Abstract
We generate families of planar periodic orbits emanating from the geostationary points, both stable and unstable. We show that, even for the unstable points, it is possible to have stable periodic orbits.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arnold, V. I.: 1961, 'The stability of the equilibrium position of a Hamiltonian system of ordinary differential equations in the general elliptic case', Soviet Math. Dokl. 2, 247–249.
Blitzer, L., Boughton, E. M., Kang, G. and Page, R. M.: 1962, 'Effect of the ellipticity of the equator on 24-hour nearly circular satellite orbits', J. Geoph. Res. 67, 329–335.
Blitzer, L.: 1965, 'Equilibrium position and stability of 24-hour satellite orbits', J. Geoph. Res. 70, 3987–3992.
Deprit, A. and Henrard, J.: 1967, 'Natural families of periodic orbits', Astron. J. 72, 158–172.
Deprit, A. and López, T. J.: 1996, 'Estabilidad orbital de sat´elites estacionarios', Rev. Matem. Univ. Complutense Madrid 9, 311–333.
Gedeon, G. S.: 1969, 'Tesseral resonance effects on satellite orbits', Celest. Mech. 1, 167–189.
Hénon, M.: 1965, 'Exploration num´erique du probl`eme restreint. II Masses ´egales, stabilit´e des orbites périodiques', Ann. Astrophys. 28, 992–1007.
Howard, J.: 1990, 'Spectral stability of relative equilibria', Celest. Mech. & Dyn. Astr. 48, 267–288.
Kamel, A., Ekman, D. and Tibbitts, R.: 1973, 'East-west stationkeeping requirements of nearly synchronous satellites due to Earth's triaxiality and luni-solar effects', Celest. Mech. 8, 129–148.
Lara, M., Deprit, A. and Elipe, A.: 1995, 'Numerical continuation of frozen orbits for the zonal problem', Celest. Mech. & Dyn. Astr. 62, 167–181.
Lara, M.: 1996, 'On numerical continuation of families of periodic orbits in a parametric potential', Mech. Res. Comm. 23, 291–298.
Milani, A., Nobili, A. M. and Farinella, P.: 1987, Non-Gravitational Perturbations and Satellite Geodesy, Adam Hilger.
Morando, B.: 1963, 'Orbites de résonance des satellites de 24 heures', Bull. Astronom. 24, 47–67.
Musen, P. and Bailie, A. E.: 1962, 'On the motion of a 24-hour satellite', J. Geoph. Res. 67, 1123–1132.
Oberti, P.: 1994, 'The main problem of geosynchronous satellite theory around an equilibrium position', Astron. Astrophys. 284, 281–284.
Soop, E. M.: 1994, Handbook to Geostationary Orbits, Kluwer Academic Publishers, Dordrecht.
Szebehely, V.: 1967, Theory of Orbits, Academic Press, New York.
Wytrzyszczak, I.: 1998, 'Stationary orbits around the Earth and Mars', Artif. Satel. 33, 11–23.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lara, M., Elipe, A. Periodic Orbits Around Geostationary Positions. Celestial Mechanics and Dynamical Astronomy 82, 285–299 (2002). https://doi.org/10.1023/A:1015046613477
Issue Date:
DOI: https://doi.org/10.1023/A:1015046613477