Computation of planetary orbits using Chebyshev polynomials

Details Computation of planetary orbits using Chebyshev polynomials Computation of planetary orbits using Chebyshev polynomials

Feb 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980a%26a....82..362r&link_type=abstract

Astronomy and Astrophysics, vol. 82, no. 3, Feb. 1980, p. 362-367. In French.

Mathematics

2

Chebyshev Approximation, Orbit Calculation, Planet Ephemerides, Solar Orbits, Numerical Integration, Polynomials, Series (Mathematics)

Scientific paper

Consideration is given to the application of Chebyshev approximations to the representation of planetary motions and the computation of planetary ephemerides. Chebyshev polynomial approximations of functions used in celestial mechanics are reviewed, with attention given to best approximation, best uniform approximation, and Pade-Chebyshev approximation schemes. The Chebyshev polynomial integration method proposed by Chapront (1977) for equations of planetary motion is then presented and applied to the computation of the ephemerides of four of the minor planets with high inclinations and eccentricities. Results of the computation are shown to agree well with independant numerical integrations, demonstrating the applicability of the method. A method for adjusting the constants of integration in the Chebyshev solutions for planetary ephemerides to agree with observations is then presented.

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