Effect of Perturbations in Coriolis and Centrifugal Forces on the Non-Linear Stability of L4 in the Photogravitational Restricted Three Body Problem

DOI: 10.4236/ijaa.2015.54031   PDF   HTML   XML   4,595 Downloads   5,012 Views   Citations

Abstract

Effect of perturbations in Coriolis and centrifugal forces on the non-linear stability of the libration point L4 in the restricted three body problem is studied when both the primaries are axis symmetric bodies (triaxial rigid bodies) and the bigger primary is a source of radiation. Moser’s conditions are utilized in this study by employing the iterative scheme of Henrard for transforming the Hamiltonian to the Birkhoff’s normal form with the help of double D’Alembert’s series. It is found that L4 is stable for all mass ratios in the range of linear stability except for the three mass ratios μc1, μc2 and μc3, which depend upon the perturbations ε1 and ε1 in the Coriolis and centrifugal forces respectively and the parameters A1,A2,A3 and A4 which depend upon the semi-axes a1,b1,c1;a2,b2,c2 of the triaxial rigid bodies and p, the radiation parameter.

Share and Cite:

Chauhan, K. , Rai, S. and Aggarwal, R. (2015) Effect of Perturbations in Coriolis and Centrifugal Forces on the Non-Linear Stability of L4 in the Photogravitational Restricted Three Body Problem. International Journal of Astronomy and Astrophysics, 5, 275-290. doi: 10.4236/ijaa.2015.54031.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Deprit, A. and Deprit-Bartholome, A. (1967) Stability of the Triangular Lagrangian Points. Astronomical Journal, 72, 173-179.
http://dx.doi.org/10.1086/110213
[2] Bhatnagar, K.B. and Hallan, P.P. (1983) The Effect of Perturbation in Coriolis and Centrifugal Forces on the Nonlinear Stability of Equilibrium Points in the Restricted Problem of Three Bodies. Celestial Mechanics, 30, 97-114.
http://dx.doi.org/10.1007/BF01231105
[3] Aggarwal, R., Taqvi, Z.A. and Ahmad, I. (2006) Non-Linear Stability of in the Restricted Three Body Problem for radiated Axes Symmetric Primaries with Resonances. Bulletin of Astronomical Society of India, 34, 327-356.
[4] Jain, M. and Aggarwal, R. (2015) A Study of Non-Collinear Libration Points in Restricted Three Body Problem with Stokes Drag Effect when Smaller Primary Is an Oblate Spheroid. Astrophysics and Space Science, 358, 51.
http://dx.doi.org/10.1007/s10509-015-2457-6
[5] Kaur, B. and Aggarwal, R. (2013) Robe’s restricted Problem of 2+2 Bodies when the Bigger Primary Is a Roche Ellipsoid. Acta Astronautica, 89, 31-37.
http://dx.doi.org/10.1016/j.actaastro.2013.03.022
[6] Singh, J. (2011) Combined Effects of Perturbations, Radiation and Oblateness on the Non-Linear Stability of Triangular Points in the R3BP. Astrophysics and Space Science, 332, 331-339.
http://dx.doi.org/10.1007/s10509-010-0546-0
[7] Szebehely, V. (1967) Theory of Orbits. Academic Press, New York, 242-264.
[8] Whittaker, E.T. (1965) A Treatise on the Analytical Dynamics of Particles and Rigid Bodies. Cambridge University Press, London, 427-430.
[9] Moser, J. (1953) Periodische Losungen des restringierten Dreikorperproblems, die sich erst nach vielen umlaufen schliessen. Mathematische Annalen, 126, 325-335.
http://dx.doi.org/10.1007/BF01343166

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.