Skip to main content
Log in

The intermediate anomaly

  • Published:
Celestial mechanics Aims and scope Submit manuscript

Abstract

A Sundman time transformation of the form

$$dt = cr^n ds$$

, wheren=3/2 andc is a constant, is integrated analytically for Keplerian motion. The integral involves an elliptic integral of the first kind. The variable s is called theintermediate anomaly.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bettis, D. and Szebehely, V.: 1971,Astrophys. Space Sci. 14, 133.

    Google Scholar 

  • Buechler, G. and Walker, D. C.: 1970, Report No. TOR-0066 (9320)-2, Vol. III, The Aerospace Corp., El Sequndo, California.

    Google Scholar 

  • Burdet, C. A.: 1969,Journal für die reine und angewändte Mathematik, Band 238, Seite 71, bis 84.

  • Cayley, A.: 1895,An Elementary Treatise on Elliptic Functions, reprinted by Dover Publ. 1961.

  • Feagin, T. and Mikkilineni, R. P.: 1976,Celest. Mech. 13, 491.

    Google Scholar 

  • Gylden, H.: 1870,Bull. Acad. Imp. Sci. St. Petersbourg XIV, 195.

    Google Scholar 

  • Hansen, P., 1856,Suppl. Comp. Rend 1, 121.

    Google Scholar 

  • Hofsommer, D. J. and Van de Riet, R. P.: 1963,Numerische Mathematik 5, 291.

    Google Scholar 

  • Janin, G.: 1974,Celest. Mech. 10, 451.

    Google Scholar 

  • Nacozy, P.: 1968,Astron. J. 74, 544.

    Google Scholar 

  • Nacozy, P.: 1971, Chehotarevet al. (eds.),The Motion, Evolution of Orbits, and Origin of Comets, D. Riedel, p. 31.

  • Nacozy, P.: 1972,Am. Inst. Aeronaut. Astronaut. J. 10, 704.

    Google Scholar 

  • Nacozy, P.: 1975, in G. Giacaglia (ed.),Satellite Dynamics, Springer-Verlag, p. 16.

  • Nacozy, P.: 1976,Celest. Mech. 13, 495.

    Google Scholar 

  • Stiefel, E.: 1970,Celest. Mech. 2, 274.

    Google Scholar 

  • Stiefel, E. and Scheifele, G.: 1971,Linear and Regular Celestial Mechanics, Springer-Verlag, New York.

    Google Scholar 

  • Sundman, K. K.: 1912,Acta Math. 36, 105.

    Google Scholar 

  • Szebehely, V. and Pierce, D. A.: 1967,Am. Inst. Aeronaut. Astronaut. 5, 1520.

    Google Scholar 

  • Velez, C. E.: 1974,Celest. Mech. 10, 405.

    Google Scholar 

  • Velez, C. E. and Hilinski, S., 1977, private communication.

  • Wong, P.: 1972,Some Special Perturbation Methods for the Integration of Artificial Satellite Orbits, UCLA Doctoral Dissertation (available from University Microfilms, Ann Arbor, Michigan, No. 72-20, p. 485).

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nacozy, P. The intermediate anomaly. Celestial Mechanics 16, 309–313 (1977). https://doi.org/10.1007/BF01232657

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01232657

Keywords

Navigation