The solution of the generalized Kepler's equation
- López, R. 13
- Hautesserres, D. 2
- San-Juan, J.F. 3
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1
Centro de Investigación Biomédica de La Rioja
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2
Centre National D'Etudes Spatiales
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3
Universidad de La Rioja
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ISSN: 0035-8711
Year of publication: 2018
Volume: 473
Issue: 2
Pages: 2583-2589
Type: Article
More publications in: Monthly Notices of the Royal Astronomical Society
Abstract
In the context of general perturbation theories, the main problem of the artificial satellite analyses the motion of an orbiter around an Earth-like planet, only perturbed by its equatorial bulge or J2 effect. By means of a Lie transform and the Krylov-Bogoliubov-Mitropolsky method, a first-order theory in closed form of the eccentricity is produced. During the evaluation of the theory, it is necessary to solve a generalization of the classical Kepler's equation. In this work, the application of a numerical technique and three initial guesses to the generalized Kepler's equation are discussed. © 2017 The Authors.