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

A. N. Beloiarov, V. A. Beloiarov, R. C. Cruz-Gómez (), C. O. Monzón and J. L. Romero
Additional contact information
A. N. Beloiarov: Departamento de Física, Universidad de Guadalajara, Blvd. Marcelino García Barragán y Calzada Olimpica, Guadalajara 44840, JA, Mexico
V. A. Beloiarov: Departamento de Física, Universidad de Guadalajara, Blvd. Marcelino García Barragán y Calzada Olimpica, Guadalajara 44840, JA, Mexico
R. C. Cruz-Gómez: Departamento de Física, Universidad de Guadalajara, Blvd. Marcelino García Barragán y Calzada Olimpica, Guadalajara 44840, JA, Mexico
C. O. Monzón: Departamento de Física, Universidad de Guadalajara, Blvd. Marcelino García Barragán y Calzada Olimpica, Guadalajara 44840, JA, Mexico
J. L. Romero: Departamento de Física, Universidad de Guadalajara, Blvd. Marcelino García Barragán y Calzada Olimpica, Guadalajara 44840, JA, Mexico

Mathematics, 2024, vol. 12, issue 13, 1-17

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 (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:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/13/2108/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/13/2108/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:13:p:2108-:d:1429178

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().