Non-collinear libration points in CR3BP when less massive primary is an heterogeneous oblate body with N-layers
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2016-03-28 https://doi.org/10.14419/ijaa.v4i1.5928 -
Celestial Mechanics, Restricted Three-Body Problem, Libration Points, Stability, Heterogeneous Oblate Spheroid. -
Abstract
In the present paper, the existence of non-collinear libration points has been shown in circular restricted three-body problem when less massive primary is a heterogeneous oblate body with N-layers. Further, the stability of non-collinear libration points is investigated in linear sense and found that the non-collinear libration points are stable for the critical value of mass parameter µ ≤ µcrit= µo – 3.32792 k1 – 1.16808 k2.
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References
[1] Danby, J.M.A.: Stability of the triangular points in the elliptic restricted problem of three bodies. The Astronomical Journal, 69 (2), 165 – 172 (1964). http://dx.doi.org/10.1086/109254.
[2] Szebehely, V.: Theory of orbits, The Restricted Problem of three bodies. Academic Press, New York and London (1967).
[3] Vidyakin, V.V.: Stability of one particular solution for the motion of three homogeneous spheroids.Soviet Astronomy, 18, 116 (1974).
[4] Sharma, R.K.: Perturbations of Lagrangian points in the restricted three-body problem. Indian Journal of Pure and Applied Mathematics, 6, 1099-1102 (1975).
[5] Subbarao, P.V., Sharma, R.K.: A note on the Stability of the triangular points of equilibrium in the restricted three body problem. Astronomy and Astrophysics, 43, 381-383 (1975).
[6] Sharma, R.K., Subbarao P.V.: Stationary solutions and their characteristic exponents in the restricted three-body problem when the more massive primary is an oblate spheroid. Celestial Mechanics and Dynamical Astronomy, 13, 137-149 (1976). http://dx.doi.org/10.1007/BF01232721.
[7] Choudhary R.K.: Libration points in the generalized elliptic restricted three body problem. Celestial Mechanics, 16, 411 – 419 (1977). http://dx.doi.org/10.1007/BF01229285.
[8] Bhatnagar, K. B., Hallan, P. P.: Effect of perturbed potentials on the stability of Libration points restricted problem. Celestial Mechanics and Dynamical Astronomy, 20(2), 95-103 (1979). http://dx.doi.org/10.1007/BF01230231.
[9] Cid, R., Ferrer, S., Caballero, J.A.: Asymptotic solutions of the restricted problem near equilateral Lagrangian points. Celestial Mechanics and Dynamical Astronomy, 35, 189-200 (1985). http://dx.doi.org/10.1007/BF01227668.
[10] El-Shaboury, S.M.: Equilibrium solutions of the restricted problem of 2+2 axisymmetric rigid bodies. Celestial Mechanics and Dynamical Astronomy, 50, 199-208 (1991). http://dx.doi.org/10.1007/BF00048764.
[11] Bhatnagar, K.B., Gupta, U., Bharadwaj, R.: Effect of perturbed potentials on the non-linear stability of Libration point L4 in the restricted problem. Celestial Mechanics and Dynamical Astronomy, 59, 45-374 (1994). http://dx.doi.org/10.1007/BF00692102.
[12] Selaru, D., Cucu-Dumitrescu, C.: Infinitesimal orbits around Lagrange points in the elliptic, restricted three-body problem. Celestial Mechanics and Dynamical Astronomy, 61 (4), 333 – 346 (1995). http://dx.doi.org/10.1007/BF00049514.
[13] Markellos, V.V., Papadakis, K.E., Perdios, E.A.: Non-linear stability zones around triangular equilibria in the plane circular restricted three-body problem with oblateness. Astrophysics and Space Science, 245, 157-164 (1996). http://dx.doi.org/10.1007/BF00637811.
[14] Subbarao, P.V., Sharma, R.K.: Effect of oblateness on the non-linear stability of L4 in the restricted three-body problem. Celestial Mechanics and Dynamical Astronomy, 65, 291-312 (1997).
[15] Khanna, M., Bhatnagar, K.B.: Existence and stability of libration points in restricted three body problem when the smaller primary is a triaxial rigid body. Indian Journal of Pure and Applied Mathematics, 29 (10), 1011-1023 (1998).
[16] Khanna, M., Bhatnagar, K.B.: Existence and stability of Libration points in the restricted three body problem when the smaller primary is a triaxial rigid body and the bigger one an oblate spheroid. Indian Journal of Pure and Applied Mathematics, 30 (7), 721-733 (1999).
[17] Esteban, E. P., Vazquez, S.: Rotating Stratified Heterogeneous Oblate Spheroid in Newtonian Physics. Celestial Mechanics and Dynamical Astronomy, 81, 299 (2001).http://dx.doi.org/10.1023/A:1013292529030.
[18] Roberts, G.E.: Linear Stability of the Elliptic Lagrangian Triangle Solutions in the three-body problem. Journal of Differential Equations, 182 (1), 191 – 218 (2002). http://dx.doi.org/10.1006/jdeq.2001.4089.
[19] Oberti, P.,Vienne, A.: An upgraded theory for Helene, Telesto and Calypso. Astronomy and Astrophysics, 397, 353-359 (2003). http://dx.doi.org/10.1051/0004-6361:20021518.
[20] Sosnytskyi, S.P.: On the Lagrange stability of motion in the three-body problem. Ukrainian Mathematical Journal, 57, 1341 – 1349 (2005). http://dx.doi.org/10.1007/s11253-005-0266-8.
[21] Perdiou, A.E., Markellos, V.V., Douskos, C.N.: The Hill problem with oblate secondary: Numerical Exploration. Earth, Moon and Planets, 97, 127-145 (2005). http://dx.doi.org/10.1007/s11038-006-9065-y.
[22] John, A. Arredondo, Jianguang, Guo, Cristina, Stoica, Claudia, and Tamayo: On the restricted three body problem with oblate primaries. Astrophysics and Space Science, 341, 315-322 (2012). http://dx.doi.org/10.1007/s10509-012-1085-7.
[23] Idrisi, M. Javed, Taqvi, Z.A.: Restricted three-body problem when one of the primaries is an ellipsoid. Astrophysics and Space Science, 348, 41-56 (2013). http://dx.doi.org/10.1007/s10509-013-1534-y.
[24] Idrisi, M. Javed: Existence and stability of the libration points in CR3BP when the smaller primary is an oblate spheroid. Astrophysics and Space Science, 354, 311-325 (2014). http://dx.doi.org/10.1007/s10509-014-2031-7.
[25] Idrisi, M. Javed, Amjad, Muhammad: Effect of elliptic angle φ on the existence and stability of libration points in restricted three-body problem in earth-moon system considering earth as an ellipsoid. International Journal of Advanced Astronomy, 3 (2), 87-96 (2015). http://dx.doi.org/10.14419/ijaa.v3i2.5313.
[26] Idrisi, M. Javed: A general solution to non-collinear equilibria in terms of largest root (k) of confocal oblate spheroid. International Journal of Advanced Astronomy, 4 (1), 01-04 (2016).http://dx.doi.org/10.14419/ijaa.v4i1.5587.
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How to Cite
Idrisi, M. J., & Shalini, K. (2016). Non-collinear libration points in CR3BP when less massive primary is an heterogeneous oblate body with N-layers. International Journal of Advanced Astronomy, 4(1), 39-42. https://doi.org/10.14419/ijaa.v4i1.5928Received date: 2016-02-23
Accepted date: 2016-03-20
Published date: 2016-03-28