Stability of Triangular Equilibrium Points in the Generalised Photogravitational Restricted Three Body Problem

Authors

  • Mahesh Kumar Research Scholar, Department of Mathematics, J.P. University, Chapra), Bihar, India Author
  • Avdhesh Kumar Assistant Professor, Department of Mathematics, Jaglal Chaudhary College, Chapra (A Constituent unit of J.P. University, Chapra), Bihar, India Author

DOI:

https://doi.org/10.32628/IJSRST26132

Keywords:

Restricted three body problem, Photo gravitational effects, Radiation pressure, Triangular equilibrium points (L4, L5), Oblateness of primaries

Abstract

This paper investigates the stability of triangular equilibrium points (L4, L5) in the generalized photogravitational restricted three‑body problem, considering the combined effects of radiation pressure and oblateness of both primaries. Using variational equations and characteristic roots, the linear stability conditions are derived. The analysis shows that triangular points are stable when the mass parameter lies within 0   < c, and unstable otherwise. The critical mass ratio c is obtained, and its range of stability is shown to increase, decrease, or remain unchanged depending on the sign of parameter p, which depends on radiation and oblateness coefficients. These results demonstrate that oblateness and radiation significantly modify the location and stability of triangular points compared to the classical restricted three‑body case, offering deeper insights into celestial mechanics and artificial satellite dynamics

Downloads

Download data is not yet available.

References

Markellos, V. V., Papadakis, K. E., & Perdios, E. A. (1996). Non-linear stability zones around triangular equilibria in the plane circular restricted three body problem with oblateness. Astrophysics and Space Science, 245(1), 157–164. https://doi.org/10.1007/BF00637811 DOI: https://doi.org/10.1007/BF00637811

Markellos, V. V., Perdios, E. A., & Papadakis, K. E. (1995). Non-linear stability zones around triangular Lagrangian points. Astrophysics and Space Science, 226(1), 95–110. https://doi.org/10.1007/BF00643967 DOI: https://doi.org/10.1007/978-1-4899-1085-1_35

Bhatnagar, K. B., & Hallan, P. P. (1994). Effect of perturbed potentials on the non-linear stability of L4. Astrophysics and Space Science, 213(2), 299–306. https://doi.org/10.1007/BF00641754 DOI: https://doi.org/10.1007/BF00641754

Marchal, C. (1991). Predictability, stability and chaos in dynamical systems. In NATO ASI Series B: Physics (Vol. 272). Springer. https://doi.org/10.1007/978-1-4684-5997-5_6 DOI: https://doi.org/10.1007/978-1-4684-5997-5_6

Schmidt, D. S. (1989). The stability of the Lagrangian point L4. In Stability of the Lagrangian Point L4. Springer. https://doi.org/10.1007/978-94-009-0985-4_34 DOI: https://doi.org/10.1007/978-94-009-0985-4_34

Sharma, R. K. (1987). Restricted problem considering oblateness and radiation. Indian Journal of Pure and Applied Mathematics.

Meyer, K. R., & Schmidt, D. S. (1986). The stability of the Lagrange triangular point and a theorem of Arnold. Journal of Differential Equations, 62(2), 222–236. https://doi.org/10.1016/0022-0396(86)90098-7 DOI: https://doi.org/10.1016/0022-0396(86)90098-7

Singh, J., & Ishwar, B. (1985). Effect of variable mass on equilibrium points in the restricted three body problem. Celestial Mechanics and Dynamical Astronomy. DOI: https://doi.org/10.1007/BF01227652

Bhatnagar, K. B., & Hallan, P. P. (1979). Effect of perturbed potentials on the stability of libration points in the restricted problem. Celestial Mechanics, 20(1), 95–103. https://doi.org/10.1007/BF01230231 DOI: https://doi.org/10.1007/BF01230231

Subbarao, P. V., & Sharma, R. K. (1975). Stability of triangular points of equilibrium in the restricted three body problem. Astrophysics and Space Science, 43(2), 381–383. https://doi.org/10.1007/BF00641712

Vidyakin, V. V. (1974). Stationary solutions and stability with oblateness in the restricted three body problem. Celestial Mechanics, 13(2), 137–149. https://doi.org/10.1007/BF01232721 DOI: https://doi.org/10.1007/BF01232721

Neokleove, V. V. (1970). Location of Lagrangian points with oblateness. Soviet Astronomy Journal.

Richards, P. (1962). Asymptotic stability of triangular points in the restricted three body problem. Astronomical Journal. DOI: https://doi.org/10.1016/0019-1035(62)90032-5

Leontovich, M. A. (1962). Critical stability of triangular equilibrium points. Soviet Physics Doklady.

Radzievskii, V. V. (1950). The restricted problem of three bodies taking account of light pressure. Astronomicheskii Zhurnal, 27, 250–256.

Downloads

Published

05-02-2026

Issue

Vol. 13 No. 1 (2026): January-February

Section

Research Articles

License

Copyright (c) 2026 International Journal of Scientific Research in Science and Technology

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

https://creativecommons.org/licenses/by/4.0

How to Cite

[1]
Mahesh Kumar and Avdhesh Kumar, Trans., “Stability of Triangular Equilibrium Points in the Generalised Photogravitational Restricted Three Body Problem”, Int J Sci Res Sci & Technol, vol. 13, no. 1, pp. 198–207, Feb. 2026, doi: 10.32628/IJSRST26132.