Abstract
Orbits repeating their ground track on the surface of the earth are found to be members of periodic-orbit families (in a synodic frame) of the tesseral problem of the Earth artificial satellite. Families of repeat ground track orbits appear as vertical bifurcations of the equatorial family of periodic orbits, and they evolve from retrograde to direct motion throughout the 180 degrees of inclination. These bifurcations are always close to the resonances of the Earth's rotation rate and the mean motion of the orbiter.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Belbruno, E., Llibre, J. and Ollé, M.: 1994, 'On the families of periodic orbits which bifurcate from the circular Sitnikov motions', Celest. Mech. & Dyn. Astr. 60, 99-129.
Broucke, R.: 1969, 'Stability of periodic orbits in the elliptic restricted three-body problem', AIAA J. 7, 1003-1009.
Coffey, S., Deprit, A. and Deprit, E.: 1994, 'Frozen orbits for satellites close to an Earth-like planet', Celest. Mech. & Dyn. Astr. 59, 37-72.
Coffey, S., Deprit, A. and Miller, B.: 1986, 'The critical inclination in artificial satellite theory', Celest. Mech. 39, 365-406.
Cutting, E., Born, G. H. and Frautnick, J. C.: 1978, 'Orbit analysis for SEASAT-A', J. Astronaut. Sci. 26, 315-342.
Davoust, E. and Broucke, R.: 1982, 'A manifold of periodic orbits in the planar general three-body problem with equal masses', Astron. Astrophys. 112, 305-320.
Decker, D. L.: 1986, 'World geodetic system 1984', in Proceedings of the Fourth International Geodetic Symposium on Satellite Positioning, Vol. 1, pp. 69-92.
Deprit, A.: 1981, 'Intrinsic variational equations in three dimensions', Celest. Mech. 24, 185-193.
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 satélites estacionarios', Revista Matemática Universidad Complutense Madrid 9, 311-333.
Hénon, M.: 1973, 'Vertical stability of periodic orbits in the restricted problem. I. Equal masses', Astron. Astrophys. 28, 415-426.
Lara, M.: 1999, 'Searching for repeat ground track orbits: a systematic approach', J. Astronaut. Sci. 47, 177-188.
Lara, M.: 1999a, SADSaM: a Software Assistant for Designing SAtelliteMissions. CNES report num. DTS/MPI/MS/MN/99-053, 75 pp.
Lara, M., Deprit, A. and Elipe, A.: 1995, 'Numerical continuation of families of frozen orbits in the zonal problem of artificial satellite theory', Celest. Mech. & Dyn. Astron. 62, 167-181.
Lara, M. and Peláez, J.: 2002, 'On the numerical continuation of periodic orbits. An intrinsic, 3-dimensional, differential, predictor-corrector algorithm', Astron. Astrophys. 389, 692-701.
Milani, A., Nobili, A. M. and Farinella, P.: 1987, Non-gravitational Perturbations and Satellite Geodesy, Adam Hilger.
Ollé, M. and Pacha, J. R.: 1999, 'The 3D elliptic restricted three-body problem: periodic orbits which bifurcate from limiting restricted problems. Complex instability', Astron. Astrophys. 351, 1149-1164.
Robin, I. A. and Markellos, V. V.: 1980, 'Numerical determination of three-dimensional periodic orbits generated from vertical self-resonant orbits', Celest. Mech. 21, 395-434.
Sabol, C., Draim, J. and Cefola, P. J.: 1996, 'Refinement of a sun-synchronous, critically inclined orbit for the ELLIPSOTM personal communication system', J. Astronaut. Sci. 44, 467-489.
Siegel, C. L. and Moser, J. K.: 1971, Lectures on Celestial Mechanics, Springer, Berlin.
Szebehely, V.: 1967, Theory of Orbits-The Restricted Problem of Three Bodies, Academic Press, New York.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lara, M. Repeat Ground Track Orbits of the Earth Tesseral Problem as Bifurcations of the Equatorial Family of Periodic Orbits. Celestial Mechanics and Dynamical Astronomy 86, 143–162 (2003). https://doi.org/10.1023/A:1024195900757
Issue Date:
DOI: https://doi.org/10.1023/A:1024195900757