TROJAN ORBITS. I. D'ALEMBERT SERIES AT L SUB 4,
Abstract
The analytical continuation of the family of long period orbits at L sub 4 represents the normal Cartesian coordinates of the asteroid as d'Alembert 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 d'Alembert series, the family of Trojan orbits is computed numerically up to the fourteenth order. Within the range of amplitudes of real Trojan planets, the d'Alembert 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 13:1 commensurability between the Trojan's libration period and Jupiter's orbital period, but to the slow convergence of the d'Alembert series all along the family of long period librations. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1965
- Accession Number
- AD0612265
Entities
People
- Andre Delie
- Andre Deprit
Organizations
- Boeing