Exploration of non-conventional techniques for the generation of element-based analytical ephemerides

A comprehensive description is presented of the many approaches to modern ephemeris generation that are found in the literature. Particularly, the generation of ephemerides build upon series of basis functions has been discussed, comparing Chebyshev, Fourier and Poisson series and supporting the arguments with factual data. For the case of Taylor series approximations, the relationship between the degree of the approximating polynomial and the total number of terms in the approximation have been qualitatively discussed as a function of the number of segments in which the time interval is split. A few examples are provided to show the accuracy and investigate the computational cost of various analytical and numerical ephemerides.