López Ortí, J.A.; Marco Castillo, F.J.; Martínez Usó, M.J. A Geometrical Study about the Biparametric Family of Anomalies in the Elliptic Two-Body Problem with Extensions to Other Families. Algorithms2024, 17, 66.
López Ortí, J.A.; Marco Castillo, F.J.; Martínez Usó, M.J. A Geometrical Study about the Biparametric Family of Anomalies in the Elliptic Two-Body Problem with Extensions to Other Families. Algorithms 2024, 17, 66.
López Ortí, J.A.; Marco Castillo, F.J.; Martínez Usó, M.J. A Geometrical Study about the Biparametric Family of Anomalies in the Elliptic Two-Body Problem with Extensions to Other Families. Algorithms2024, 17, 66.
López Ortí, J.A.; Marco Castillo, F.J.; Martínez Usó, M.J. A Geometrical Study about the Biparametric Family of Anomalies in the Elliptic Two-Body Problem with Extensions to Other Families. Algorithms 2024, 17, 66.
Abstract
In the present paper, we efficiently solve the two-body problem for extreme cases such as those with high eccentricities. The use of numerical methods, with the usual variables, cannot maintain the perihelion passage accurately. In previous articles, we have verified that this problem is treated more adequately through temporal reparametrizations related to the mean anomaly through the partition function. The biparametric family of anomalies, with an appropriate partition function, allows a systematic study of these transformations. In the present work, we consider the elliptical orbit as a meridian section of the ellipsoid of revolution, and the partition function depends on two variables raised to specific parameters. One of the variables is the mean radius of the ellipsoid at the secondary, and the other is the distance to the primary. One parameter regulates the concentration of points in the apoapsis region, and the other produces a symmetrical displacement between the polar and equatorial regions. The three most used geodesy latitude variables are also studied, resulting in one not belonging to the biparametric family. However, it is in the one introduced now, which implies an extension of the biparametric method. The results obtained by the method presented here now allow a causal interpretation of the operation of numerous reparametrizations used in the study of orbital motion.
Keywords
Mathematical models in engineering; Celestial mechanics; Two-body problem; Orbital motion; Analytical regularization of the step size.
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
