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

The equations of motion of planar elliptic restricted three body problem are transformed to four decoupled Hill's equations. By using the Floquet theorem analytic solution to the oscillator equations with time dependent periodic coefficients are presented. We show that the new analytic approach is valid for system parameters $0 < e \leq 0.05$ and $0 < \mu \leq 0.01$ where $e$ denotes the eccentricity of primaries while $\mu$ is the mass parameter, respectively. We also clarify the transformation details that provide the applicability of the method.