Locations of Lagrangian points and periodic orbits around triangular points in the photo gravitational elliptic restricted three-body problem with oblateness
Keywords:Critical Mass, ER3BP, Oblateness, Oblate Spheroid, Lagrangian Points, Photogravitational, Radiation Pressure, Transition Curve, Tadpole Orbits.
Locations of the Lagrangian points are computed and periodic orbits are studied around the triangular points in the photogravitational elliptic restricted three-body problem (ER3BP) by considering the more massive primary as the source of radiation and smaller primary as an oblate spheroid. A new mean motion taken from Sharma et al.  is used to study the effect of radiation pressure and oblateness of the primaries. The critical mass parameter Â that bifurcates periodic orbits from non-periodic orbits tends to reduce with radiation pressure and oblateness. The transition curves defining stable region of orbits are drawn for different values of radiation pressure and oblateness using the analytical method of Bennet . Tadpole orbits with long- and short- periodic oscillations are obtained for Sun-Jupiter and Sun-Saturn systems.
 Danby. (1964). "Stability of the Triangular Points in the Elliptic Restricted Problem", The Astronomical Journal, 69, 165-172. https://doi.org/10.1086/109254.
 S.K. Sahoo and B.Ishwar (2000). "Stability of collinear equilibrium points in the generalized photogravitational elliptic restricted three-body problem". Astronomical Society of India, 28, 579-586.
 Jagadish Singh, Aishetu Umar (2012). "On out of plane equilibrium points in the ER3BP with radiating and oblate primaries". Astrophys, Space Science, 344, 13-19. https://doi.org/10.1007/s10509-012-1292-2.
 Szebehely, V. (1967). â€œTheory of Orbits, The Restricted Problem of Three bodiesâ€, Academic Press, New York. https://doi.org/10.1016/B978-0-12-395732-0.50007-6.
 Broucke, R. A. (1969). "Periodic orbits in the Elliptic Restricted Three-Body Problem," JPL, California Institute of Technology, Pasadena, California, 32-1360. https://doi.org/10.2514/3.5267.
 Subba Rao, P. V. and Sharma, R. K. (1975). "A note on the Stability of the Triangular Points of the Equilibrium in the Restricted Three-body Problem". Astron and Astrophys. 43, 381-383.
 Raheem, A. and Singh, J. (2006). â€œCombined effects of perturbations, radiation, and oblateness on the stability of equilibrium points in the restricted three-body problemâ€. The Astronomical Journal, 131, 1880â€“1885. https://doi.org/10.1086/499300.
 Isravel, H. and Sharma, R. K. (2017). â€œEffect of Oblateness on Transition Curves in Elliptic Restricted Three-body Problemâ€. First International Conference on Recent Advances in Aerospace Engineering (ICRAAE). https://doi.org/10.1109/ICRAAE.2017.8297237.
 Grebenikov, E. A. (1964). â€œOn the stability of the Lagrangian triangle solutions of the Restricted Elliptic Three-Body Problemâ€, Soviet Astronomy- AJ, 8, 451-459.
 Y. Sharon Ruth, Y. S. and Sharma, R. K. (2018). â€œPeriodic orbits in the photogravitational Elliptical Restricted Three-Body Problemâ€. Advances in Astrophysics, 3, 154-170.
 Murray, C. D. and S. F. Dermott, S. F. (1999). "Solar System Dynamics", Cambridge University Press, Cambridge, UK.
 Anderlecht, A. G. (2016), "Tadpole orbits in the L4/L5 region: Construction and links to other families of periodic orbits", MS Thesis, Purdue University, West Lafayette, Indiana, USA.
 Sharma, R. K., Sellamuthu, H., Isravel, H. â€œEffect of oblateness on the locations and linear stability of collinear points in elliptic restricted three-body problemâ€, communicated to Planetary and Space Science, August 2018.
 Bennett, A. (1965). "Analytical Determination of Characteristic Exponents," AIAA/ION Astrodynamics Specialist Conference, Monterey, California, No. 65-685. https://doi.org/10.2514/6.1965-685.