Skip to main content
SpringerLink
Log in

A recurrence relation for inclination functions

  • Published:
Celestial mechanics Aims and scope Submit manuscript

Abstract

When the terms of the series expansion for the gravitational potential of the Earth are expressed in terms of the orbital elements of an arbitrary Earth satellite, the orbital inclination,i, appears in each, term as the argument of a function of inclination only. For the special case when the field is axi-symmetric, studied in an earlier paper, a recurrence relation was given for a normalized inclination function,A k l(i), with two parameters. The present paper gives a recurrence relation for a general normalized function,K k lm(i), with three parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Allan, R. R.: 1965, ‘On the Motion of Nearly Synchronous Satellites,’Proc. Roy. Soc. A. 288, 60–68.

    Google Scholar 

  • Allan, R. R.: 1967, ‘Resonance Effects Due to the Longitude Dependence of the Gravitational Field of a Rotating Primary,’Planetary Space Sci. 15, 53–76.

    Google Scholar 

  • Garfinkel, B.: 1964, ‘Addition Theorem for a Derivative of a Legendre Polynomial,’Astron. J. 69 (8), 567–569.

    Google Scholar 

  • Gooding, R. H.: 1966, ‘Satellite Motion in an Axi-Symmetric Field, with an Application to Luni-Solar Perturbations’, Royal Aircraft Est. Tech. Report 66018.

  • Groves, G. V.: 1960, ‘Motion of a Satellite in the Earth's Gravitational Field,’Proc. Roy. Soc. A 254, 48–65.

    Google Scholar 

  • Hagihara, Y.: 1962, ‘Recommendations on Notation of the Earth Potential,’Astron. J. 67 (1), 108.

    Google Scholar 

  • Izsak, I. G.: 1964, ‘Tesseral Harmonics of the Geopotential and Corrections to Station Coordinates,’J. Geophys. Res. 69, 2621–2630.

    Google Scholar 

  • Jeffreys, Bertha, S.: 1965, ‘Transformation of Tesseral Harmonics Under Rotation,’Geophys. J. 10, 141–145.

    Google Scholar 

  • Kaula, W. M.: 1961, ‘Analysis of Gravitational and Geometric Aspects of Geodetic Utilization of Satellites,’Geophys. J. 5 (2), 104–133.

    Google Scholar 

  • Merson, R. H.: 1966, ‘The Dynamic Model of PROP, a Computer Program for the Refinement of the Orbital Parameters of an Earth Satellite’, Royal Aircraft Est. Tech. Report 66255.

Download references

Author information

Authors and Affiliations

  1. Royal Aircraft Establishment, Farnborough, England

    R. H. Gooding

Authors
  1. R. H. Gooding
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gooding, R.H. A recurrence relation for inclination functions. Celestial Mechanics 4, 91–98 (1971). https://doi.org/10.1007/BF01230324

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01230324

Keywords

Search

Navigation