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Calculation of \(X_{0}^{n,m}\) and \(X_{0}^{{ - \left( {n + 1} \right),m}}\) and Their Derivatives

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Hansen Coefficients in Satellite Orbital Dynamics

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Abstract

The definition of Hansen coefficient \(X_{k}^{n,m}\) is (Plummer in An introductory treatise on dynamical astronomy, Cambridge University Press, London, 1918).

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References

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

    Google Scholar 

  2. Laskar J, Boué G (2010) Explicit expansion of the three-body disturbing function for arbitrary eccentricities and inclinations. Astron Astrophys 522:A60

    Article  ADS  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. 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 

  5. Cook GE (1973) Basic theory for PROD, a program for computing the development of satellite orbits. Celest Mech 7(3):301–314

    Article  ADS  Google Scholar 

  6. Laskar J (2005) Note on the generalized Hansen and Laplace coefficients. Celest Mech Dyn Astron 91(3–4):351–356

    Article  ADS  MathSciNet  Google Scholar 

  7. Hansen PA (1855) Entwickelung der products einer potenz des radius vectors mit dem sinus oder cosinus eines vielfachen der wahren anomalie in reihen, Abhandl. d. K. S. Ges. d. Wissensch, vol IV, pp 182–281

    Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Google Scholar 

  10. 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 

  11. 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 

  12. 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 

  13. Vakhidov AA (2001) Some recurrence relations between Hansen coefficients. Celest Mech Dyn Astron 81(3):177–190

    Article  ADS  MathSciNet  Google Scholar 

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Correspondence to Lianda Wu or Mingjiang Zhang .

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Wu, L., Zhang, M. (2024). Calculation of \(X_{0}^{n,m}\) and \(X_{0}^{{ - \left( {n + 1} \right),m}}\) and Their Derivatives. In: Hansen Coefficients in Satellite Orbital Dynamics. Springer Aerospace Technology. Springer, Singapore. https://doi.org/10.1007/978-981-97-0456-9_2

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