Abstract
Time elements are introduced in terms of Keplerian (classical) orbital elements for use with time transformations of the Sundman type. Three different time elements are introduced. One time element is associated with the eccentric anomaly, a second time element is associated with the true anomaly, and a third time element is associated with theintermediate anomaly.
Numerical results are presented that show accuracy improvements of from one to two orders of magnitude when time elements are employed along with Sundman time transformations, compared with using time transformations alone.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baumgarte, J.: 1976,Celes. Mech. 14, 121.
Bettis, D. and Szebehely, V.: 1971,Astrophys. Space Sci. 14, 133.
Buechler, G. and Walker, D.: 1970, Report No. TOR-0066 (9320)-2, Vol. III, The Aerospace Corp., El Segundo, California.
Burdet, C.: 1969,J. Reine Angew. Math. 238, 71.
Cayley, A.: 1895,An Elementary Treatise on Elliptic Functions, Dover reprint, 1961.
Czuchry, A. and Pitkin, E.: 1970,J. Spacecraft and Rockets 7, 882.
Danby, J.: 1962,Fundamentals of Celestial Mechanics, MacMillan.
Feagin, T. and Mikkilineni, R.: 1976,Celes. Mech. 13, 491.
Giacaglia, G.: 1963, U.S. Surface Naval Weapons Laboratory Technical Memorandum, No. K-88/63.
Gylden, H.: 1870,Bull. Acad. Imp. Sci. St. Petersbourg 14, 195.
Hansen, P.: 1856,Suppl. Comp. Rend. 1, 121.
Hofsommer, D. and Van de Riet, R.: 1963,Num. Math. 5, 291.
Janin, G.: 1974,Celes. Mech. 10, 451.
Kyner, T., and Walker, D.: 1969, Presented at the meeting of the Division of Dynamical Astronomy of the AAS, held at The University of Texas at Austin, January, 1969.
Nacozy, P.: 1968a, Doctoral Dissertation, Yale University, available from University Microfilms, Ann Arbor, Michigan.
Nacozy, P.: 1968b,Astron. J. 74, 544.
Nacozy, P.: 1971, in Chebotarev et al. (eds.),The Motion, Evolution of Orbits, and Origin of Comets, D. Reidel Publishing Co., Dordrecht, p. 31.
Nacozy, P.: 1972,AIAA J. 10, 704.
Nacozy, P.: 1974a, Presented to COSPAR Symposium, Sao Paulo, Brazil.
Nacozy, P.: 1974b, presented to AIAA-AAS Flight Mechanics Conference, Anaheim, California.
Nacozy, P.: 1974c, AIAA paper No. 74-841, available from AIAA Library, 750 3rd Ave., New York.
Nacozy, P.: 1975, in G. Giacaglia, (ed.),Satellite Dynamics, Springer-Verlag, Berlin, p. 16.
Nacozy, P.: 1976a,Celes. Mech. 13, 495.
Nacozy, P.: 1976b,Celes. Mech. 14, 129.
Nacozy, P.: 1977,Celes. Mech. 16, 309.
Stiefel, E. and Scheifele, G.: 1971,Linear and Regular Celestial Mechanics, Springer-Verlag, Berlin.
Stokes, A.: 1978,Celes. Mech. 17, 137.
Sundman, K.: 1912,Acta Math. 36, 105.
Szebehely, V.: 1967,Theory of Orbits, Academic Press, New York.
Szebehely, V. and Pierce, D.: 1967,AIAA J. 5, 1520.
Tapley, B., Szebehely, V. and Lewallen, J.: 1969,AIAA J. 7, 1010.
Velez, C.: 1974,Celes. Mech. 10, 405.
Velez, C. and Hilinski, S.: 1978,Celes. Mech. 17, 83.
Wagner, W. and Velez, C.: 1972, GTDS Documentation, NASA Goddard Space Flight Center, X-552-72-244.
Wong, P.: 1972, Doctoral Dissertation, U.C.L.A., available from University Microfilms, Ann Arbor, Michigan.
Zare, K. and Szebehely, V.: 1975,Celes. Mech. 11, 469.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nacozy, P.E. Time elements in Keplerian orbital elements. Celestial Mechanics 23, 173–198 (1981). https://doi.org/10.1007/BF01229552
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01229552