central configurations of the Newtonian five-body problem with positive masses is finite, apart from some explicitly given special cases of mass values.
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Acknowledgments Some of our computations were run on one of the Sage Foundation’s 24-core Sun X4450s, supported by National Science Foundation Grant No. DMS-0821725. We were also both supported by the American Institute of Mathematics. Furthermore, the second author was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft (DFG)) through the Institutional Strategy of the University of Göttingen.
- Albouy-Chenciner equations
- Central configurations
- Polyhedral fan
- Tropical geometry
- n-Body problem