Astronomy and Astrophysics – Astronomy
Scientific paper
Jan 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979navig..26....1d&link_type=abstract
Navigation (USA), Vol. 26, No. 1, p. 1 - 11
Astronomy and Astrophysics
Astronomy
1
Chebyshev Approximation, Discrete Functions, Ephemerides, Interpolation, Error Analysis, Gibbs Phenomenon, Least Squares Method, Satellite Tracking
Scientific paper
Polynomial representations of astronomical ephemerides are usually derived from discrete least-squares approximations. Ideally, to ensure a uniform distribution of the error, one should aim at a continuous Chebyshev approximation. This is feasible when the ephemeris is generated from a literal (analytical or semianalytical) development. But a discrete Chebyshev approximation is a realistic compromise. Application to the moon and geosynchronous satellites has given good results. On the whole, long ranges (several times the sidereal period) may be covered by polynomials of degree 30 to 50 with a moderate error. A low-degree approximation over half the period usually delivers a high accuracy. Gibbs' phenomena, i.e. rapid oscillations of increasing amplitudes in the error curve at both ends of the approximation interval, are of course absent, contrary to what usually happens in a least-squares approximation.
Deprit Andre
Pickard H. M.
Poplarchek W.
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