A Review on Iterative and Series Solutions for Kepler's Equation
The purpose is to review iterative and series methods applied to the solution of Kepler’s equation, which is solved over the entire range of elliptic motion. The method whose results will work as a reference is the Newton-Raphson’s numerical method. The results will be discussed around the number of iterations required until the convergence criterion is satisfied: residual error in eccentric anomaly lower; and the processing time (for iterative and series-based methods). The advantages and drawbacks of each method will be presented.
A Review on Iterative and Series Solutions for Kepler's Equation
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DOI: https://doi.org/10.22533/at.ed.8292128103
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Palavras-chave: Kepler’s Equation; Numerical Methods; Iterative Solutions; Series Solutions
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Keywords: Kepler’s Equation; Numerical Methods; Iterative Solutions; Series Solutions
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Abstract:
The purpose is to review iterative and series methods applied to the solution of Kepler’s equation, which is solved over the entire range of elliptic motion. The method whose results will work as a reference is the Newton-Raphson’s numerical method. The results will be discussed around the number of iterations required until the convergence criterion is satisfied: residual error in eccentric anomaly lower; and the processing time (for iterative and series-based methods). The advantages and drawbacks of each method will be presented.
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Número de páginas: 15
- Mariana P Melo
- João F N Oliveira
- Leonardo O Ferreira
- Pedro N Nishimoto
- Roberta V Garcia
- Paula C P M Pardal
