# Talk:Relativistic astrometry

I shall not try a detailed review of the whole article. I find it globally well built, well written and worded.

A. In the section "The scaling rules", I have suggestions that would mean some re-writing.

1) On the use of IAU Resolutions: The IAU 2000 resolutions do not "recommend" to re-scale the BCRS time coordinate, as stated after Eq 46. The re-scaling (i.e. the use use of TDB as time coordinate) is only "acknowledged" by some IAU resolutions (other than IAU 2000) e.g. Rec IV of Resolution A4 (1991) recomends that "the time reference for apparent geocentric ephemerides be Terrestrial Time TT", or Resolution B3 (2006) that redefines TDB.

We also note that Resolution B6 (1997) recommends that "the spatial coordinates of the Barycennic and Geocentric Reference Systems as defined by the IAU (1991) resolutions be used for celestial and terrestrial reference frames, respectively, without any scaling factors," and "the use of TT for convenience of observational data analysis not be accompanied by scaling of the spatial geocentric coordinates,"

Therefore it can be argued that the IAU resolutions are not clear about how to interpret scaled coordinates. In any case they clearly do NOT recommend to use them.

To summarize:

The text around equation 47 (from "For practical reasons .." to ".. are included in the IAU 2000 resolutions") should be reworded to express

- that scaled coordinates (TT in the GCRS, TDB in the BCRS) have been used before the IAU adopts a consistent relativistic framework and are still in use for continuity;
- that scaled coordinates had then been introduced for practical reasons: to make TT equivalent (within nearly negligible effects) to the proper time of a clock on the geoid; to remove (nearly completely) the constant L_C from equation 46;
- that the relations between TCB and TDB (eq 47) and between TCG and TT (not given explicitly) involves the constants L_B and L_G (respectively) which are now defining constants, i.e. not subject to change; L_B is defined by Resolution B3 (2006), L_G by B1.9 (2000);
- that IAU Resolutions in general, and IAU 2000 in particular, do not recommend scaled coordinates, they just acknowledge their use.

2) The solution proposed (Eq 48-49) to eliminate the drift between T and t without explicit rescaling of t may be OK in principle, but it is not so clear how it is applied. And it is not clear if it solves the main problem which is that people actually use of time coordinates TDB and TT, instead of TCB (i.e. t) and TCG (i.e. T). Also what would be the status of L_C? defining constant or measurable and subject to change?

B. In the sections "BCRS" and "GCRS", the presentation is fine. However, because the link to the IAU resolutions is explicit and the text is phrased as if it represents the IAU resolutions, it should be mentioned that the IAU Resolutions in fact propose to use the formalism of the PN multipole moments (Resolution B1.4 2000). Thus the equations 28 and 29 (and equivalent in GCRS) which appear in the defining relations (IAU Resolution B1.3 2000) don't need to be used in the applications.

C. Other minor comments

- There is a mismatch between equations 30-31 and the notations in the following line for the gravitational potentials of external bodies.

- Paragraph after equation 49: some typos e.g. the GCRS metric / g_{ij} (either capital G or BCRS); GSRC -> GCRS

## Reviewer B:

My comments on this article by Prof. Kopeikin are as follows:

1. Articles are missing in many places; someone with English as native language should check these little problems;

2. The author alludes to his work on what he calls 'speed of gravity'. This part, starting with: In general relativity ..... (Fomalont et al. 2010), should be dropped from the article not only for the reason that it had caused a lot of controversial discussions. Keeping this part would only lead to more confusion.

3. Maybe vectors could be denoted by bold face quantities rather than by arrows.

## Reviewer A:

Suggested wording

1. Last sentence of section "Geocentric Celestial Reference System"

TCG differs in rate from the Terrestrial Time (TT) scale, which has the same rate as clocks placed on geoid (Fukushima 1989, see section "The scaling rules").

2. Section "The scaling rules"

............both TCB and TCG.
The secular divergence between the two time scales is eliminated by selecting other coordinate times, TDB for the BCRS and TT for the GRS, chosen to have the same rate as atomic clocks on the geoid.

The new barycentric time scale TDB is defined by equation

TDB = t (1-L_B),

and the new geocentric time scale TT is defined by equation

TT = T (1-L_G),

where the constants L_B and L_G are now defining constants

L_G = 6.969290134\times 10^{-10}\;,\qquad\qquad L_B = 1.55051976772\times 10^{-8}\;.

Because

L_B ≈ L_C + L_G - L_C L_G,

the calibration procedure has effectively rescaled TCB (that is t) and TCG (that is T) so that the constant L_C was removed from (46).

The scaled coordinates ....