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Revista mexicana de física
versión impresa ISSN 0035-001X
Rev. mex. fis. vol.61 no.5 México sep./oct. 2015
Investigación
The Jacobi elliptic functions and their applications in the advance of mercury's perihelion
A. H. Salas S.*, J. E. Castillo H.** y C. E. Restrepo R.***
* Grupo FIZMAKO, Universidad de Caldas, Departamento de Matemáticas, Universidad Nacional de Colombia Sede Manizales-Nubia Campus. e-mail: asalash2002@yahoo.com
** Grupo FIZMAKO, Universidad Distrital Francisco Jose de Caldas, Bogotá. e-mail: jcastillo@udistrital.edu.co
*** Grupo FIZMAKO, Universidad de Cundinamarca, Universidad Distrital Francisco Jose de Caldas, Bogotá. e-mail: carloserestrepor@gmail.com
Received 19 May 2015.
Accepted 28 July 2015.
Abstract
In this paper we find the exact solution of the nonlinear differential equation describing the trajectory of mercury considering relativistic effects. Instead of the classical perturbation method we use the Jacobi elliptic functions to obtain the exact solution. The deviation of the perihelion of Mercury and other planets is calculated. The results may be of great interest to astronomers and for those interested in the study of nonlinear differential equations.
Keywords: Perihelion; aphelion; analytic solution; Jacobi elliptic functions.
PACS: 02.30Gp, 03.65Fd, 05.45 Yv
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