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Abstract

The disturbing functions are required to be expanded as explicit ones of time and orbital elements.

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References

  1. Wu LD, Wang HB, Ma JY (2012) Inclination function in satellite dynamics. Science Press, Beijing

    Google Scholar 

  2. Gaposchkin EM (1973) 1973 Smithsonian standard earth (III). SAO Special Report No. 353, Smithsonian Astrophysical Observatory, Cambridge, Massachusetts

    Google Scholar 

  3. Wu LD (2011) Orbit and detection of artificial satellites and space debris. China Science and Technology Press, Beijing (In Chinese)

    Google Scholar 

  4. Kaula WM (1966) Theory of satellite geodesy: applications of satellites to geodesy. Blaisdell Publishing Company

    Google Scholar 

  5. Kaula WM (1961) Analysis of gravitational and geometric aspects of geodetic utilization of satellites. Geophys J Int 5(2):104–133

    Article  ADS  Google Scholar 

  6. Kaula WM (1962) Development of the lunar and solar disturbing function for a close satellite. Astron J 67(5):300–303

    Article  ADS  MathSciNet  Google Scholar 

  7. Plummer HC (1918) An introductory treatise on dynamical astronomy. Cambridge University Press, London

    Google Scholar 

  8. Cayley A (1861) Tables of the developments of functions in the theory of elliptic motion. Mem R Astron Soc 29:191–306

    ADS  Google Scholar 

  9. Cherniack JR (1972) Computation of Hansen coefficients. SAO Special Report No. 346, Smithsonian Astrophysical Observatory

    Google Scholar 

  10. Hughes S (1981) The computation of tables of Hansen coefficients. Celest Mech 25(1):101–107

    Article  ADS  MathSciNet  Google Scholar 

  11. Newcomb S (1895) A development of the perturbative function in cosines of multiples of the mean anomalies and of angles of multiples of the mean anomalies and of angles between the perihelia and common node and in powers of the eccentricities and mutual inclination. U.S. Nautical Almanac Office, Washington

    Google Scholar 

  12. Izsak IG, Gerard JM, Efimba R, Barnett MP (1964) Construction of Newcomb operators on a digital computer. SAO Special Report No. 140, Smithsonian Astrophysical Observatory

    Google Scholar 

  13. Petit G, Luzum B (eds) (2010) IERS conventions (2010), IERS Technical Note No. 36, Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am Main

    Google Scholar 

  14. Wnuk E (1997) Highly eccentric satellite orbits. Adv Space Res 19(11):1735–1740

    Article  ADS  Google Scholar 

  15. Wu LD, Zhang MJ (2012) Recursive methods for computation of Hansen coefficients \(X_{0}^{n,m}, X_{0}^{-(n+1),m}\) and their derivatives. J Astrodyn 2(4):1–10 (In Chinese)

    Google Scholar 

  16. Wu LD, Zhang MJ (2022) Direct calculation methods of Hansen coefficients and their derivatives. Chin Astron Astrophy 46(1):137–151

    Article  Google Scholar 

  17. Giacaglia GEO (1976) A note on Hansen’s coefficients in satellite theory. Celest Mech 14(4):515–523

    Article  ADS  MathSciNet  Google Scholar 

  18. McClain WD (1978) A recursively formulated first-order semianalytic artificial satellite theory based on the generalized method of averaging. Volume II. The explicit development of the first-order averaged equations of motion for the nonspherical gravitational and nonresonant third-body perturbations. NASA CR-156783

    Google Scholar 

  19. Proulx RJ, McClain WD (1988) Series representations and rational approximations for Hansen coefficients. J Guidance 11(4):313–319

    Article  MathSciNet  Google Scholar 

  20. Wu LD, Zhang MJ (2021) Two new recursion formulae of Hansen coefficients. Chin Astron Astrophy 45(4):531–541

    Article  ADS  Google Scholar 

  21. Wu LD, Zhang MJ (2022) Computational efficiency of the recursion of Hansen coefficients. Chin Astron Astrophy 46(2):65–72

    Article  ADS  Google Scholar 

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Correspondence to Lianda Wu or Mingjiang Zhang .

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Wu, L., Zhang, M. (2024). Introduction. In: Hansen Coefficients in Satellite Orbital Dynamics. Springer Aerospace Technology. Springer, Singapore. https://doi.org/10.1007/978-981-97-0456-9_1

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