Mathematics
Scientific paper
Dec 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..28..415c&link_type=abstract
Celestial Mechanics, vol. 28, Dec. 1982, p. 415-430.
Mathematics
5
Celestial Mechanics, Chebyshev Approximation, Fourier Series, Moon, Planet Ephemerides, Time Series Analysis, Radii, Run Time (Computers), Time Functions, Vectors (Mathematics)
Scientific paper
A Fourier-Chebyshev approximation is presented for the calculation of the motions of celestial objects, and extended in its representational range. The approximation is applied to Fourier series with a large number of terms slowly varying in time. It is shown that high frequencies are approximate multiples of a base frequency, and can be represented by short periodic terms. Slowly variable time functions on a given interval, including long time periods, are approximated by Chebyshev polynomials. The method permits long time period calculations with reduced computer time. A numerical example is provided to show that the Fourier-Chebyshev approximation smoothly degrades outside of its range of representation. Comparison between results of calculation of the radius vector of the moon over an 8-day period obtained with the old and new methods is presented.
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