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Celestial mechanics

, Volume 12, Issue 2, pp 189–201 | Cite as

Collinear equilibria and their characteristic exponents in the restricted three-body problem when the primaries are oblate spheroids

  • Ram Krishan Sharma
  • P. V. Subba Rao
Article

Abstract

In this paper location of the collinear libration points is investigated numerically, by taking the oblateness of the primaries into consideration, for 19 systems of astronomical interest. It is found that in some of the systems the shifts are significant. These equilibria are shown to be unstable in general, though the existence of conditional, infinitesimal (linearized) periodic orbits around them can be established, in the usual way. It is shown that the eccentricity and synodic period of these orbits are functions of oblateness too. Numerical study, in this connection, with the above systems, revealed that the orbits around the libration point, which is farthest from the primary whose oblateness effect is included, exhibit a different trend from those around the other two points.

Keywords

Periodic Orbit Libration Point Paper Location Characteristic Exponent Oblate Spheroid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Danby, J. M. A.: 1962,Fundamentals of Celestial Mechanics, Macmillan.Google Scholar
  2. McCuskey, S. W.: 1963,Introduction to Celestial Mechanics, Addisson-Wesley.Google Scholar
  3. Nikolaev, S. I.: 1970, ‘A Certain Generalization of the Restricted Three Body Problem,’Math. Phys. No. 8 (Russian), 131–137.Google Scholar
  4. Sharma, R. K.: 1974, ‘Perturbations of Lagrangian Points in the Restricted Three Body Problem,’ to appear in theInd. J. Pure Appl. Math. Google Scholar
  5. Szebehely, V.: 1967,Theory of Orbits, Academic Press.Google Scholar

Copyright information

© D. Reidel Publishing Company 1975

Authors and Affiliations

  • Ram Krishan Sharma
    • 1
  • P. V. Subba Rao
    • 1
  1. 1.Applied Mathematics DivisionVikram Sarabhai Space CentreTrivandrumIndia

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