
Mathematical Biosciences and Engineering, 2019, 16(6): 81448161. doi: 10.3934/mbe.2019411.
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Photogravitational perturbations in the infinitesimal orbits around the libration points in the oblate RTBP
1 Department of Mathematics, Faculty of Science, Taibah University, AlMadinah, KSA
2 Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt
3 Department of Astronomy, Faculty of Science, Cairo University, Cairo,12613, Egypt
Received: , Accepted: , Published:
Keywords: infinitesimal orbits; RTBP; libration points; a lie operator; oblateness perturbations; photogravitational perturbations
Citation: S. E. Abd ElBar, F. A. Abd ElSalam. Photogravitational perturbations in the infinitesimal orbits around the libration points in the oblate RTBP. Mathematical Biosciences and Engineering, 2019, 16(6): 81448161. doi: 10.3934/mbe.2019411
References:
 1. M. K. Ahmed, F. A. Abd ElSalam and S. E. Abd ElBar, On the stability of the triangular Lagrangian equilibrium points in the relativistic restricted threebody problem, Am. J. Appl. Sci., 3 (2006), 1993–1998.
 2. C. N. Douskos, E. A. Perdios, On the stability of equilibrium points in the relativistic restricted threebody problem, Celest. Mech. Dyn. Astron., 82 (2002), 317–321.
 3. F. A. Abd ElSalam, S. E. Abd ElBar, Formulation of the postNewtonian equations of motion of the restricted three body problem, Appl. Math., 2 (2011), 155–164.
 4. F. A. Abd ElSalam, S. E. Abd ElBar, Combined effects of oblatness and photogravitational perturbations of the stability of the equilibrium points in the relativistic RTBP, Can. J. Phys., 93 (2015), 300–311.
 5. F. A. Abd ElSalam, D. A. Katour, Relativistic restricted three body problem with oblatness and photogravitational corrections to triangular equilibrium points, Astrophys. Space Sci., 351 (2014), 143–149.
 6. F. A. Abd ElSalam, Stability of triangular equilibrium points in the elliptic restricted three body problem with oblate and triaxial primaries, Astrophys. Space Sci., 357 (2015), 1–9.
 7. R. Duncombe, V. Szebehely, Methods of Astrodynamics and Celestial Mechanics, New York: Academic press, 1966.
 8. D. L. Richardson, Analytic construction of periodic orbits about the collinear points, Celest. Mech. Dyn. Astron., 22 (1980), 241–253.
 9. B. T. Barden, K. C. Howell, Fundamental motions near collinear libration points and their transitions, J. Astronaut. Sci., 46 (1998), 361–378.
 10. K. C. Howell, Families of orbits in the vicinity of the collinear libration points, J. Astronaut. Sci., 49 (2001), 107–125.
 11. G. Gómez, J. Masdemont and C. Simo, Quasihalo orbits associated with libration points, J. Astronaut. Sci., 46 (1998), 135–176.
 12. G. Gómez, A. Jorba, J. Masdemont, et al., Study of the transfer between halo orbits, Acta Astronaut., 43 (1998), 493–520.
 13. D. Selaru, C. CucuDumitrescu, Infinitesimal orbit around Lagrange points in the elliptic restricted three body problem, Celest. Mech. Dyn. Astron., 61 (1995), 333–346.
 14. F. Namouni, C. D. Murray, The effect of eccentricity and inclination on the motion near the Lagrangian points L_{4} and L_{5}, Celest. Mech. Dyn. Astron., 76 (2000), 131–138.
 15. M. Corbera, J. Llibre, Periodic orbits of a collinear restricted threebody problem, Celest. Mech. Dyn. Astron., 86 (2003), 163–183.
 16. A. Hamdy, M. K. Ahmed, M. Radwan, et al., Infinitesimal orbits around the libration points in the elliptic restricted three body problem, Earth, Moon, Planets, 93 (2003), 261–273.
 17. F. A. Abd ElSalam, Periodic and degenerate orbits around the equilibrium points in the relativistic restricted threebody problem, Iran. J. Sci. Technol. A, 43 (2018), 173–192.
 18. A. H. Ibrahim, M. N. Ismail, A. S. Zaghrout, et al., Orbital motion around the collinear libration points of the restricted threebody problem, JAMCS, 29 (2018), 1–16.
 19. R. D. Tiwary, V. K. Srivastava and B. S. Kushvah, Computation of threedimensional periodic orbits in the SunEarth system, Phys. Astron. Int. J., 2 (2018), 98–107.
 20. R. D. Tiwary, B. S. Kushvah, Computation of halo orbits in the photogravitational SunEarth System with oblateness, Astrophys. Space Sci., 357 (2015), 73.
 21. M. Delva, Integration of the elliptic restricted threebody problem with Lie series. Celest. Mech. Dyn. Astron., 34 (1984), 145–154.
 22. A. Hanslmeier, Application of LieSeries to regularized problem in celestial mechanics, Celest. Mech. Dyn. Astron., 34 (1984), 135–143.
 23. A. Mittal, Md. S. Suraj and R. Aggarwal, The analysis of periodic orbits generated by Lagrangian solutions of the restricted threebody problem with nonspherical primaries, New Astron., 74 (2020), 101287.
 24. H. Peng, J. Zhao, Z. Wu, et al., Optimal periodic controller for formation flying on libration point orbits, Acta Astronaut., 69 (2011), 537–550.
 25. H. Peng, X. Jiang and B. Chen, Optimal nonlinear feedback control of spacecraft rendezvous with finite low thrust between libration orbits, Nonlinear Dyn., 76 (2014), 1611–1632.
 26. Y. Jiang, Equilibrium points and orbits around asteroid with the full gravitational potential caused by the 3D irregular shape, Astrodyn., 2 (2018), 361–373.
 27. X. Wang, H. Peng, A symplectic moving horizon estimation algorithm with its application to the EarthMoon L_{2} libration point navigation, Astrodyn., 3 (2019), 137–153.
 28. F. A. Abd ElSalam, D. A. Katour and M. O. Shaker, On the equilibrium point L_{1} in the photogravitational oblate relativistic R3BP with application on Sunplanet systems, Eur. Phys. J. Plus, 130 (2015), 54.
 29. F. A. Abd ElSalam and S. E. Abd ElBar, On the collinear point L_{3} in the generalized relativistic R3BP, Eur. Phys. J. Plus, 130 (2015), 234.
 30. F. A. Abd ElSalam and S. E. Abd ElBar, The photogravitational and oblateness effects in the location of collinear point L_{2} in the relativistic R3BP, Sylwan, 158 (2014), 126–149.
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