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accurate to 10"9 analytic programming language Andoyer expansion Applying the averaging averaging operator basic parameters Broucke coefficients computation of terms constant term constants of integration contain cross-effects deduce derive the expansion derive the value determine differential operators disturbing function electronic machines Equations 48 equations for terms equations of motion expand the differential expanded form extraction operator Faa-de-Bruno form suitable FORMAC formation given characteristic higher characteristics Hill and Brown Hill-Brown theory homogeneous polynomials iteration step iteration to iteration iterative procedure iterative process linear equations lunar theory mean orbital eccentricity method of iteration monomial operators in powers orbital inclination orders and higher parallax Performing Organization positive characteristics powers and products prescribed characteristic process of iteration rectangular coordinates right-hand side solar orbit Substituting 14 Taking into account Taylor operator terms of higher terms with positive theories of satellites trigonometric series value of c0 w3 _ y2 and a2