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Abstract <p>In the paper, the main aspects of practical calculations by the formulas of Keplerian motion have been considered. The initial value under consideration is the mean anomaly and five other constant parameters. Much attention has been paid to solving the Kepler equation. An overview of the methods for solving has been given. A method for specifying the accuracy of calculations with allowance for the limited accuracy of representing numbers in a computer system has been considered. Examples of solving the Kepler equation and examples of motion trajectories have been provided. According to the considered concept, an optimal program for calculations has been compiled in the programming languages C/C++, Fortran, Python and offered on the Internet pages. The user has been given the opportunity to select a method for solving the Kepler equation from those considered in the paper.</p>

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Efficient Computations in Keplerian Motion and Kepler’s Equation

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • I. A. Moiseev,
  • N. V. Emelyanov

摘要

Abstract

In the paper, the main aspects of practical calculations by the formulas of Keplerian motion have been considered. The initial value under consideration is the mean anomaly and five other constant parameters. Much attention has been paid to solving the Kepler equation. An overview of the methods for solving has been given. A method for specifying the accuracy of calculations with allowance for the limited accuracy of representing numbers in a computer system has been considered. Examples of solving the Kepler equation and examples of motion trajectories have been provided. According to the considered concept, an optimal program for calculations has been compiled in the programming languages C/C++, Fortran, Python and offered on the Internet pages. The user has been given the opportunity to select a method for solving the Kepler equation from those considered in the paper.