What question did this study set out to answer?

To explore specific central configurations in the five-body problem that are represented by convex pentagons with right angles.

April 11, 2026Open Access

Some convex central configurations in the planar five-body problem

Key Points

To explore specific central configurations in the five-body problem that are represented by convex pentagons with right angles.
Analyzed convex irregular pentagons with one to three right interior angles.
Examined cases where three right angles can be consecutive or non-consecutive.
Considered central configurations both with and without symmetries.
Identified various central configurations for five bodies positioned at the vertices of convex pentagons.
Demonstrated that configurations can vary based on the arrangement of right angles.

Abstract

Abstract Convex irregular pentagons can have one, two, or three right interior angles. There are two possibilities for the case with three right interior angles: The right angles can be consecutive or non-consecutive. This article investigates some central configurations of the five-body problem in a plane with the following properties: The bodies are at the vertices of a convex pentagon, and three interior angles of the pentagon are right angles. Central configurations are obtained both with and without symmetries.

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