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Three-Dimensional Version of Hill’s Problem with Variable Mass

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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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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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  1. College of Science and Arts at Buraidha, Qassim University, Qassim, Saudi Arabia

    Ferdous Bouaziz-Kellil

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  1. Ferdous Bouaziz-Kellil
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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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