Abstract
A Sundman time transformation of the form
, 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.
Similar content being viewed by others
References
Bettis, D. and Szebehely, V.: 1971,Astrophys. Space Sci. 14, 133.
Buechler, G. and Walker, D. C.: 1970, Report No. TOR-0066 (9320)-2, Vol. III, The Aerospace Corp., El Sequndo, California.
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.
Gylden, H.: 1870,Bull. Acad. Imp. Sci. St. Petersbourg XIV, 195.
Hansen, P., 1856,Suppl. Comp. Rend 1, 121.
Hofsommer, D. J. and Van de Riet, R. P.: 1963,Numerische Mathematik 5, 291.
Janin, G.: 1974,Celest. Mech. 10, 451.
Nacozy, P.: 1968,Astron. J. 74, 544.
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.
Nacozy, P.: 1975, in G. Giacaglia (ed.),Satellite Dynamics, Springer-Verlag, p. 16.
Nacozy, P.: 1976,Celest. Mech. 13, 495.
Stiefel, E.: 1970,Celest. Mech. 2, 274.
Stiefel, E. and Scheifele, G.: 1971,Linear and Regular Celestial Mechanics, Springer-Verlag, New York.
Sundman, K. K.: 1912,Acta Math. 36, 105.
Szebehely, V. and Pierce, D. A.: 1967,Am. Inst. Aeronaut. Astronaut. 5, 1520.
Velez, C. E.: 1974,Celest. Mech. 10, 405.
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).
Author information
Authors and Affiliations
Rights 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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01232657