A new perturbative solution to the motion around triangular Lagrangian points in the elliptic restricted three-body problem

Abstract

The equations of motion of the planar elliptic restricted three-body problem are transformed to four decoupled Hill’s equations. By using the Floquet theorem, a perturbative solution to the oscillator equations with time-dependent periodic coefficients are presented. We clarify the transformation details that provide the applicability of the method. The form of newly derived equations inherently comprises the stability boundaries around the triangular Lagrangian points. The analytic approach is valid for system parameters 0 < e le 0.05 and 0 < mu le 0.01 where e denotes the eccentricity of the primaries, while mu is the mass parameter. Possible application to known extrasolar planetary systems is also demonstrated.