• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology


Indian Journal of Science and Technology

Year: 2020, Volume: 13, Issue: 16, Pages: 1630-1640

Original Article

Periodic orbits in the planar restricted photo-gravitational problem when the smaller primary is an oblate spheroid

Received Date:25 April 2020, Accepted Date:11 May 2020, Published Date:08 June 2020


Background/Objectives: This study deals wit h the stationary solutions of the planar circular restricted three-body problem when the more massive primary is a source of radiation and the smaller primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. The objective is to study the location of the Lagrangian points and to find the values of critical mass. Also, to study the periodic orbits around the Lagrangian points. Methods: A new mean motion expression by including the secular perturbation due to oblateness utilized by(1,2) is used in the present studies. The characteristic roots are obtained by linearizing the equation of the motion around the Lagrangian points. Findings: The critical mass parameter µcrit(3,4) , which decreases radiation force, whereas it increases with oblateness when we consider the value of new mean motion. Through special choice of initial conditions, retrograde elliptical periodic orbits exist for the case µ = µcrit, whose eccentricity increases with oblateness and decreases with radiation force for non-zero oblateness, although there is slight variation in L2 location.

Keywords: Restricted three body problem; Lagrangian points; Eccentricity; Oblateness; Critical mass; Radiation force; Mean motion.


  1. Mittal A, Ahmad I, Bhatnagar KB. Periodic orbits in the photogravitational restricted problem with the smaller primary an oblate body. Astrophysics and Space Science. 2009;323(1):65–73. doi: 10.1007/s10509-009-0038-2
  2. Patak VON, Thomas EI, Abouelmagd. The perturbed photogravitational restricted three-body problem: Analysis of resonant periodic orbits. Discrete & Continuous Dynamic Systems-S. American Institute of Mathematical Sciences. 2019;12(4 & 5):849–875. doi: 10.3934/dcdss.2019057
  3. Bello N, Singh J. On the Stability ofL4,5in the Relativistic R3BP with Oblate Secondary and Radiating Primary. Advances in Astronomy. 2015;2015:1–12. doi: 10.1155/2015/489120
  4. Das MK, Narang P, Mahajan S, Yuasa M. Effect of radiation on the stability of equilibrium points in the binary stellar systems: RW-Monocerotis, Krüger 60. Astrophysics and Space Science. 2008;314(4):261–274. doi: 10.1007/s10509-008-9765-z
  5. Singh J, Amuda TO. Effects of Poynting-Robertson (P-R) drag, radiation, and oblateness on motion around the L4,5 equilibrium points in the CR3BP. Journal of Dynamical Systems and Geometric Theories. 2017;15(2):177–200. doi: 10.1080/1726037x.2017.1411043
  6. Szebehely V, , . Theory of Orbits. (pp. 19670055303) New York. Academic Press. 1967a.
  7. Danby JMA. Fundamentals of Celestial Mechanics. (2nd). Willmann-Bell, Inc. 1988.
  8. Curtis HD. Orbital Mechanics for Engineering Students. (3rd). Elsevier. 2014.
  9. Chernikov YA. The photogravitational restricted three-body problem. Astronam.Z. 1970;47:217–223.


© 2020 Arohan, Sharma. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Published By Indian Society for Education and Environment (iSee)


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