Physics
Scientific paper
Apr 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986cemec..38..377m&link_type=abstract
Celestial Mechanics (ISSN 0008-8714), vol. 38, April 1986, p. 377-387.
Physics
1
Earth Orbits, Satellite Perturbation, Zonal Harmonics, Chaos, Numerical Integration
Scientific paper
With the Hamiltonian parameters developed for the two-fixed-centers problem, a simple and very accurate expression of the 'quasi-integral' can be given for the motion of artificial satellites perturbed by the earth's zonal harmonics. This motion can be considered as integrable. A theoretical analysis shows that Henon's (1966) 'semiergodic regions' or 'chaotic regions' are extremely small in this problem, and almost all orbits are of the 'regular' or 'quasi-periodic' type. Furthermore, the relative difference between the true motion and the corresponding integrable motion remains forever less than 10 to the -14th for all regular orbits, even in the vicinity of critical inclinations. For chaotic orbits this very small difference remains verified at least for centuries. Nevertheless, there are some exceptional orbits that finally diverge from the integrable model.
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