A second-and higher-order perturbation analysis of two-body trajectories

An approach to the development of a second- andhigher-order perturbation theory for twobody trajectories is presented. It is shown that the higher order analysis can be developed in a systematic manner in terms of series solutionsto the two-body problem as functions of the timevariable. Simple algebraic recursive formulas forthe determination of the series coefficients are derived and the radii of convergence for these series solutions are determined. Their accuracy and the rate of convergence are investigated in a number of numerical cases.