Abstract
In the zonal problem of a satellite around the Earth, we continue numerically natural families of periodic orbits with the polar component of the angular momentum as the parameter. We found three families; two of them are made of orbits with linear stability while the third one is made of unstable orbits. Except in a neighborhood of the critical inclination, the stable periodic (or frozen) orbits have very small eccentricities even for large inclinations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barton, D., Williers, I.M. and Zahar, R. V. M.: 1971, ‘Taylor Series Methods for Ordinary Differential Equations—An Evaluation’, in J. R. Rice (ed.),Mathematical Software, pp. 369–390, Academic Press, New York.
Birkhoff, G.: 1917,Trans. Amer. Math. Soc. 18, 199–300.
Broucke, R.: 1994,Celest. Mech. 58, 99–123.
Coffey, S., Deprit, A. and Miller, B.: 1986,Celest. Mech. 39, 365–406.
Coffey, S., Deprit, A. and Deprit, E.: 1994,Celest. Mech. 59, 37–72
Deprit, A.: 1981,Celest. Mech. 24, 185–193.
Deprit, A. and Zahar, R. V. M.: 1966,Z. Angew. Math. Phys. 17, 425–430.
Deprit, A. and Henrard, J.: 1967,Astron. J. 72, 158–172.
Deprit, A. and Price, J.: 1965,Astron. J. 70, 836–846.
Legendre, P.: 1994, Private communication.
Palmore, J.: 1982,Celest. Mech. 27, 151–156.
Wolfram, S.: 1991,Mathematica. A System for Doing Mathematics by Computer, Second Edition. Addison-Wesley Publishing Company, Inc..
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lara, M., Deprit, A. & Elipe, A. Numerical continuation of families of frozen orbits in the zonal problem of artificial satellite theory. Celestial Mech Dyn Astr 62, 167–181 (1995). https://doi.org/10.1007/BF00692085
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00692085