ROUTH'S CRITICAL MASS RATIO AT THE TRIANGULAR LIBRATION CENTERS.
BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH
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Rouths criterion concerning the existence of periodic solutions around the triangular libration centers is shown to be valid only at the first order. For mass ratios greater than Rouths critical value, the analytical relations between the mass ratio and the lower bound of the orbital parameter is expanded in power series up to the fourteenth order. The corresponding dAlembert series representing the limiting periodic orbits up to the same order are used to provide approximate initial conditions for a numerical integration method. For mass ratios as high as 0.044 in canonical units, the Jacobi constant of the limiting orbits is a slightly increasing function of the mass ratio their characteristic exponents are of the stable type. As the mass goes on increasing, the multipliers keep moving on the unit circle in the complex plane from the real unit point to its opposite. The orbits evolve from infinitesimal ellipses centered at L sub 4 into large size asymmetrical ovals around that point. Author