Spectral Decomposition of Geopotential, Earth and Ocean Tidal Perturbations in Linear Satellite Theory

The equivalence-class structure of the frequency mapping is investigated for the nonresonant cases of both geopotential and tidal perturbations of orbits with circulating or frozen perigee. Kaula's (1961) linear satellite theory is the foundation for a technique for deriving the spectra of the perturbations as complex terms which depend on four indices. A set of algorithms are developed which describe the frequencies and terms with equivalent frequencies in the expansion of the perturbations in linear theory. The composition rule of frequency allows the generation of all the combinations of indices up to a maximum degree L and maximum value Q. An application of the algorithm is given for the spectral decomposition of geopotential perturbations. The algorithm permits the direct application of Kaula's theory without searching the set of frequencies.