Revisiting the Dynamics of Two-Body Problem in the Framework of the Continued Fraction Potential

Sergey Ershkov (), Ghada F. Mohamdien, M. Javed Idrisi and Elbaz I. Abouelmagd
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Sergey Ershkov: Department of Scientific Researches, Plekhanov Russian University of Economics, Scopus Number 60030998, 36 Stremyanny Lane, 117997 Moscow, Russia
Ghada F. Mohamdien: Celestial Mechanics and Space Dynamics Research Group (CMSDRG), Astronomy Department, National Research Institute of Astronomy and Geophysics (NRIAG), Helwan 11421, Cairo, Egypt
M. Javed Idrisi: Department of Mathematics, College of Natural and Computational Science, Mizan-Tepi University, Tepi 121, Ethiopia
Elbaz I. Abouelmagd: Celestial Mechanics and Space Dynamics Research Group (CMSDRG), Astronomy Department, National Research Institute of Astronomy and Geophysics (NRIAG), Helwan 11421, Cairo, Egypt

Mathematics, 2024, vol. 12, issue 4, 1-12

Abstract: In this analytical study, a novel solving method for determining the precise coordinates of a mass point in orbit around a significantly more massive primary body, operating within the confines of the restricted two-body problem (R2BP), has been introduced. Such an approach entails the utilization of a continued fraction potential diverging from the conventional potential function used in Kepler’s formulation of the R2BP. Furthermore, a system of equations of motion has been successfully explored to identify an analytical means of representing the solution in polar coordinates. An analytical approach for obtaining the function t = t ( r ), incorporating an elliptic integral, is developed. Additionally, by establishing the inverse function r = r ( t ), further solutions can be extrapolated through quasi-periodic cycles. Consequently, the previously elusive restricted two-body problem (R2BP) with a continued fraction potential stands fully and analytically solved.

Keywords: dynamics of a mass point; restricted two-body problem (R2BP); continued fraction potential; Kepler’s formulation of R2BP (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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