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A Series-Solution Method for Cometary Orbits

Published online by Cambridge University Press:  14 August 2015

P. E. Nacozy
P. E. Nacozy*
Affiliation:
Dept. of Aerospace Engineering and Engineering Mechanics, University of Texas, Austin, Tex., U.S.A.

Abstract

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A series-solution method for highly-eccentric perturbed orbits using a modified form of Hansen's method of partial anomalies is presented. Series in Chebyshev polynomials in the eccentric anomaly of a comet and the mean anomaly at an epoch of a planet provide a theory valid to first order with respect to the masses. The first-order solution becomes a reference solution about which higher-order perturbations are obtained by the method of successive approximations. The first-order solutions are valid approximations for long durations of time, whereas the higher orders are valid only over the interval of time that is selected for the Chebyshev expansions. The method is somewhat similar to Encke's method of special perturbations except that for each successive interval of time perturbations about a first-order solution are calculated instead of perturbations about a conic solution.

Type
Part II/General Methods of Orbit Theory
Information
Symposium - International Astronomical Union , Volume 45: The Motion, Evolution of Orbits and Origin of Comets , 1972 , pp. 43 - 51
Copyright
Copyright © Reidel 1972 

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