  Linear equations with periodic coefficients describe the behavior of various
dynamical systems. This studying is devoted to their applications to the
planetary restricted three-body problem (RTBP). Here we consider the Laplace
method for determining perturbation in coordinates. We show that classical
theory of perturbation leads to a linear equation with periodic coefficients.
Than we present a modification of Laplace method. This modification allows us
to study motion over a longer time interval.
