Short period elimination in satellite theory

In the present paper a completely analytic third order solution to the main problem in the theory of an artificial satellite is announced. The short period terms were eliminated by two canonical transformations of the Lie type. A third Lie transformation produced to order 4 the secular Hamiltonian which agrees through order 3 with Kozai. All the transformations were produced by computer in closed form without expansions in the eccentricity. Compared with the usual procedure of using two von Zeipel transformations, as in Brouwer's theory, this solution significantly reduces the number of terms in the transformations between the state and the averaged variables.