STABILITY OF THE TROJAN POINTS IN THE FOURBODY PROBLEM,
RAND CORP SANTA MONICA CALIF
Pagination or Media Count:
This memorandum investigates the positional stability of possible dust clouds in the vicinity of the Earth-Moon Trojan libration points by solving for the motion of their centers of mass in the presence of Earth, Moon, and Sun. A restricted four-body model is considered first, in which Earth and Moon are assumed to move along circular orbits. The lumped mass of the dust cloud is treated as the infinitesimal particle. The general restricted four-body equations of motion of a particle in the combined force fields of Earth, Moon, and Sun are set up in the usual rotating, baricenter-attached, coordinate frame of the restricted three-body problem. The linearized version of these equations for the neighborhood of the Trojan points is considered, and it is shown that the out-of-plane equation becomes uncoupled and can readily be solved. The solution of the set of linear coplanar equations is attempted by a perturbation technique and by the method of variation of constants, and it is shown that neither method is suitable due to unsatisfactory convergence of the resulting expansions. The orbital paths of the particle, determined by numerical integration of both linear and nonlinear equations on an IBM 7090, are shown in a series of figures.