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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References

1. A. Einstein, Ann. d. Phys. 49 (1916) 769.         [ Links ]

2. A. Einstein, Berl. Ber. (1915) 778, 799, 844.         [ Links ]

3. G. V. Kraniotis, S. B. Whitehouse, Compact calculation of the perihelion precession of Mercury in general relativity, the cos-mological constant and Jacobi's inversion problem, Classical and Quantum Gravity, 20 (2003).         [ Links ]

4. K. Wilhelm, B.N. Dwivedi, Secular perihelion advances of the inner planets and asteroid Icarus, New Astronomy, 31 (2014) 51-55.         [ Links ]

5. K. Schwarzschild, Berl. Ber. 189 (1916)        [ Links ]

6. A. F. Bogoroski, Eisten field equations and their applications in astronomy. (University of Kiev 1962).         [ Links ]

7. http://astronomy.swin.edu.au/cosmos/S/Sidereal+Period

8. https://solarsystem.nasa.gov/planets