TITLE:
Existence and Stability of Equilibrium Points in the Robe’s Restricted Three-Body Problem with Variable Masses
AUTHORS:
Jagadish Singh, Oni Leke
KEYWORDS:
Robe’s Problem; Meshcherskii Law; GMP; Equilibruim Points
JOURNAL NAME:
International Journal of Astronomy and Astrophysics,
Vol.3 No.2,
June
4,
2013
ABSTRACT:
The positions and linear stability of the equilibrium
points of the Robe’s circular restricted three-body problem, are generalized
to include the effect of mass variations of the primaries in accordance with
the unified Meshcherskii law, when the motion of the primaries is determined by
the Gylden-Meshcherskii problem. The autonomized dynamical system with constant
coefficients here is possible, only when the shell is empty or when the
densities of the medium and the infinitesimal body are equal. We found that the
center of the shell is an equilibrium point. Further, when k﹥1; kbeing the constant
of a particular integral of the Gylden-Meshcherskii problem; a pair of
equilibrium point, lying in the -planewith each forming
triangles with the center of the shell and the second primary exist. Several of
the points exist depending on k; hence every point inside the shell
is an equilibrium point. The linear stability of the equilibrium points is
examined and it is seen that the point at the center of the shell of the
autonomized system is conditionally stable; while that of
the non-autonomized system is unstable. The triangular equilibrium points on
the -plane of both systems are
unstable.