Periods, Eccentricities and Axes around L4,5 in the ER3BP under Radiating and Oblate Primaries

Show more

References

[1] Lagrange (1772) Collected Works Paris, VI, 229.

[2] Laplace and Delaunay (1867) Memoire sur la theorie de la Lune, Mem. De l’des Science, 28 and 29.

[3] Poincare (1892) Les Methodes Nouevelles de la Mechanique ce’leste Guthier villars, Paris, Chap. V, 250. (Published in English in Three Volumes).

[4] Birkhoff (1927) Dynamical System. American Mathematical Society, New York.

[5] Szebehely, V.G. (1967) Theory of Orbits. Academic Press, New York.

[6] Danby, J.M.A. (1988) Fundamentals of Celestial Mechanics. 2nd Edition, Willmann-Bell, Inc., Virginia.

[7] Radzievskii, V.V. (1950) The Restricted Problem of Three Bodies Taking Account of Light Pressure. Astronomical Journal, 27, 249.

[8] Chernikov, Yu.A. (1970) The Photo Gravitational Restricted Three Body Problem. Soviet Astronomy—AJ, 14, 176-181.

[9] Kunitsyn, A.L. and Perezhogin, A.A. (1978) On the Stability of Triangular Libration Points of the Photo Gravitational Circular Restricted Three-Body Problem. Celestial Mechanics and Dynamical Astronomy, 18, 395-408.

[10] Schuerman, D.W. (1980) The Restricted Three Body Problem including Radiation Pressure. The Astrophysical Journal, 238, 337-342.

http://dx.doi.org/10.1086/157989

[11] Luk’yanov, L.G. (1984) Lagrangian Solutions in the Photogravitational Restricted Circular Three-Body Problem. Astronomicheskii Zhurnal, 789, 94; Soviet Astronomy, 28, 329-333.

[12] Luk’yanov, L.G. (1988) On the Family of Libration Points in the Restricted Three-Body Problem. Astronomicheskii Zhurnal, 65, 422, 432; Soviet Astronomy, 32, 6.

[13] Simmons, J.F.L., McDonald, A.J.C. and Brown, J.C. (1985) The Restricted 3-Body Problem with Radiation Pressure. Celestial Mechanics, 35, 145-187.

http://dx.doi.org/10.1007/BF01227667

[14] Kunitsyn, A.L. and Tureshbaev, A.T. (1985) On the Collinear Libration Points of the Photogravitational Restricted Three-Body Problem. Celestial Mechanics, 35, 105, 112.

[15] Kunitsyn, A.L. (2000) The Stability of Triangular Libration Points in the Photogravitational Three-Body Problem. Journal of Applied Mathematics and Mechanics, 64, 757-763.

http://dx.doi.org/10.1016/S0021-8928(00)00105-2

[16] Kunitsyn, A.L. (2001) The Stability of Collinear Libration Points in the Photogravitational Three-Body Problem. Journal of Applied Mathematics and Mechanics, 65, 703-706.

http://dx.doi.org/10.1016/S0021-8928(01)00075-2

[17] AbdulRaheem, A. and Singh, J. (2006) Combined Effects of Perturbations, Radiation and Oblateness on the Stability of Equilibrium Points in the Restricted Three-Body Problem. Astronomical Journal, 131, 1880-1885.

[18] AbdulRaheem, A. and Singh, J. (2008) Combined Effects of Perturbations, Radiation and Oblateness on the Periodic Orbits in the Restricted Three-Body Problem. Astrophysics and Space Science, 317, 9-13.

http://dx.doi.org/10.1007/s10509-008-9841-4

[19] Singh, J. and Ishwar, B. (1999) Stability of Collinear Equilibrium Points in the Generalized Photogravitational Elliptic Restricted Three-Body Problem. Bulletin of the Astronomical Society of India, 27, 415.

[20] Singh, J. and AbdulKarim, A. (2014) Instability of Triangular Libration Points in the Perturbed Photogravitational R3BP with Poynting-Robertson (P-R) Drag. Astrophysics and Space Science, 351, 473-482.

http://dx.doi.org/10.1007/s10509-014-1862-6

[21] Shankaran, S.J.P. and Ishwar, B. (2011) Out-of-Plane Equilibrium Points and Stability in the Generalized Photogravitational Restricted Three-Body Problem. Astrophysics & Space Science, 332, 115.

[22] Sharma, R.K., Taqvi, Z.A. and Bhatnagar, K.B. (2001) Existence and Stability of Libration Points in the Restricted Three-Body Problem When the Primaries Are Triaxial Rigid Bodies. Celestial Mechanics and Dynamical Astronomy, 79, 119-133.

http://dx.doi.org/10.1023/A:1011168605411

[23] Singh, J. and Umar, A. (2012) Motion in the Photogravitational Elliptic Restricted Three-Body Problem under an Oblate Primary. The Astronomical Journal, 143, 109-131.

http://dx.doi.org/10.1088/0004-6256/143/5/109

[24] Singh, J. and Umar, A. (2012) On the Stability of Triangular Equilibrium Points in the Elliptic R3BP under Radiating and Oblate Primaries. Astrophysics and Space Science, 341, 349-358.

http://dx.doi.org/10.1007/s10509-012-1109-3

[25] Singh, J. and Umar, A. (2013) On “out of Plane” Equilibrium Points in the Elliptic Restricted Three-Body Problem with Radiating and Oblate Primaries. Astrophysics and Space Science, 344, 13-19.

http://dx.doi.org/10.1007/s10509-012-1292-2

[26] Singh, J. and Umar, A. (2013) Collinear Equilibrium Points in the Elliptic R3BP with Oblateness and Radiation. Advances in Space Research, 52, 1489-1496.

http://dx.doi.org/10.1016/j.asr.2013.07.027

[27] Das, M.K., Narang, P., Mahajan, S. and Yuasa, M. (2009) Effect of Radiation on the Stability of a Retrograde Particle Orbit in Different Stellar Systems. Planetary and Space Science, 57, 836-845.

http://dx.doi.org/10.1016/j.pss.2009.02.007

[28] Sharma, R.K. (1987) The Linear Stability of Libration Points of the Photogravitational Restricted Three-Body Problem When the Smaller Primary Is an Oblate Spheroid. Astrophysics and Space Science, 135, 271-281.

http://dx.doi.org/10.1007/BF00641562

[29] Ishwar, B. and Kushvah, B.S. (2006) Linear Stability of Triangular Equilibrium Points in the Generalized Photogravitational Restricted Three Body Problem with Poynting_Robertson Drag. Journal of Dynamical Systems and Geometric Theories, 4, 79-86.

http://dx.doi.org/10.1080/1726037X.2006.10698504

[30] Tsirogiannis, G.A., Douskos, C.N. and Perdios, E.A. (2006) Computation of the Liapunov Orbits in the Photogravitational RTBP with Oblateness. Astrophysics and Space Science, 305, 389-398.

http://dx.doi.org/10.1007/s10509-006-9171-3

[31] Vishnu Namboori, N.I., Sudheer Reedy, D. and Sharma, R.K. (2008) Effect of Oblateness and Radiation Pressure on Angular Frequencies at Collinear Points. Astrophysics and Space Science, 318, 161-168.

http://dx.doi.org/10.1007/s10509-008-9934-0

[32] Mital, A., Ahmad, I. and Bhatnagar, K.B. (2009) Periodic Orbits in the Photogravitational Restricted Problem with the Smaller Primary an Oblate Body. Astrophysics and Space Science, 323, 65-73.

http://dx.doi.org/10.1007/s10509-009-0038-2

[33] Sahoo, S.K. and Ishwar, B. (2000) Stability of Collinear Equilibrium Points in the Generalized Photogravitational Elliptic Restricted Three-Body Problem. Bulletin of the Astronomical Society of India, 28, 579-586.

[34] Abouelmagd, E.I. (2012) Existence and Stability of Triangular Points in the Restricted Three-Body Problem with Numerical Applications. Astrophysics and Space Science, 342, 45-53.

[35] Singh, J. and Haruna, S. (2014) Periodic Orbits around Triangular Points in the Restricted Problem of Three Oblate Bodies. American Journal of Astronomy and Astrophysics, 2, 22-26.

[36] Sarris, E. (1989) Families of Symmetric-Periodic Orbits in the Elliptic Three-Dimensional Restricted Three-Body Problem. Astrophysics and Space Science, 162, 107-122.

http://dx.doi.org/10.1007/BF00653348

[37] Kumar, V. and Choudry, R.K. (1990) Nonlinear Stability of the Triangular Libration Points for the Photo Gravitational Elliptic Restricted Problem of Three Bodies. Celestial Mechanics and Dynamical Astronomy, 48, 299-317.

http://dx.doi.org/10.1007/BF00049387

[38] Markellos, V.V., Perdios, E. and Labropoulou, P. (1992) Linear Stability of the Triangular Equilibrium Points in the Photogravitational Elliptic Restricted Problem I. Astrophysics and Space Science, 194, 207-213.

http://dx.doi.org/10.1007/BF00643991

[39] Zimovshchikov, A.S. and Tkhai, V.N. (2004) Instability of Libration Points and Resonance Phenomena in the Photogravitational Elliptic Restricted Three-Body Problem. Solar System Research, 38, 155-164.

http://dx.doi.org/10.1023/B:SOLS.0000022826.31475.a7

[40] Ammar, M.K. (2008) The Effect of Solar Radiation Pressure on the Lagrangian Points in the Elliptic Restricted Three-body Problem. Astrophysics and Space Science, 313, 393-408.

http://dx.doi.org/10.1007/s10509-007-9709-z

[41] Kumar, S. and Ishwar, B. (2009) Solutions of Generalized Photogravitational Elliptic Restricted Three-Body Problem. AIP Conference Proceedings, 1146, 456-460.

http://dx.doi.org/10.1063/1.3183564

[42] Kumar, S. and Ishwar, B. (2011) Location of Collinear Equilibrium Points in the Generalized Photogravitational Elliptic Restricted Three-Body Problem. International Journal of Engineering, Science and Technology, 3, 157-162.

http://dx.doi.org/10.4314/ijest.v3i2.68143

[43] Singh, J. and Umar, A. (2014) On Motion around the Collinear Libration Points in the Elliptic Restricted Three-Body Problem with a Bigger Triaxial Primary. New Astronomy, 29, 36-41.

http://dx.doi.org/10.1016/j.newast.2013.11.003

[44] Charlier, C.I. (1899) Die Mechanik des Himmels. Walter de Gryter and Co., Berlin and Leipzig.

[45] Plummer, H.C. (1901) On Periodic Orbits in the Neighborhood of Centres of Liberation. Monthly Notices of the Royal Astronomical Society, 62, 6.

[46] Riabov, U.A. (1952) Preliminary Orbits Trojan Asteroids. Soviet Astronomy, 29, 5.

[47] Elipe, A. and Lara, M. (1997) Periodic Orbits in the Restricted Three-Body Problem with Radiation Pressure. Celestial Mechanics and Dynamical Astronomy, 68, 1-11.

http://dx.doi.org/10.1023/A:1008233828923

[48] Hadjidemetriou, J.D. (1984) Periodic Orbits. Celestial Mechanics, 34, 379-393.

http://dx.doi.org/10.1007/BF01235816

[49] Khanna, M. and Bhatnagar, K.B. (1999) 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, 721-723.

[50] Perdios, E.A. (2003) Critical Symmetric Periodic Orbits in the Photogravitational Restricted Three-Body Problem. Astrophysics and Space Science, 286, 501-513.

http://dx.doi.org/10.1023/A:1026328832021

[51] Kushvah, B.S., Kishor, R. and Dolas U. (2012) Existence of Equilibrium Points and Their Linear Stability in the Generalized Photogravitational Chermykh-Life Problem with Power-Law Profile. Astrophysics and Space Science, 337, 115-125.

http://dx.doi.org/10.1007/s10509-011-0857-9

[52] Beevi, A. and Sharma, R.K. (2012) Oblateness Effect of Saturn on Periodic Orbits in Saturn-Titan Restricted Three-Body Problem. Astrophysics and Space Science, 340, 245-261.

http://dx.doi.org/10.1007/s10509-012-1052-3

[53] Singh, J. and Begha, J.M. (2011) Stability of Equilibrium Points in the Generalized Perturbed Restricted Three-Body Problem. Astrophysics and Space Science, 331, 511-519.

http://dx.doi.org/10.1007/s10509-010-0464-1

[54] Abouelmagd, E.I. and El-Shaboury, S.M. (2012) Periodic Orbits under Combined Effects of Oblateness and Radiation in the Restricted Problem of Three Bodies. Astrophysics and Space Science, 341, 331-341.

[55] McCuskey, S.W. (1963) Introduction to Celestial Mechanics. Addison-Wesley, New York.

[56] Ishwar, B. and Elipe, A. (2001) Secular Solutions at Triangular Equilibrium Point in the Generalized Photogravitational Restricted Three Body Problem. Astrophysics and Space Science, 277, 437-446.

http://dx.doi.org/10.1023/A:1012528929233