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Shapes and Mass Variation Effects of the Bodies in the Generalized Elliptic Restricted 3-Body Problem

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Abstract

The elliptic restricted three-body problem is used to investigate the motion behavior of the smallest body (test particle), where the primaries move in elliptical orbits around their common center of mass. Here the primary is taken as a radiating oblate body and the secondary is considered as a dipole, while the third smallest body is varying its mass according to the Jeans law. Under these assumptions we determine the equations of motion and the quasi-Jacobian integral for the test particle which is moving in space under the gravitational forces of the primaries. The locations of stationary points and their stability states are determined and then, after regions of motion, Poincaré surfaces of section and basins of attraction are illustrated.

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REFERENCES

  1. G. Beutler, Methods of Celestial Mechanics, Vol. 1: Physical, Mathematical, and Numerical Principles (Springer, New York, 2005).

  2. S. V. Ershkov, Adv. Astron. 2015, 615029 (2015).

  3. S. V. Ershkov and D. Leshchenko, Astrophys. Space Sci. 364 (11), 207 (2019).

    Article  ADS  Google Scholar 

  4. A. Abozaid, H. H. Selim, K. A. Gadallah, I. A. Hassan, and E. I. Abouelmagd, Appl. Math. Nonlin. Sci. 5, 157 (2020).

    Google Scholar 

  5. R. K. Sharma and P. V. S. Rao, Celest. Mech. 13, 137 (1976).

    Article  ADS  Google Scholar 

  6. A. Abdulraheem and J. Singh, Astrophys. Space Sci. 317, 9 (2008).

    Article  ADS  Google Scholar 

  7. E. I. Abouelmagd, Astrophys. Space Sci. 342, 45 (2012).

    Article  ADS  Google Scholar 

  8. L. B. T. Santos, F. Antonio, B. A. Padro, and D. M. Sanchez, Astrophys. Space Sci. 362, 61 (2017).

    Article  ADS  Google Scholar 

  9. F. Bouaziz-Kellil, Adv. Astron. 2020, 1 (2020).

    Article  Google Scholar 

  10. A. Ansari, New Astron. 83, 101496 (2021).

  11. A. Ansari and R. Kellil, Roman. Astron. J. 31, 81 (2021).

    ADS  Google Scholar 

  12. A. Ansari, Astron. Rep. 65, 1178 (2021).

    Article  ADS  Google Scholar 

  13. S. K. Sahdev and A. A. Ansari, Sci. Int. (Lahore) 33, 147 (2021).

    Google Scholar 

  14. S. K. Sahdev and A. A. Ansari, Gedrag Organis. Rev. 34, 1 (2021).

    Google Scholar 

  15. V. V. Radzievsky, Astron. Zh. 27, 250 (1950).

    Google Scholar 

  16. V. V. Radzievsky, Astron. Zh. 30, 225 (1953).

    Google Scholar 

  17. Y. A. Chernikov, Sov. Astron. 14, 176 (1970).

    ADS  Google Scholar 

  18. A. Perezhogin, Sov. Astron. Lett. 2, 174 (1976).

    ADS  Google Scholar 

  19. L. Kunitsyn, J. Appl. Math. Mech. 65, 703 (2001).

    Article  MathSciNet  Google Scholar 

  20. J. Singh and A. Umar, Astron. J. 143 (5), 109 (2012).

    Article  ADS  Google Scholar 

  21. V. Szebehely and G. E. O. Giacaglia, Astron. J. 69, 230 (1964).

    Article  ADS  Google Scholar 

  22. A. Bennett, Icarus 4, 177 (1965).

    Article  ADS  Google Scholar 

  23. R. Broucke, Am. Inst. Aeronaut. Astronaut. 7, 1003 (1969).

    Article  Google Scholar 

  24. S. Ichtiaroglou, Astron. Astrophys. 92, 139 (1980).

    ADS  MathSciNet  Google Scholar 

  25. E. Sarris, Astrophys. Space Sci. 162, 107 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  26. Ch. Lhotka, Thesis for Doktor Reris Naturalis (2008). https://doi.org/10.13140/RG.2.1.2101.3848

  27. J. Singh and A. Umar, Astrophys. Space Sci. 341, 349 (2012).

    Article  ADS  Google Scholar 

  28. H. Peng and S. Xu, Celest. Mech. Dyn. Astron. 123, 279 (2015).

    Article  ADS  Google Scholar 

  29. A. Umar and J. Singh, Adv. Space Res. 55, 2584 (2015).

    Article  ADS  Google Scholar 

  30. J. Singh and R. K. Tyokyaa, Eur. Phys. J. Plus 131, 365 (2016).

    Article  Google Scholar 

  31. A. Narayan, A. Chakraborty, and A. Dewangan, Few-Body Syst. 59, 43 (2018).

    Article  ADS  Google Scholar 

  32. F. Ferrari and M. Lavagna, Nonlin. Dyn. 93, 453 (2018).

    Article  Google Scholar 

  33. A. Delshams, V. Kaloshin, A. Dela Rosa, and T. M. Seara, Commun. Math. Phys. 366, 1173 (2019).

    Article  ADS  Google Scholar 

  34. A. Ansari, L. Narain, and S. N. Prasad, Gedrag Organis. Rev. 33, 398 (2020).

    Google Scholar 

  35. S. Ershkov, E. Abouelmagd, and A. Rachinskaya, Arch. Appl. Mech. 91, 4599 (2021).

    Article  ADS  Google Scholar 

  36. A. Ansari, Roman. Astron. J. 31, 275 (2021).

    ADS  Google Scholar 

  37. S. Ershkov, D. Leshchenko, and E. Y. Prosviryakov, Arch. Appl. Mech. 93, 823 (2022).

    Article  Google Scholar 

  38. J. Singh and B. Ishwar, Celest. Mech. 35, 201 (1985).

    Article  ADS  Google Scholar 

  39. L. G. Lukyanov, Astron. Lett. 35, 349 (2009).

    Article  ADS  Google Scholar 

  40. J. Singh, O. Leke, and A. Umar, Astrophys. Space Sci. 327, 299 (2010).

    Article  ADS  Google Scholar 

  41. M. J. Zhang, C. Y. Zhao, and Y. Q. Xiong, Astrophys. Space Sci. 337, 107 (2012).

    Article  ADS  Google Scholar 

  42. A. Ansari, Ital. J. Pure Appl. Math. 38, 581 (2017).

    Google Scholar 

  43. A. Ansari, Appl. Appl. Math. Int. J. 13, 818 (2018).

    Google Scholar 

  44. A. Ansari and S. N. Prasad, Astron. Lett. 46, 275 (2020).

    Article  ADS  Google Scholar 

  45. A. Ansari, K. R. Meena, and S. N. Prasad, Roman. Astron. J. 30, 135 (2020).

    ADS  Google Scholar 

  46. F. Bouaziz and A. A. Ansari, Astron. Nachr. 342, 666 (2021).

    Article  ADS  Google Scholar 

  47. S. Ferraz-Mello, A. Rodríguez, and H. Hussmann, Celest. Mech. Dyn. Astron. 101, 171 (2008).

    Article  ADS  Google Scholar 

  48. S. V. Ershkov, Earth, Moon Planets 120, 15 (2017).

    Article  ADS  Google Scholar 

  49. S. Ershkov, D. Leshchenko, and E. Aboeulmagd, Eur. Phys. J. Plus 136, 387 (2021).

    Article  Google Scholar 

  50. J. M. A. Danby, Fundamentals of Celestial Mechanics, 2nd ed. (Willmann-Bell, Richmond, VA, 1988).

    Google Scholar 

  51. J. Singh and R. K. Tyokyaa, New Astron. 98, 101917 (2023).

  52. E. I. Abouelmagd and A. Mostafa, Astrophys. Space Sci. 357, 58 (2015).

    Article  ADS  Google Scholar 

  53. J. H. Jeans, Astronomy and Cosmogony (Cambridge Univ. Press, Cambridge, 1928).

    MATH  Google Scholar 

  54. V. Meshcherskii, Works on the Mechanics of Bodies of Variable Mass (GITTL, Moscow, 1949).

    MATH  Google Scholar 

  55. A. Ansari, R. Kellil, and S. K. Sahdev, Mech. Solids 57, 1104 (2022).

    Article  ADS  Google Scholar 

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ACKNOWLEDGMENTS

The authors are thankful to the editor and reviewer both for giving us opportunity to improve our paper up to the present form.

Funding

We are thankful to The Deanship of scientific research, Majmaah University, KSA.

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Authors and Affiliations

  1. Department of Mathematics, College of Science Al-zulfi, Majmaah University, Al-Majmaah, Kingdom of Saudi Arabia

    A. B. Albidah

  2. Shivaji College, University of Delhi, Delhi, India

    Abdullah A. Ansari

  3. International Center for Advanced Interdisciplinary Research (ICAIR), Sangam Vihar, New Delhi, India

    Abdullah A. Ansari

Authors
  1. A. B. Albidah
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  2. Abdullah A. Ansari
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Correspondence to A. B. Albidah or Abdullah A. Ansari.

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Albidah, A.B., Ansari, A.A. Shapes and Mass Variation Effects of the Bodies in the Generalized Elliptic Restricted 3-Body Problem. Astron. Rep. 67, 393–403 (2023). https://doi.org/10.1134/S1063772923040017

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