Length of arc as independent argument for highly eccentric orbits. (English) Zbl 0759.70008

Analytic step regulation for highly eccentric orbits may be achieved rather simply by choosing as independent argument the arc length \(s\) determined by an ordinary differential equation. In unperturbed motion the dependence of \(s\) on time \(t\) is expressed by means of elliptic functions. Equations of perturbed motion may prove very useful for numerically integrating highly eccentric orbits.


70F05 Two-body problems
Full Text: DOI


[1] Ferrandiz, J.M.: 1986, ?Linearization in Special Cases of Perturbed Keplerian Motions?, Celes. Mech. 39, 23. · Zbl 0619.70008
[2] Ferrandiz, J.M., Ferrer, S. and Sein-Echaluce, M.L.: 1987, ?Generalized Elliptic Anomalies?, Celes. Mech. 40, 315. · Zbl 0652.70007
[3] Janin, G.: 1974, ?Accurate Computation of Highly Eccentric Satellite Orbits?, Celes. Mech. 10, 451. · Zbl 0303.70045
[4] Nacozy, P.E.: 1981, ?Time Elements in Keplerian Orbital Elements?, Celes. Mech. 23, 173. · Zbl 0449.70012
[5] Stiefel, E.L. and Scheifele, G.: 1971, Linear and Regular Celestical Mechanics, Springer, Berlin-Heidelberg-New York. · Zbl 0226.70005
[6] Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T.: 1989, Numerical Recipes. The Art of Scientific Computing (FORTRAN Version). Cambridge University Press, Cambridge-New York-Port Chester-Melbourne-Sydney. · Zbl 0698.65001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.