Luni-solar perturbations in the extended phase space representation of the Vinti problem
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Perturbation theory is applied to the Vinti problem-motion about an oblate spheroid-to include the gravitational effects of the sun and moon. The problem is formulated using the extended phase space method which introduces a new independent variable similar to the true anomaly. The disturbing Hamiltonian H1 for third bodies is of order J22 (second order) and the final goal is a theory including second order short and long period terms and third order secular terms. The current paper however carries the development only to the second order in the secular terms and the first order in the periodic terms. Problems of including the higher orders are discussed. Therefore, in the development of H1 all terms of order 10-9 or larger are retained. The lunar emphemeris retains terms to e2 in the lunar eccentricity. The perturbation analysis is carried out by means of Lie series and is developed through the first order only which is consistent with the final accuracy desired. The generating function W1 is obtained and separated into the long period, short period and secular terms. From W1 the coordinates are defined from the Lie series by means of a transformation equation. These coordinates are non-singular for small eccentricity and inclination. Because of the complexity of the equations all algebraic computations were accomplished by means of a computerized Poisson series manipulator developed at the Naval Research Laboratory. 1978.
