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Approximation of artificial satellites’ preliminary orbits: the efficiency challenge. (English) Zbl 1235.70032
Summary: 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.

##### MSC:
 70F15 Celestial mechanics 70-04 Software, source code, etc. for problems pertaining to mechanics of particles and systems
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##### References:
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