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TROJAN ORBITS. I. D'ALEMBERT SERIES AT L SUB 4,
BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH
The analytical continuation of the family of long period orbits at L sub 4 represents the normal Cartesian coordinates of the asteroid as dAlembert series in function of an orbital parameter. By means of a program that enables a computer to calculate symbolically in the real graded algebra of dAlembert series, the family of Trojan orbits is computed numerically up to the fourteenth order. Within the range of amplitudes of real Trojan planets, the dAlembert series are in very close agreement with the numerical results of Prof. E. Rabe. Outside this range, the poor convergence of the Fourier series is found to be imputed, not to a 131 commensurability between the Trojans libration period and Jupiters orbital period, but to the slow convergence of the dAlembert series all along the family of long period librations. Author
Also available from the authors.