ПИСЬМА В АСТРОНОМИЧЕСКИЙ ЖУРНАЛ, 2021, том 47, № 4, с. 300
Three-Dimensional Version of Hill’s Problem with Variable Mass1
© 2021 г. F. Bouaziz-Kellil
College of Science and Arts at Buraidha, Qassim University, Qassim, Saudi Arabia
Поступила в редакцию 22.01.2021 г.
После доработки 25.02.2021 г.; принята к публикации 04.03.2021 г.
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.
Keywords: Hill’s problem, Variable mass, Jacobi quasi-integral, equilibrium points, stability, Basins of
attraction.
DOI: 10.31857/S0320010821040045
1Полная версия статьи публикуется в англоязычной версии журнала (Astronomy Letters, Vol. 47, No. 4, 2021).
*E-mail: fm.boazuez@qu.edu.sa
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