Year: 2026
Type: article
Abstract: I study central configurations in the four-body problem, i.e., configurations in which the forces on all the bodies point to a fixed, single point in space. The newly formulated pair-space formalism yields a set of vectorial equations that fully characterize such configurations. I investigate a sub-class of solutions in which at least two pairs of inter-body distances are equal. The only such non-collinear configurations are the tetrahedron (the unique nonplanar configuration), kites and the isosceles trapezium. The specific shapes (internal angles) are determined by the ratio of the masses of the bodies. Mathematical expressions are given for all these relations.
Author: Alon Drory
Institution: Afeka College of Engineering
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W7204092185