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An analytical method for solving the problem of the satellite around theoblated Earth is discussed. Such a method goes back to Dirk Brouwer (1959) andseems to be still widely used in real applications. We reformulate in a moreconcise way the core of the method which is essentially based on a technique ofcompositions of power series. In this way we derive some general formulas whichcover, all at once, all the cases treated in the original paper and allow tocompute some terms which were omitted there. We also show some simplecomputation we performed to test the formulas.

On an analytical method for the satellite problem revisited