We present a numerical time ephemeris, TE405, which approximates a relativistic time-dilation integral (, see Eq. ) that is required to transform (see Eqs.  and ) between terrestrial time, , and either the independent variable of a modern ephemerides, , or the (solar-system) barycentric coordinate time, . We calculate TE405 using numerical quadrature of quantities supplied by the JPL ephemeris, DE405, and the results are presented (at ftp://astroftp.phys.uvic.ca/pub/irwin/tephemeris/ ) as a file of Chebyshev interpolation coefficients and associated software similar to the JPL ephemeris itself. The results are meant to be a companion to DE405 and can be used to quickly interpolate values of the time ephemeris or its derivative for any epoch within the range of DE405 (1600 to 2200). The interpolation errors are 0.3 ps in the time ephemeris and in its derivative which provides a numerically clean result for comparison with future time ephemerides. The accuracy (maximum total error from all sources aside from mean rate adjustments) is estimated to be the order of 0.1 ns in the time ephemeris and in its derivative. These levels of accuracy should satisfy all current needs.
We have investigated errors in the the time-ephemeris series of FB. The published coefficients were given with an invalid angular frequency transformation, and this affected the comparisons with both the FB and FB2 series given in Paper I (although the FB3 form of this series as privately communicated from Bretagnon for the present paper does not have this transformation applied). Truncation of the series at a finite number of terms can be another substantial source of error (Fig. 2), and it is essential to use an amplitude limit of at most 10 ps (the limit of the 1705-term FB3 series) in order to obtain precise series results. A mass transformation reduces the discrepancies of short time-scale between the FB3 series and TE405 but still leaves a long-term residual which still deviates by 15 ns from TE405 (Fig. 3). We suggest that the long-term residuals (which can be fit by two sinusoids [Table 2 and Fig. 4]) and somewhat smaller short-term residuals reflect known differences between the analytical VSOP82/ELP2000 ephemerides upon which the FB3 series is based and the numerical JPL ephemeris, DE200.
We use the hybrid technique of Paper I in combination with TE405 and the sinusoid- and mass-corrected form of the FB3 series to determine the value which we use to adjust the rate of TE405 and ultimately determine the K value (Eq. ). The K value relates ephemeris units for time and distance and the corresponding SI units for the same quantities.
© European Southern Observatory (ESO) 1999
Online publication: July 26, 1999