Abstract
The object of this investigation is to make a critical comparison and evaluation of three commonly used methods of special perturbations. The actual orbits used for this comparison were typical of lunar shots. Although conclusions apply directly to lunar orbits, more general conclusions may also be drawn.
The methods considered are those of Cowell and Encke, as well as the device of the variation of parameters. Also included is an evaluation of two numerical integration schemes, a fourth-order Runge-Kutta-Gill, and a sixth-order backward difference scheme.
Rather than compare the results of these methods against each other, an absolute standard of comparison, namely, the exact solution of the problem of two fixed centers of gravitation, is chosen. Three lunar orbits were computed with high precision.
The reasons for this choice and the various alternatives available are discussed. Also included is a discussion of the solution of the problem of two fixed centers.
The comparison of the results leads to the conclusion that the Encke method is superior in speed and accuracy for trajectories for which the two-body problem furnishes a good local approximation (with the variation of parameters comparable as regards accuracy, but inferior with regard to speed). Cowell’s method seems markedly worse than Encke’s method in accuracy and speed, but is much simpler to program.
The limitations of the Encke method and the method of variation of parameters are discussed, and procedures for the removal of these difficulties are recommended.
This report was prepared from a study carried out at Republic Aviation Corporation for the Aeronautical Research Laboratories at Wright Field [10]. The authors wish to express their appreciation for the active interest and participation of Mr. K. E. Kissell and Dr. K. G. Guderley of the Aeronautical Research Laboratories in the formulation of the problem and throughout the course of the investigation.
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Pines, S., Payne, M., Wolf, H. (1962). Comparison of Special Perturbation Methods in Celestial Mechanics with Application to Lunar Orbits. In: Fleisig, R., Hine, E.A., Clark, G.J. (eds) Lunar Exploration and Spacecraft Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-6439-7_3
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DOI: https://doi.org/10.1007/978-1-4899-6439-7_3
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