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Astron. Astrophys. 348, 642-652 (1999)

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A numerical time ephemeris of the Earth

A.W. Irwin 1 and T. Fukushima 2

1 Department of Physics and Astronomy, University of Victoria, P.O. Box 3055, Victoria, British Columbia, Canada, V8W 3P6 (irwin@uvastro.phys.uvic.ca)
2 National Astronomical Observatory, 2-21-1, Ohsawa, Mitaka, Tokyo 181-8588, Japan (Toshio.Fukushima@nao.ac.jp)

Received 3 May 1999 / Accepted 14 June 1999


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, [FORMULA], and the (solar-system) barycentric time scales [FORMULA] or [FORMULA]. [FORMULA] is a linear transformation of [FORMULA] 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 [FORMULA]. We have not included the periodic post-Newtonian and asteroid effects in the time-ephemeris calculation because they are negligible. However, when we add an average post-Newtonian and asteroid corrections of [FORMULA] and [FORMULA] to [FORMULA] the result is [FORMULA]. When this result is combined with a recent result for the potential at the geoid (Bursa et al. 1997) corresponding to [FORMULA] we obtain


The factor K relates ephemeris units for time and distance and the corresponding SI units for the same quantities.

Key words: ephemerides – time – solar system: general

Send offprint requests to: Alan W. Irwin

© European Southern Observatory (ESO) 1999

Online publication: July 26, 1999