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 .

\PACS 34D10 70F07 34A25