AbstractThe emergence of satellite navigation has brought about the need for compact representations of satellite ephemerides. Polynomial representations offer several advantages. Polynomial representations of navigational and astronomical ephemerides are usually derived from discrete least squares approximations. However, to ensure a uniform distribution of the error, one should aim at a continuous Chebyshev approximation, whereby the maximum error in absolute value taken over the entire interval is minimized. This is feasible when the ephemeris is generated from a literal (analytical or semi‐analytical) development. But a discrete Chebyshev approximation, whereby the maximum error in absolute value is considered only over a finite set of reference points in the interval, 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 happens usually in a least squares approximatio