Remarks on Chebyshev representation of ephemeris

Abstract

Chebyshev coefficients of a coordinate representation can be used to form the corresponding velocity representation. One way is to directly apply them to the derivatives of Chebyshev polynomials, another is to compute from them the Chebyshev coefficients of the velocity representation. The advantages of the latter over the former ways are illustrated. Also, the approach of generating Chebyshev coefficients developed by Newhall (1989) is extended such that coordinate, velocity and acceleration are consistently treated. The resulting representations are all continuous.