Equilibrium solutions of the restricted problem of 2 + 2 bodies

Details Equilibrium solutions of the restricted problem of 2 + 2 bodies Equilibrium solutions of the restricted problem of 2 + 2 bodies

Jul 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984cemec..33..271w&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 33, July 1984, p. 271-294.

Physics

15

Celestial Mechanics, Equilibrium Equations, Lagrangian Equilibrium Points, Many Body Problem, Gravitation Theory, Orbit Calculation, Perturbation Theory, Systems Stability, Tables (Data)

Scientific paper

Fourteen equilibrium solutions of the restricted problem of 2+2 bodies are shown to exist. Six of these solutions are located about the collinear Lagrangian points of the classical restricted problem of three bodies. Eight solutions are found in the neighborhood of the triangular Lagrangian points. Linear stability analysis reveals that all of the equilibrium solutions are unstable with the exception of four solutions; two in the vicinity of each of the triangular Lagrangian points. These four solutions are found to be stable provided the mass parameter of the primary masses is less than a critical value which depends also on the mass of the minor bodies.

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