An analytical theory for the orbit of nereid

A complete analytical dynamic theory for the motion of Nereid has been constructed, accurate to approximately 0.01 arc second over several hundred years. The solution uses the Lie transform approach advanced by Deprit and is consistent with respect to the magnitudes of the disturbing functions, including all perturbations to an accuracy of 10^–8 relative to the two-body potential (oblateness and third-body). Multiple short-period variables in the third-body perturbations are related via the ratio of their mean motions, reducing the number of independent variables. Extensive use is made of expansions giving trigonometric functions of the true anomaly as analytical Fourier series in the mean anomaly. Initial constants and mass parameters come from the data obtained during the Voyager II encounter with Neptune in 1989.