Quasi-Analytical Solution of Kepler’s Equation as an Explicit Function of Time

Beloiarov, A. N.; Beloiarov, V. A.; Cruz-Gómez, R. C.; Monzón, C. O.; Romero, J. L.

doi:10.3390/math12132108

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Open AccessArticle

Quasi-Analytical Solution of Kepler’s Equation as an Explicit Function of Time

by

A. N. Beloiarov

,

V. A. Beloiarov

,

R. C. Cruz-Gómez

^*

,

C. O. Monzón

and

J. L. Romero

Departamento de Física, Universidad de Guadalajara, Blvd. Marcelino García Barragán y Calzada Olimpica, Guadalajara 44840, JA, Mexico

^*

Author to whom correspondence should be addressed.

Mathematics 2024, 12(13), 2108; https://doi.org/10.3390/math12132108

Submission received: 14 May 2024 / Revised: 29 June 2024 / Accepted: 2 July 2024 / Published: 4 July 2024

(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)

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Abstract

Although Kepler’s laws can be empirically proven by applying Newton’s laws to the dynamics of two particles attracted by gravitational interaction, an explicit formula for the motion as a function of time remains undefined. This paper proposes a quasi-analytical solution to address this challenge. It approximates the real dynamics of celestial bodies with a satisfactory degree of accuracy and minimal computational cost. This problem is closely related to Kepler’s equation, as solving the equations of motion as a function of time also provides a solution to Kepler’s equation. The results are presented for each planet of the solar system, including Pluto, and the solution is compared against real orbits.

Keywords: Kepler’s equation; quasi-analytical solution; celestial bodies; Kepler’s laws

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MDPI and ACS Style

Beloiarov, A.N.; Beloiarov, V.A.; Cruz-Gómez, R.C.; Monzón, C.O.; Romero, J.L. Quasi-Analytical Solution of Kepler’s Equation as an Explicit Function of Time. Mathematics 2024, 12, 2108. https://doi.org/10.3390/math12132108

AMA Style

Beloiarov AN, Beloiarov VA, Cruz-Gómez RC, Monzón CO, Romero JL. Quasi-Analytical Solution of Kepler’s Equation as an Explicit Function of Time. Mathematics. 2024; 12(13):2108. https://doi.org/10.3390/math12132108

Chicago/Turabian Style

Beloiarov, A. N., V. A. Beloiarov, R. C. Cruz-Gómez, C. O. Monzón, and J. L. Romero. 2024. "Quasi-Analytical Solution of Kepler’s Equation as an Explicit Function of Time" Mathematics 12, no. 13: 2108. https://doi.org/10.3390/math12132108

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Quasi-Analytical Solution of Kepler’s Equation as an Explicit Function of Time

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