A numerical time ephemeris of the Earth

Abstract

We present a time ephemeris of the Earth, TE405, which approximates a relativistic time-dilation integral from 1600 to 2200 using numerical quadrature of quantities supplied by the recent JPL ephemeris, DE405. The integral is required to transform between terrestrial time, TT, and the (solar-system) barycentric time scales Teph or TCB. Teph is a linear transformation of TCB that represents the independent variable of a modern ephemeris such as DE405. Our time-ephemeris results have an accuracy of order 0.1 ns, and we distribute them (at ftp://astroftp.phys.uvic.ca/pub/irwin/tephemeris/) in a Chebyshev form that requires much less computer time to evaluate than a detailed time-ephemeris series. We find angular-frequency and mass-transformation corrections that should be applied to the time-ephemeris series of Fairhead & Bretagnon (1990). These corrections make an extended form of this series with 1705 terms agree with our work to within 15 ns over the epoch range. We find a further correction of two long-term sinusoids that reduces this maximum residual to 5 ns. We suggest the long-term residuals fit by these sinusoids and the remaining short-term residuals are the result of errors in the fit of VSOP82/ELP2000 (the analytical ephemeris upon which the Fairhead & Bretagnon series is based) to the earlier JPL ephemeris, DE200. Following previous work (Fukushima 1995) we eliminate the linear term from TE405 by comparing with the corrected series results. The result for the linear coefficient of the term that is subtracted is ∆L C = 1.480 826 855 94 × 10−8 ± 1. × 10−17. We have not included the periodic postNewtonian and asteroid effects in the time-ephemeris calculation because they are negligible. However, when we add an average post-Newtonian and asteroid corrections of ∆L C = 109.7×10−18 and∆L C = (5. ± 5.) × 10−18 to∆L C the result is LC = 1.480 826 867 41 × 10−8 ± 2. × 10−17. When this result is combined with a recent result for the potential at the geoid (Bursa et al. 1997) corresponding to LG = 6.969 290 112 × 10−10 ± 6. × 10−18 we obtain K ≡ dTCB dTeph ≡ 1 (1 − LC)(1 − LG) = 1 + (1.550 519 791 54 × 10−8 ± 3. × 10−17). Send offprint requests to: Alan W. Irwin The factor K relates ephemeris units for time and distance and the corresponding SI units for the same quantities.