Explicit and high-precision period approximations for the circular Sitnikov restricted four-body problem

Abstract

Abstract This brief note presents an explicit analytical approximation to the period of the circular Sitnikov restricted four-body problem. The proposed approximation achieves superior accuracy and greater algebraic compactness compared to existing analytical approximations across the full range of oscillation amplitudes. As the oscillation amplitude approaches infinity, the relative error of the approximate period with respect to the numerical exact period is less than 0.3%.