Hostname: page-component-6bf8c574d5-j5c6p Total loading time: 0 Render date: 2025-03-07T03:48:00.568Z Has data issue: false hasContentIssue false
  • English
  • Français

Orbital Arc Length as a Universal Independent Variable

Published online by Cambridge University Press:  12 April 2016

Luis Floria
Luis Floria*
Affiliation:
Grupo de Mecánica Celeste I, Universidad de Valladolid Valladolid, Spain

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A uniform treatment of the two-body problem leads to a differential time transformation to introduce the arc length along the orbit as the independent variable. The transformation is integrated in terms of the classical anomalies.

Type
Theory of Motion
Information
International Astronomical Union Colloquium , Volume 165: Dynamics and Astrometry of Natural and Artificial Celestial Bodies , 1997 , pp. 405 - 410
Copyright
Copyright © Kluwer 1997

References

Battin, R.H.: 1987, An Introduction to the Mathematics and Methods of Astrodynamics, American Institute of Aeronautics and Astronautics Education Series, New York.Google Scholar
Brumberg, E.V.: 1992, “Length of arc as independent argument for highly eccentric orbits”, Celest. Mech. & Dyn. Astron. 53, 323–328.CrossRefGoogle Scholar
Byrd, P.F. and Friedman, M.D.: 1971, Handbook of Elliptic Integrals for Engineers and Scientists, Springer-Verlag, New York, Heidelberg, Berlin.CrossRefGoogle Scholar
Ferrándiz, J.M., Ferrer, S. and Sein-Echaluce, M.L.: 1987, “Generalized elliptic anomalies”, Celest. Mech. 40, 315–328.Google Scholar
Floría, L.: 1996, “On two-parameter linearizing transformations for uniform treatment of two-body motion”, in: Dynamics, Ephemerides and Astrometry of the Solar System (Ferraz-Mello, S., Morando, B., Arlot, J.E., eds), Kluwer, Dordrecht, 299–302.Google Scholar
Gradshteyn, I.S. and Ryzhik, I.M.: 1980, Table of Integrals, Series and Products (Corrected and Enlarged Edition), Academic Press, New York.Google Scholar
Stiefel, E.L. and Scheifele, G.: 1971, Linear and Regular Celestial Mechanics. Springer-Verlag, Berlin, Heidelberg, New York.CrossRefGoogle Scholar
Stumpff, K.: 1959, Himmelsmechanik, I, VEB Deutscher Verlag der Wissenschaften, Berlin.Google Scholar