Abstract This paper deals with the coverage analysis problem of elliptical orbits. An algorithm based on ergodic theory, for long-term coverage of elliptical orbits, is proposed. The differential form of the invariant measure is constructed via the perturbation on mean orbital elements resulted from the $J_{2}$ term of non-spherical shape of the earth. A rigorous proof for this is then given. Different from the case of circular orbits, here the flow and its space of the dynamical system are defined on a physical space, and the real-value function is defined as the characteristic function on station mask. Therefore, the long-term coverage is reduced to a double integral via Birkhoff--Khinchin theorem. The numerical implementation indicates that the ergodic algorithm developed is available for a wide range of eccentricities.
Fund: Project supported by the Innovation
Foundation of BUAA (Beijing University of Aeronautics and
Astronautics) for PhD Graduates, and the National Natural Science
Foundation of China (Grant No 60535010).
Cite this article:
Xu Ming(徐明) and Xu Shi-Jie(徐世杰) An ergodic algorithm for long-term coverage of elliptical orbits 2008 Chin. Phys. B 17 343
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