The Existence and Stability of Equilibrium Points in the Robe's Restricted Three-Body Problem

Details The Existence and Stability of Equilibrium Points in the Robe's Restricted Three-Body Problem The Existence and Stability of Equilibrium Points in the Robe's Restricted Three-Body Problem

Feb 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001cemda..79..145h&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 79, Issue 2, p. 145-155 (2001).

Astronomy and Astrophysics

Astronomy

2

Restricted Three-Body Problem, Equilibrium Points, Buoyancy Force, Stability, Restricted Three-Body Problem, Equilibrium Points, Buoyancy Force, Stability

Scientific paper

The existence of all the equilibrium points, their location and stability in the Robe's (1977) restricted three—body problem have been studied. It is seen that the center of the first primary is always an equilibrium point, whatever be the values of the density parameter K, eccentricity parameter eand mass parameter μ. The other equilibrium points exist only when K ≠ 0 and e = 0 that is when the second primary, a mass point, moves around the first, a spherical shell filled with fluid, in a circular orbit. When K > 1, there is one additional equilibrium point lying on the line joining the center of the first primary and the second primary. When K + μ = 1, there are infinite number of equilibrium points in the x—yplane lying on a circle of radius one and center as the second primary, provided the points are inside the spherical shell. When K < 0 and K + μ > 0, there are two more equilibrium points lying in the x—z plane forming triangles with the center of the shell and the second primary. Results of the stability of the equilibrium point (-μ,0,0), center of the first primary are the same as those given by Robe (1977). Circular points and triangular points are always unstable. The equilibrium point collinear with the center of the shell and the second primary is stable provided μ and Ksatisfy the inequality 16μ (K - 1)^2 < (μ + sqrt {μ ( - 4 + 4K + μ )} )^3 .

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