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Astron. Astrophys. 348, 642-652 (1999) 1. Introduction
The relativistic time-dilation integral,
The observational errors of spacecraft ranges pose a stringent
constraint on the maximum acceptable errors of a time-ephemeris
derivative. The typical error of a spacecraft range observed with the
Deep Space Network is 1 m (DSN 1999). At the distance of Pluto
this translates to a relative range error and corresponding
time-ephemeris derivative error of The observational errors of daily mean pulse-arrival epochs of pulsars pose a stringent constraint on the maximum acceptable errors of a time ephemeris. These epoch errors are less than 1 µs and are beginning to approach 0.1 µs (Kaspi et al. 1994). We adopt this latter value as the nominal best error of a daily mean pulse-arrival epoch. Using the criterion that systematic errors should be 2 orders of magnitude less than the smallest random errors leads to a maximum acceptable error for a time ephemeris of 1 ns. This error limit requires some care to achieve because it is 6 orders of magnitude smaller than the maximum absolute value of the time-ephemeris, 2 ms. Efforts to obtain analytical approximations for
As an alternative to the series approach, one may directly calculate a time ephemeris using numerical quadrature of quantities supplied by a planetary and lunar ephemeris (see Backer & Hellings 1986). The mass-corrected series results and numerical results made privately available from the JPL group to Fairhead and Bretagnon agreed within 3 ns over the epoch range from 1900 to 2000 (see Fig. 3 of FB). The 3-ns level of agreement between the JPL and FB time ephemerides was not obtained by subsequent much more extensive comparisons of numerical and analytical time ephemerides (Fukushima 1995, Paper I). For example, the RMS deviation of TE200 (a numerical time ephemeris based on the JPL ephemeris, DE200) with the FB2 series (an extended form of the FB series containing 791 terms) is 26 ns (Table 7 of Paper I). Subsequently, we found the source of this large disagreement was an inappropriate angular-frequency transformation (see discussion in Sect. 4) that was used for the published FB coefficients. Presumably, this source of error was not present in the published comparison between the FB results and the numerical time ephemeris from the JPL group. The purpose of the current paper is to follow up Paper I by
presenting new results for a numerical time ephemeris, series
corrections, and the ratio of ephemeris units to SI units (the
K value). We rigorously define in Sect. 2 the relativistic
time-dilation integral that is used to transform between Earth-based
and solar-system-based time scales. We present in Sect. 3 a numerical
approximation of this integral, TE405, which has an unprecedented
accuracy of 0.1 ns. We present in Sect. 4 angular-frequency and
mass transformations of the FB time-ephemeris series which reduce its
maximum errors to 15 ns from 1600 to 2200 and suggest the
remaining long-term residuals (which can be fit by two sinusoids) and
short-term residuals are due to errors in the fit of VSOP82/ELP2000 to
DE200. We use in Sect. 5 the combination of TE405 and the corrected FB
series to determine ![]() ![]() ![]() ![]() © European Southern Observatory (ESO) 1999 Online publication: July 26, 1999 ![]() |