Abstract
By use of the secular perturbing potential due to oblateness, the existence of periodic orbits of the third kind is established through Poincaré's method of analytic continuation using Delaunay's canonical variables and other three sets of canonical variables which are linear combinations of Delaunay's variables, in the three-dimensional restricted three-body problem when the more massive primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. For two sets of the canonical variables, the singularities are found at the inclinationsi=68 °. 5833,111 °. 4167, while for the other two sets of the canonical variables, the singularities are ati=55 °. 3854, 103 °. 575.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bhatnagar, K. B.: 1972,Indian J. Pure Appl. Math. 3, 101.
Duboshin, G. N.: 1964,Celestial Mechanics, Analytical and Qualitative Methods, Nauka, Moscow, pp. 178–184 (in Russian).
Giacaglia, G. E. O.: 1967,Astron. J. 72, 386.
Goudas, C. L.: 1961,Bull. Soc. Math. de Grèce 2, 1.
Jefferys, W. H.: 1965,Astron. J. 70, 393.
Sharma, R. K.: 1974,Indian J. Pure Appl. Math. 5, 147.
Sharma, R. K.: 1976, ‘Study of Periodic Orbits for Restricted Problem Taking the Bigger Primary an Oblate Spheroid’, Ph.D. Thesis, University of Delhi.
Stiefel, E. L. and Scheifele, G.: 1971,Linear and Regular Celestial Mechanics, Springer-Verlag, Berlin.
Szebehely, V.: 1967,Theory of Orbits, Academic Press, New York.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sharma, R.K. Periodic orbits of the third kind in the restricted three-body problem with oblateness. Astrophys Space Sci 166, 211–218 (1990). https://doi.org/10.1007/BF01094894
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01094894