Circular 4, 20 October 1998Reminder: For the distribution of documents with scientific notations, many members asked for Tex/Latex only, while none requested Word only. Therefore the documents will be distributed as Latex files, and will be available as postscript files or in paper upon request. The Web site of the JCR has been opened. You are invited to visit it at http://www.bipm.fr/WG/CCTF/JCR/welcome.html. JCR04.2. Received contributions I maintain a list of the contributions which are distributed to the whole group. I start by using a simple identification of the type aa.x where aa is the number of the latest circular and x a consecutive letter. In the fortunate case when there are more than 26 contributions following a circular, we'll adapt it. The complete updated list of contributions is in the Web site.
JCR04.3. Realization of barycentric coordinate times After the diffusion of document 03.a, different discussions took place and some documents were circulated (see above). While the documents are long and technical in nature, I would like to sum-up here my understanding of the question so that we may discuss i) if we reach an agreement on some points and ii) if on those points we may draw conclusions that would eventually be the source of a formal Recommendation. I propose below for several items a short explanatory text based on parts of the circulated documents and the corresponding STATEMENTS upon which your opinion is requested. JCR04.3.1.The constants $L_B$ and $L_C$ Since those constants exist and have some use it is better to provide clear definitions for them but $L_B$ and $L_C$ should not be used in such a way that the utmost accuracy is needed in their determination. In this respect, when transformations are needed with utmost accuracy it is necessary to consider the full (space-time) transformations rather than use the average rates. If, however, it is necessary to consider the transformation between the time argument $T_{eph}$ of an ephemeris and TCB, then a specific study should determine a specific constant ($K_{eph}$) adapted to this ephemeris, with the accuracy needed. STATEMENT 1: We provide clear definitions for $L_B$ and $L_C$ based on differential formulas. We recommend NOT to use these constants when utmost accuracy is needed. From the present definitions, it is not logical to interpret $L_B$ as a defining constant for TDB. But we could change this and turn a specific value of $L_B$ into a defining constant thus providing a good definition of TDB since we have to live with it. STATEMENT 2: We provide in retrospect a good definition for TDB by choosing a specific value for $L_B$. JCR04.3.2.The constant $L_G$ Presently $L_G$ is not a defining constant for TT, since the definition involves the geoid. Turning a specific value of $L_G$ into a defining constant is an interesting option that we should discuss. See also section 04.4 below and document 04.a. STATEMENT 3: The status of $L_G$ should be discussed. This is deferred to after the diffusion of document 04.a (shortly). JCR04.3.3. Quantities and units: The question is whether each coordinate quantities should imply one "coordinate unit" (or name it "scale unit", or "unit of measurement" or ...) which is different from the "SI unit" used to measure proper quantities. The problem exists not only to relate quantities differing just by scaling but is a more general one. It is acute in time because we are sensitive to the difference between the proper quantity and several different coordinate quantities. Some views have been expressed by S. Klioner, B. Guinot, B.W. Petley (see documents listed in 04.2 above). I favour the option of one "scale unit" per coordinate quantity. STATEMENT 4: The question of "units for coordinate quantities" should receive a conventional answer. Although the question is a general one, we might as well provide a convention only for the (space and time) coordinates we are dealing with (I favour the option of one "scale unit" per coordinate quantity). JCR04.3.4. Extension of the metric: conditions of application and choices For the conditions of applications: they should be below the uncertainties of realization and measurements in the near future; the chosen formalism should allow unambiguous definitions within the chosen conditions; the chosen conditions and formalism should not be too ambitious. For the chosen formalism (GR only or parametrized), the opinions in the group are more or less evenly separated with a slight advantage for GR. I believe that it is not the goal of a conventional formalism to describe all the possible models so that the best choice is GR. For the gauge condition, in view of the present studies one practical solution could be to keep no explicit terms in $\chi$ neither in $g_{00}$ nor in $g_{0i}$. This may look odd in theory but I believe that it is not so odd as a conventional choice. We specify that it is equivalent to the harmonic gauge within xxxx (values and conditions to be specified) and that, whenever more accuracy is needed, the full metric in the harmonic gauge (including $\chi$ terms in $g_{00}$) should be used. For example (see section 6 of 03.a, and further comments in 03.c and 03.e) the limitation for the rate is a few parts in $10^{18}$ in the vicinity of the Earth and a few parts in $10^{17}$ in the vicinity of Jupiter, with precise values and conditions to be agreed upon. We indicate in addition that it is equivalent to standard PN gauge within xxxx (values and conditions to be specified) and in which cases this difference is likely to be important. For example (see 03.c and 03.e) the limitation for the rate may be a few parts in $10^{16}$ for a close flyby of Jupiter, with precise values and conditions to be agreed upon. Note that in 03.c Klioner points out that location dependent terms of order $c^{-4}$ might not be negligible depending on the distance of the point of interest from the geocenter. Indeed, for the TCG-TCB transformation within a geostationary orbit (the main region of interest for clocks on satellites), these terms may amount to up to 1.5 ps for the linear term in $r_E$ (Klioner & Voinov Phys. Rev. D 48, 1451, 1993 "KV93", Fukushima 1995). In addition these terms are subject to some additional coordinate freedom (JCR03.c, KV93). So some additional specification for the TCB-TCG transformation is required, for example the choice made in KV93. In any case some more work in relation to these terms is required (e.g. evaluating orders of magnitude for rate as well as time difference, also for the non- linear terms, alternatives to KV93 if any???). STATEMENT 5: We propose 0.3 ps for time and $3\times10^{-18}$ for rate as the present aim for the conditions of application. Formulas should be valid in the vicinity of the Earth at least up to the geostationary orbit. Precise conditions of applications should be stated in each case. STATEMENT 6: We propose as the convention a formalism in GR (without parametrization). The conventional metric would have no explicit terms in $\chi$ neither in $g_{00}$ nor in $g_{0i}$. We specify that it is equivalent to the harmonic gauge within xxxx (values and conditions to be specified) and that, whenever more accuracy is needed, the full metric in the harmonic gauge (including $\chi$ terms in $g_{00}$) should be used. We indicate in addition that it is equivalent to standard PN gauge within xxxx (values and conditions to be specified) and in which cases this difference is likely to be important. STATEMENT 7: We propose that, in the vicinity (to be specified) of the Earth, the recommended realization of TCB is via the formula 15 of 03.a, after sign correction as mentioned by Klioner in 03.c, and after specification of the location dependent terms of order $c^{-4}$. JCR04.4. Realization of geocentric coordinate times The document "Definition and realization of TCG and TT" (contributors G. Petit and P. Wolf) will be distributed shortly and will be referenced as document JCR.04.a in our list. Its conclusions are presented below for quick reference and are open to discussion, with a view of providing new definitions and/or guidelines that might be submitted to the Unions at a later stage. Please consult the document itself to get the full references, formulae etc.. Considering that the definition of TT is limited by uncertainties in the knowledge of the potential on the rotating geoid at one part in $10^{17}$, that in the near future one can expect that clocks onboard terrestrial satellites will reach uncertainties of that order, and that for some applications it is desirable to maintain a time scale in continuity with TT but not limited by uncertainties in the definition, it seems reasonable to investigate the possibility of defining a conventional value for the rate difference between TCG and TT in continuity with the best estimate of $W_0/c^2$. At the same time it could be convenient to turn this W_0 value into a defining constant for GRS2000 (Groten 1998). This would in effect amount to a relativistic definition of the geoid as suggested by (Bjerhammar, Soffel et al., Kopeikin). The most practical way of realizing TT or TCG from clocks in the vicinity of the Earth is: (i) For clocks on satellites: transform the proper time of the clock to TCG using the IAU(1991) metric, then apply the conventional TT/TCG rate to obtain TT. (ii) For clocks on the EarthÆs surface: Determine the gravity potential difference between the position of the clock and the geoid and use it to transform the proper time to TT. TCG can then be obtained by application of the conventional TT/TCG rate. These transformations require no additional term to the IAU metric. JCR04.5. Comments and call for contributions Please do not hesitate to comment on the STATEMENTS in part 04.3 above. Looking forward to your contributions (to be sent to jcr@bipm.org for automatic distribution (to be sent to jcr@bipm.org for automatic distribution or gpetit@bipm.org) (no automatic distribution), or gpetit@bipm.org) (no automatic distribution), Gerard Petit |