EL PROBLEMA DE LOS DOS CUERPOS Y EL PROBLEMA PRINCIPAL DEL SATELITE ARTIFICIAL EN ECUACIONES DIFERENCIALES DE PRIMER ORDEN

José Gregorio Portilla B.

doi:10.18257/raccefyn.20(76).1996.3016

Vol. 20 No. 76 (1996), Natural Sciences

Vol. 20 No. 76 (1996)

TWO BODY AND MAIN SATELLITE PROBLEMS IN DIFFERENTIAL EQUATIONS OF FIRST ORDER

Natural Sciences

https://doi.org/10.18257/raccefyn.20(76).1996.3016

Published 2024-08-09

José Gregorio Portilla B.⁺⁻

José Gregorio Portilla B.

Observatorio Astronómico Nacional, Facultad de Ciencias, Universidad Nacional de Colombia. Apartado Aéreo 2584, Santafé de Bogotá, Colombia.

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How to Cite

Portilla B., J. G. (2024). TWO BODY AND MAIN SATELLITE PROBLEMS IN DIFFERENTIAL EQUATIONS OF FIRST ORDER. Revista De La Academia Colombiana De Ciencias Exactas, Físicas Y Naturales, 20(76), 25–32. https://doi.org/10.18257/raccefyn.20(76).1996.3016

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Abstract

A derivation of the differential equations which govern the. three-dimensional two-body problem utilizing variables such as the velocity, azimuth, flight-path angle and spherical coordinates is presented. Besides, the deduction of the equations is presented when a perturbation force appears due to oblateness of the central body. Direct transformation between these and rectangular coordinates (and inverse) is commented.

https://doi.org/10.18257/raccefyn.20(76).1996.3016

Keywords

Celestial mechanics | two-body problem | main artificial satellite problem | differential equations | numerical integration

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References

Baldwin, B. & Y. Sheaffer. 1971. Ablation and breakup of large meteoroids during atmospheric entry. J. Geophys. Res. 76 (19): 4653-4668.

Brouwer, D. 1959. Solution of the problem of artificial satellite theory without drag. Astron. J. 64 (1274): 378-397.

Brouwer, D. & G. Clemence. 1961. Methods of celestial mechanics. Academic Press, Londres.

Cowell, P. & A. Crommelin. 1910. Investigation of the motion of Halley's comet from 1759-1910. Appendix to Greenwich Observations 1909. Neill, Bellevue, Londres.

Everhart, E. 1985. An efficient integrator that uses Gauss-Radau spacings. Dynamics of comets: Their origin and evolution, Carusi y Valsecchi (eds.): 185-202.

Feeley, T. & J. Speyer. 1993. Approximate optimal guidance for the advanced launch system. NASA Contractor Report 4568.

Garfinkel, B. 1959. The orbit of a satellite of an oblate planet. Astron. J. 64 (1274): 353-367.

Goldstein, H. 1963. Mecánica clásica. Aguilar Ediciones, Madrid.

Irigoyen, R. & C. Simó. 1993. Non-integrability of the J2 problem. Cel. Mech. & Dyn. Astron. 55 (3): 281-287.

Kaula, W. 1966. Theory of satellite geodesy. Blaisdell Publ. Comp., Waltham, Massachusetts.

Kinoshita, H. & H. Nakai. 1989. Numerical integration methods in dynamical astronomy. Cel. Mech. & Dyn. Astron. 45 (3): 231-244.

Kinoshita, H. & H. Yoshida. 1991. Symplectic integrators and their application to dynamical astronomy. Cel. Mech. & Dyn. Astron. 50 (1): 59-71.

Kosai, Y. 1959. The motion of close Earth satellites. Astron. J. 64 (1274): 367-377.

McCuskey, S. 1963. Introduction to celestial mechanics. Addison-Wesley, Reading, Massachusetts.

Seidelmann, P. K. 1992. Explanatory supplement to the astronomical almanac. University Science Books, Mill Valley, California.

Standish, E. 1982. The JPL planetary ephemerides. Cel. Mech. & Dyn. Astron. 26 (2): 181-186.

Stiefel, E. & G. Scheifele. 1971. Linear and regular celestial mechanics. Springer-Verlag, Berlin.

Teukolsky, S. 1992. Numerical recipes in Fortran. Cambridge Univ. Press, New York.

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