中国物理B ›› 2008, Vol. 17 ›› Issue (1): 343-349.doi: 10.1088/1674-1056/17/1/060

• GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS • 上一篇    下一篇

An ergodic algorithm for long-term coverage of elliptical orbits

徐明, 徐世杰   

  1. Beijing University of Aeronautics and Astronautics, Beijing 100083, China
  • 出版日期:2008-01-20 发布日期:2008-01-20
  • 基金资助:
    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).

An ergodic algorithm for long-term coverage of elliptical orbits

Xu Ming(徐明)† and Xu Shi-Jie(徐世杰)   

  1. Beijing University of Aeronautics and Astronautics, Beijing 100083, China
  • Online:2008-01-20 Published:2008-01-20
  • Supported by:
    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).

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摘要： 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.

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.

Key words: ergodic algorithm, coverage analysis, elliptical orbit

中图分类号:  (Orbit determination and improvement)

  • 95.10.Eg
95.10.Ce (Celestial mechanics (including n-body problems))