Impact of Albedo, Heterogeneity, Perturbations and Circumstellar Dust in the Circular Restricted Three-body Problem

Jagadish Singh; Sunusi Haruna

doi:doi:10.11648/j.sdp.20260101.17

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Impact of Albedo, Heterogeneity, Perturbations and Circumstellar Dust in the Circular Restricted Three-body Problem

Jagadish Singh

, Sunusi Haruna^*

Published in Science Discovery Physics (Volume 1, Issue 1)

Received: 12 April 2025 Accepted: 4 May 2025 Published: 12 March 2026

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Abstract

This paper explore the dynamical influence of multiple astrophysical motivated perturbations in the framework of the circular restricted three-body problem (CR3BP), focusing on the stability and evolution of trajectories near the triangular libration points. The model incorporates albedo-related radiation pressure, mass heterogeneity of the primaries, additional perturbing forces, and the gravitational potential from a circumstellar dust belt, simulating a more realistic environment such as that found in binary stellar systems surrounded by debris disks. By extending the classical CR3BP to include these effects, we investigate their combined impact on the topology of the phase space, the location and stability of the libration points. Numerical simulations reveal that circumstellar dust and reflective radiation can significantly deform the effective potential landscape, leading to shifts in equilibrium locations and the emergence of new dynamical behaviours. The findings provide insight into the complex dynamical environments of young stellar binaries, protoplanetary systems, and dust-rich exoplanetary configurations, and may inform future observational or mission-planning efforts in such contexts. Besides the three collinear libration points typically seen in classical models, the effects of heterogeneity and the belt introduce an additional collinear point, though it is linearly unstable. The findings of this study could be applied to the motion of celestial bodies under the influence of perturbing forces such as heterogeneity, the Albedo effect, and the belt.

Published in	Science Discovery Physics (Volume 1, Issue 1)
DOI	10.11648/j.sdp.20260101.17
Page(s)	70-87
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

CR3BP, Perturbation, Albedo, Heterogeneous Spheroid, Potential from a Belt

References

[1]	AbdulRaheem, A. and Singh, J. (2006). Combined effects of perturbations, radiation and oblateness on the stability of libration points in the restricted three-body problem. Astronomical journal, 131: 1880-1885. https://doi.org/10.1086/500654
[2]	Ansari, A. A., Alhussain, Z. A and Prassad, S. N. (2018). ER3BP when the smaller Primaries are heterogeneous Spheroid of three layers and infinitesimal body varies its mass. J. Astrophys. Astron. 39, 57. https://doi.org/10.1007/s12036-018-9540-7
[3]	Idrisi, M. J. (2017). A study of libration points in CR3BP under albedo effect. International Journal of Advanced Astronomy, 5: 1-6.
[4]	Idrisi, M. J. (2017a). A Study of Libration Points in Modified CR3BP Under Albedo Effect when Smaller Primary is an Ellipsoid. Journal of the Astronautical Sciences, 64: 379-398. https://doi.org/10.1007/s40295-017-0115-7
[5]	Idrisi, M. J. and Ullah, M. S. (2018). Non-collinear libration points in ER3BP with albedo effect and oblateness. Journal of Astrophysics and Astronomy, 39: 1-10. https://doi.org/10.1007/s12036-018-9520-y
[6]	Idrisi, M. J. and Ullah, M. S. (2020). A Study of Albedo Effects on Libration Points in the Elliptic Restricted Three-Body Problem. Journal of the Astronautical Sciences, 67: 863-879.
[7]	Jiang, I. G and Yeh, L. C.(2006). On the chermnyks-like, The equilibrium points. Astrophs. space sci. 306, 189-200 https://doi.org/10.1007/s10509-006-9186-9
[8]	Kumari Shalini. M. Javed Idrisi. J. K. Singh. M. Shahbaz ullah (2023). Stability analysis in the R3BP under the effect of heterogeneous Spheroid. New Astronomy. (2023).104, 102556. https://doi.org/10.1016/j.newast.2023.102556
[9]	Kumari Shalini. Md sanam Suraj. Rajiv Aggarwal (2016). The Nonlinear stability of L₄ in the R3BP when the smaller Primary is a heterogeneous Spheroid. American Astronautical society. 64, 18: 49 (2016). https://doi.org/10.1007/s40295-016-0093-1
[10]	Md sanam Suraj. M. R. Hassan. Md chan Asique (2014). The Photo gravitational R3BP when the Primaries are Heterogeneous Spheroid with Three Layers. American Astronautical society. 61, 133 (2014). https://doi.org/10.1007/s40295-014-0026-9
[11]	Shipra Chauhan, Denish Kumar and Bhavneet Kaur (2018). Restricted Three body problem under the effect of Albedo, when the smaller primary is a finite straight segment. Appl. math. ISSN: 1932-9466, vol. 13, 2 (2018), pp: 1200-1215.
[12]	Singh, J. and Haruna (2014). Equilibrium Points and stabilty under effect of Radiation, perturbating forces in the Restricted Problem of Three oblate bodies. Astrophysics and Space Science, 349, 107-115. https://doi.org/10.1007/s10509-013-1627-7
[13]	Singh, J. and Haruna (2020). Motion around the Triangular Equilibrium Points in the Circular Restricted Three-Body Problem with radiating heterogeneous primaries surrounde by a belt. Scientific report (2020). 18861. https://doi.org/10.1038/s41598-020-75174-7
[14]	Singh, J. and Taura, J. J. (2013). Motion in the generalized restricted three-body problem” Astrophysics and Space Science, 343: 95-106. https://doi.org/10.1007/s10509-012-1225-0
[15]	Singh, J. and Taura, J. J. (2014). Effect of Triaxial, oblateness and Gravitational potential from the belt on the linear stability of L_4,5 in the R3BP. Astrophysics and Space Science, 35: 729-743. https://doi.org/10.1007/s12036-014-9308-7
[16]	Singh, J. and Tyokyaa, K. R. (2023). Albedo effects in the ER3BP with an oblate primary, a triaxial secondary and a potential due to belt. Scientific reports, (2023) 13: 4286. https://doi.org/10.1038/s41598-023-30671-3
[17]	Singh, J., and Ishwar, B. (1999). Stability of triangular points in the generalized photo gravitational restricted three body problem. Aryabhatta Research Institute of Observatory Science. India, 27: 415-424.
[18]	Singh, J. and Amuda T. O (2019). Stability analysis of triangular equilibrium points in the restricted three-body problem under effects of circumbinary disc, radiation and drag forces. Journal of Astrophysics and Astronomy 40, 5. https://doi.org/10.1007/s12036-019-9573-6
[19]	Singh, J. and Taura, J. J (2016). Combined effects of oblateness, radiation and cluster of material points on the stability of triangular libration points in R3BP. Astrophysics and space science. https://doi.org/10.1007/s10509-014-1860-8

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APA Style

Singh, J., Haruna, S. (2026). Impact of Albedo, Heterogeneity, Perturbations and Circumstellar Dust in the Circular Restricted Three-body Problem. Science Discovery Physics, 1(1), 70-87. https://doi.org/10.11648/j.sdp.20260101.17

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ACS Style

Singh, J.; Haruna, S. Impact of Albedo, Heterogeneity, Perturbations and Circumstellar Dust in the Circular Restricted Three-body Problem. Sci. Discov. Phys. 2026, 1(1), 70-87. doi: 10.11648/j.sdp.20260101.17

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AMA Style

Singh J, Haruna S. Impact of Albedo, Heterogeneity, Perturbations and Circumstellar Dust in the Circular Restricted Three-body Problem. Sci Discov Phys. 2026;1(1):70-87. doi: 10.11648/j.sdp.20260101.17

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@article{10.11648/j.sdp.20260101.17,
  author = {Jagadish Singh and Sunusi Haruna},
  title = {Impact of Albedo, Heterogeneity, Perturbations and Circumstellar Dust in the Circular Restricted Three-body Problem},
  journal = {Science Discovery Physics},
  volume = {1},
  number = {1},
  pages = {70-87},
  doi = {10.11648/j.sdp.20260101.17},
  url = {https://doi.org/10.11648/j.sdp.20260101.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sdp.20260101.17},
  abstract = {This paper explore the dynamical influence of multiple astrophysical motivated perturbations in the framework of the circular restricted three-body problem (CR3BP), focusing on the stability and evolution of trajectories near the triangular libration points. The model incorporates albedo-related radiation pressure, mass heterogeneity of the primaries, additional perturbing forces, and the gravitational potential from a circumstellar dust belt, simulating a more realistic environment such as that found in binary stellar systems surrounded by debris disks. By extending the classical CR3BP to include these effects, we investigate their combined impact on the topology of the phase space, the location and stability of the libration points. Numerical simulations reveal that circumstellar dust and reflective radiation can significantly deform the effective potential landscape, leading to shifts in equilibrium locations and the emergence of new dynamical behaviours. The findings provide insight into the complex dynamical environments of young stellar binaries, protoplanetary systems, and dust-rich exoplanetary configurations, and may inform future observational or mission-planning efforts in such contexts. Besides the three collinear libration points typically seen in classical models, the effects of heterogeneity and the belt introduce an additional collinear point, though it is linearly unstable. The findings of this study could be applied to the motion of celestial bodies under the influence of perturbing forces such as heterogeneity, the Albedo effect, and the belt.},
 year = {2026}
}

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TY  - JOUR
T1  - Impact of Albedo, Heterogeneity, Perturbations and Circumstellar Dust in the Circular Restricted Three-body Problem
AU  - Jagadish Singh
AU  - Sunusi Haruna
Y1  - 2026/03/12
PY  - 2026
N1  - https://doi.org/10.11648/j.sdp.20260101.17
DO  - 10.11648/j.sdp.20260101.17
T2  - Science Discovery Physics
JF  - Science Discovery Physics
JO  - Science Discovery Physics
SP  - 70
EP  - 87
PB  - Science Publishing Group
UR  - https://doi.org/10.11648/j.sdp.20260101.17
AB  - This paper explore the dynamical influence of multiple astrophysical motivated perturbations in the framework of the circular restricted three-body problem (CR3BP), focusing on the stability and evolution of trajectories near the triangular libration points. The model incorporates albedo-related radiation pressure, mass heterogeneity of the primaries, additional perturbing forces, and the gravitational potential from a circumstellar dust belt, simulating a more realistic environment such as that found in binary stellar systems surrounded by debris disks. By extending the classical CR3BP to include these effects, we investigate their combined impact on the topology of the phase space, the location and stability of the libration points. Numerical simulations reveal that circumstellar dust and reflective radiation can significantly deform the effective potential landscape, leading to shifts in equilibrium locations and the emergence of new dynamical behaviours. The findings provide insight into the complex dynamical environments of young stellar binaries, protoplanetary systems, and dust-rich exoplanetary configurations, and may inform future observational or mission-planning efforts in such contexts. Besides the three collinear libration points typically seen in classical models, the effects of heterogeneity and the belt introduce an additional collinear point, though it is linearly unstable. The findings of this study could be applied to the motion of celestial bodies under the influence of perturbing forces such as heterogeneity, the Albedo effect, and the belt.
VL  - 1
IS  - 1
ER  -

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Author Information

Jagadish Singh

Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria

Contact Email

http://orcid.org/0000-0003-3198-2839
Sunusi Haruna

Department of Science and Engineering, Kano State Polytechnic, Kano, Nigeria

Contact Email

http://orcid.org/0000-0002-8217-9192

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APA Style

Singh, J., Haruna, S. (2026). Impact of Albedo, Heterogeneity, Perturbations and Circumstellar Dust in the Circular Restricted Three-body Problem. Science Discovery Physics, 1(1), 70-87. https://doi.org/10.11648/j.sdp.20260101.17

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ACS Style

Singh, J.; Haruna, S. Impact of Albedo, Heterogeneity, Perturbations and Circumstellar Dust in the Circular Restricted Three-body Problem. Sci. Discov. Phys. 2026, 1(1), 70-87. doi: 10.11648/j.sdp.20260101.17

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AMA Style

Singh J, Haruna S. Impact of Albedo, Heterogeneity, Perturbations and Circumstellar Dust in the Circular Restricted Three-body Problem. Sci Discov Phys. 2026;1(1):70-87. doi: 10.11648/j.sdp.20260101.17

Copy | Download

@article{10.11648/j.sdp.20260101.17,
  author = {Jagadish Singh and Sunusi Haruna},
  title = {Impact of Albedo, Heterogeneity, Perturbations and Circumstellar Dust in the Circular Restricted Three-body Problem},
  journal = {Science Discovery Physics},
  volume = {1},
  number = {1},
  pages = {70-87},
  doi = {10.11648/j.sdp.20260101.17},
  url = {https://doi.org/10.11648/j.sdp.20260101.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sdp.20260101.17},
  abstract = {This paper explore the dynamical influence of multiple astrophysical motivated perturbations in the framework of the circular restricted three-body problem (CR3BP), focusing on the stability and evolution of trajectories near the triangular libration points. The model incorporates albedo-related radiation pressure, mass heterogeneity of the primaries, additional perturbing forces, and the gravitational potential from a circumstellar dust belt, simulating a more realistic environment such as that found in binary stellar systems surrounded by debris disks. By extending the classical CR3BP to include these effects, we investigate their combined impact on the topology of the phase space, the location and stability of the libration points. Numerical simulations reveal that circumstellar dust and reflective radiation can significantly deform the effective potential landscape, leading to shifts in equilibrium locations and the emergence of new dynamical behaviours. The findings provide insight into the complex dynamical environments of young stellar binaries, protoplanetary systems, and dust-rich exoplanetary configurations, and may inform future observational or mission-planning efforts in such contexts. Besides the three collinear libration points typically seen in classical models, the effects of heterogeneity and the belt introduce an additional collinear point, though it is linearly unstable. The findings of this study could be applied to the motion of celestial bodies under the influence of perturbing forces such as heterogeneity, the Albedo effect, and the belt.},
 year = {2026}
}

Copy | Download

TY  - JOUR
T1  - Impact of Albedo, Heterogeneity, Perturbations and Circumstellar Dust in the Circular Restricted Three-body Problem
AU  - Jagadish Singh
AU  - Sunusi Haruna
Y1  - 2026/03/12
PY  - 2026
N1  - https://doi.org/10.11648/j.sdp.20260101.17
DO  - 10.11648/j.sdp.20260101.17
T2  - Science Discovery Physics
JF  - Science Discovery Physics
JO  - Science Discovery Physics
SP  - 70
EP  - 87
PB  - Science Publishing Group
UR  - https://doi.org/10.11648/j.sdp.20260101.17
AB  - This paper explore the dynamical influence of multiple astrophysical motivated perturbations in the framework of the circular restricted three-body problem (CR3BP), focusing on the stability and evolution of trajectories near the triangular libration points. The model incorporates albedo-related radiation pressure, mass heterogeneity of the primaries, additional perturbing forces, and the gravitational potential from a circumstellar dust belt, simulating a more realistic environment such as that found in binary stellar systems surrounded by debris disks. By extending the classical CR3BP to include these effects, we investigate their combined impact on the topology of the phase space, the location and stability of the libration points. Numerical simulations reveal that circumstellar dust and reflective radiation can significantly deform the effective potential landscape, leading to shifts in equilibrium locations and the emergence of new dynamical behaviours. The findings provide insight into the complex dynamical environments of young stellar binaries, protoplanetary systems, and dust-rich exoplanetary configurations, and may inform future observational or mission-planning efforts in such contexts. Besides the three collinear libration points typically seen in classical models, the effects of heterogeneity and the belt introduce an additional collinear point, though it is linearly unstable. The findings of this study could be applied to the motion of celestial bodies under the influence of perturbing forces such as heterogeneity, the Albedo effect, and the belt.
VL  - 1
IS  - 1
ER  -

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