The stability of the triangular libration points for the plane circular restricted three-body problem with light pressure

TL;DR

This paper analyzes the fourth-order stability of triangular libration points in the circular restricted three-body problem considering light pressure, extending previous numerical results with explicit analytical conditions.

Contribution

It provides an explicit fourth-order Birkhoff normal form and stability conditions incorporating light pressure effects, correcting previous inaccuracies.

Findings

Derived explicit stability conditions using the Arnold-Moser theorem

Extended previous numerical results to include light pressure effects

Reduced to classical gravitational case in specific limits

Abstract

We study the fourth-order stability of the triangular libration points in the absence of resonance for the three-body problem when the infinitesimal mass is affected not only by gravitation but also by light pressure from both primaries. A comprehensive summary of previous results is given, with some inaccuracies being corrected. The Lie triangle method is used to obtain the fourth-order Birkhoff normal form of the Hamiltonian, and the corresponding complex transformation to pre-normal form is given explicitly. We obtain an explicit expression for the determinant required by the Arnold-Moser theorem, and show that it is a rational function of the parameters, whose numerator is a fifth-order polynomial in the mass parameter. Particular cases where this polynomial reduces to a quartic are described. Our results reduce correctly to the purely gravitational case in the appropriate limits, and extend numerical work by previous authors.