On the Nonexistence of Centered Co-Circular Central Configurations With Three Unequal masses

TL;DR

This paper proves that certain symmetric three-mass configurations cannot exist in a general n-body problem with power-law potential, especially when most masses are equal and the three special masses are distinct or improperly arranged.

Contribution

It establishes the nonexistence of centered co-circular central configurations with three arbitrary masses in specific mass arrangements, extending understanding of n-body problem configurations.

Findings

Centered co-circular configurations do not exist under specified conditions.

Nonexistence holds for systems with mostly equal masses and three distinct or improperly arranged special masses.

Results apply to general power-law potential n-body problems.

Abstract

This paper examines the existence of centered co-circular central configurations in the general power-law potential n-body problem. We prove the nonexistence of such configurations when the system consists of n-3 equal masses and three arbitrary masses, under the condition that the three special masses are distinct or, if two of them are equal, not arranged in a specific manner.