Abstract
In this paper the problem of the determination of the preliminary orbit of a celestial body is studied. We compare the results obtained by the classical Gauss’s method with those obtained by some higher-order iterative methods for solving nonlinear equations. The original problem of the determination of the preliminary orbits was posed by means of a nonlinear equation. We modify this equation in order to obtain a nonlinear system which describes the mentioned problem and we derive a new efficient iterative method for solving it. We also propose a new definition of optimal order of convergence for iterative methods for solving nonlinear systems. © 2010 Elsevier Ltd. All rights reserved.
Keywords
Orbit determination Gauss’s method Nonlinear systems Order of convergence Efficiency index
Referencia
V. Arroyo, A. Cordero, J.R. Torregrosa. Approximation of artificial satellites’ preliminary orbits: The efficiency challenge. Mathematical and Computer Modelling 54 (2011) 1802–1807.
