Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Close-in orbits in the restricted problem of three bodies

Author: Richard B. Barrar
Journal: Quart. Appl. Math. 27 (1969), 396-398
MSC: Primary 85.34
DOI: https://doi.org/10.1090/qam/255225
MathSciNet review: 255225
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Utilizing a transformation due to Birkhoff [3], we establish for the restricted problem of three bodies the existence of conditionally periodic orbits that move in a small neighborhood of one of the primaries. These orbits result from perturbation of elliptic orbits and are valid for all mass ratios of the two primaries.

References [Enhancements On Off] (What's this?)

  • [1] R. F. Arenstorf, A new method of perturbation theory and its application to the satellite problem of celestial mechanics, J. Reine Angew. Math. 221, 113-145 (1966) MR 0189785
  • [2] R. B. Barrar, A proof of the convergence of the Poincaré-von Zeipel procedure in celestial mechanics, Amer. J. Math. 88, 206-220 (1966) MR 0199490
  • [3] G. Birkhoff, The restricted problem of three bodies, Rend. Circ. Mat. Palermo 39, 265-334 (1915)
  • [4] C. C. Conley, On some new long periodic solutions of the plane restricted three body problem, Comm. Pure Appl. Math. 16, 449-467 (1963) MR 0154724
  • [5] H. Poincaré, Les méthodes nouvelles de la mécanique celeste, v. I (1892); Reprint, Dover, New York, 1957.
  • [6] C. L. Siegel, Vorlesungen über Himmelsmechanik, Springer-Verlag, Berlin, 1956, §23. MR 0080009
  • [7] A. Wintner, Über eine Revision der Sortentheorie des restringierten Dreikörperproblems, Sitzungsberichte der Sächsischen Akademie der Wissenschaften zu Leipzig, 82, 3-56 (1930)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 85.34

Retrieve articles in all journals with MSC: 85.34

Additional Information

DOI: https://doi.org/10.1090/qam/255225
Article copyright: © Copyright 1969 American Mathematical Society

American Mathematical Society