Abstract
A method is suggested for choosing the first approximation in Newton's iterations to expand the planetary disturbing function. The method ensures convergence of the process for any planetary orbits. An estimation is given for the number of iterations depending on a given accuracy of calculation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Broucke, R. A.: 1971,Comm. ACM 14, 32–35.
Broucke, R. A. and Smith, G.: 1971,Celes. Mech. 4, 490–499.
Chapront, J., Bretagnon, P., and Mehl, M.: 1975,Celes. Mech. 11, 379–399.
Demidovich, B. P.: 1966,Foundations of the Calculating Mathematics, Nauka, Moscow (in Russian).
Escobal, P. R.: 1968,Methods of Astrodynamics, New York.
Lautsenieks, L.: 1971,Uchenye zapisky of Latvian State University 148, 6 (in Russian).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Petrovskaya, M.S. Convergence of Newton's iteration for the expansion of the planetary disturbing function. Celestial Mechanics 15, 125–129 (1977). https://doi.org/10.1007/BF01229053
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01229053