COMPUTERIZED EXPANSIONS IN ELLIPTIC MOTION

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Abstract
The functions of the Keplerian elliptic motion are expanded with respect to mean anomaly and the eccentricity by applying Poincare's method of continuation in a direct manner to the equations of motion. Two algorithms are proposed; both lead to programs by which the classical expansions are constructed symbolically and automatically on a computer in double precision arithmetic. Even to as high a degree as 30 in the eccentricity, the procedures are remarkably swift. Special care is taken here in describing significant error controls at each step of the recurrences.

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