Continua of central configurations with a negative mass in the n-body problem

摘要

The number of equivalence classes of central configurations of n ≤ 4 bodies of positive mass is known to be finite, but it remains to be shown if this is true for n ≥ 5. By allowing one mass to be negative, Gareth Roberts constructed a continuum of inequivalent planar central configurations of n = 5 bodies. We reinterpret Roberts' example and generalize the construction of his continuum to produce a family of continua of central configurations, each with a single negative mass. These new continua exist in even dimensional spaces R~k for k ≥ 4.