Expansion of the secular and resonant parts of the disturbing function in the theory of the motion of long-period comets

A method for the expansion of the disturbing function in the restricted circular three-body problem for cometary orbits is proposed. A formula is obtained for the development of functions in the elliptic motion as the power series of epsilon = (1 - e)/2, (where e is the eccentricity of the cometary orbit). For long-period comets the convergence region of these series extends to distances where planetary perturbations can be ignored. Formulas and recurrence relations for the calculations of the secular and resonant parts of the perturbation are derived.