Abstract
The purpose of the present paper is to investigate the motion’s properties of an infinitesimal body in three-dimensional version of Hill’s problem where the mass of the infinitesimal body is supposed to vary with time. As commonly done, the infinitesimal body is assumed to move under the influence of the other massive and oblate bodies that also have radiation effects. We suppose that the whole system is subject to a perturbation on Coriolis and on centrifugal forces. By using the various transformations, we extract the equations of motion and Jacobi quasi-integral. The properties like the locations of equilibrium points, regions of motion, surfaces with projection, trajectories allocation and the basins of attraction are investigated for various values of mass parameters. The stability is examined by using Meshcherskii space-time inverse transformations.
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REFERENCES
A. Abdulraheem and J. Singh, Astrophys. Space Sci. 317, 9 (2008).
E. I. Abouelmagd and S. M. El-Shaboury, Astrophys. Space Sci. 341, 331 (2012). http://dx.doi.org/10.1007/s10509-012-1093-7.
E. I. Abouelmagd and A. Mostafa, Astrophys. Space Sci. 357, 58 (2015). http://dx.doi.org/10.1007/s10509-015-2294-7.
E. I. Abouelmagd, A. A. Ansari, M. S. Ullah, and J. L. G. Guirao, The Astronomical Journal 160 (5), 216 (2020). http://dx.doi.org/10.3847/1538-3881/abb1bb.
A. A. Ansari, Italian Journal of Pure and Applied Mathematics 38, 581 (2017).
A. A. Ansari, Applications and Applied Mathematics: An International Journal 13 (2), 818 (2018).
A. A. Ansari, New Astronomy 83 (2020a) http://dx.doi.org/10.1016/j.newast.2020.101496.
A. A. Ansari, Sultan Qaboos University Journal for Science 25 (1), 61 (2020b).
A. A. Ansari and A. Mahtab, International Journal of Advanced Astronomy 5 (1), 19 (2017).
A. A. Ansari and S. N. Prasad, Astron. Lett. 46, 275 (2020). http://dx.doi.org/10.1134/S1063773720040015
A. A. Ansari, R. Kellil, A. Ali, and M. Alam, Applications and Applied Mathematics: An International Journal 14 (2), 985 (2019).
A. A. Ansari, K. R. Meena, and S. N. Prasad, Romanian Astron. J. 30, 135 (2020).
A. A. Ansari, M. Alam, K. R. Meena, and A. Ali, Appl. Math. Inf. Sci. 15 (2), 189 (2021).
A. S. Beevi and R. K. Sharma, Astrophys. Space Sci. 340, 245–261 (2012). http://dx.doi.org/10.1007/s10509-012-1052-3.
K. B. Bhatnagar and P. P. Hallan, Celest. Mech. 20, 95 (1979).
F. Bouaziz-Kellil, Advances in Astronomy, 1 (2020).https://doi.org/10.1155/2020/6684728.
C. N. Douskos, Astrophys. Space Sci. 326, 263 (2010).
J. H. Jeans, Astronomy and Cosmogony (Cambridge University Press, Cambridge, 1928).
A. L. Kunitsyn, J. of Applied Mathematical Mechanics 65, 703 (2001).
L. G. Lukyanov, Astronomy Letters 35 (5), 349 (2009).
M. P. Markakis, A. E. Perdiou, and C. N. Douskos, Astrophys. Space Sci. 315 (2), 297 (2008).
V. V. Markellos and A. E. Roy, Celestial Mechanics 23 (2), 269 (1981).
V. V. Markellos, A. E. Roy, M. J. Velgakis, and S. S. Kanavos, Astrophys. Space Sci. 271 (2), 293 (2000).
V. V. Markellos, A. E. Roy, E. A. Perdios, and C. N. Douskos, Astrophys. Space Sci. 278 (2), 295 (2001).
I. V. Meshcherskii, Works on the Mechanics of Bodies of Variable Mass (GITTL, Moscow, 1949).
A. E. Perdiou, V. V. Markellos, and C. N. Douskos, Earth, Moon, and Planets 97, 127 (2006). https://doi.org/10.1007/s11038-006-9065-y.
R. K. Sharma and P. V. SubbaRao, Celest. Mech. 13, 137 (1976). http://dx.doi.org/10.1007/BF01232721.
J. Singh and B. Ishwar, Celest. Mech. 35, 201 (1985).
J. Singh and J. J. Taura, Astrophys. Space Sci. 343, 95 (2013). http://dx.doi.org/10.1007/s10509-012-1225-0.
V. Szebehely, Theory of Orbits (Academic Press, New York, 1967).
M. J. Zhang, C. Y. Zhao, and Y. Q. Xiong, Astrophys. Space Sci. 337, 107 (2012). http://dx.doi.org/10.1007/s10509-011-0821-8.
E. E. Zotos, Astrophys. Space Sci. 362, 190 (2017). https://doi.org/10.1007/s10509-017-3169-x.
ACKNOWLEDGMENTS
The author is thankful to the Deanship of Scientific Research, College of Science at Buraidha, Qassim University, Saudi Arabia, for providing all the research facilities in the completion of this research work. The author wishes to express her sincere thanks to referees who provided precious expertise that greatly helped to improve the paper.
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Bouaziz-Kellil, F. Three-Dimensional Version of Hill’s Problem with Variable Mass. Astron. Lett. 47, 262–276 (2021). https://doi.org/10.1134/S1063773721040034
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DOI: https://doi.org/10.1134/S1063773721040034