-- Formulate questions even though one solution might appear obvious.

-- Address all questions in relation to the accuracy level that might be required by the most demanding applications at present and in the near future, not less but not more. As far as the JCR and the WG RCMA are concerned, there should be a constant interaction between the studies related to the items in parts I-VII and the estimation of the levels of accuracy (part VIII).

-- Provide a complete mathematical model (including all mathematical formulas explicitly) for the various issues.

-- Establish a uniform system of notations for quantities and units (see part V).

Should the problems be formulated in general relativity or in some PPN framework?

There are reasons to formulate the problems first in the framework of Einstein's theory of gravity. The reason for this lies not so much in the fact that so far Einstein's theory passed all experimental tests with flying colours. One deep reason is that the theory of reference frames so far has been elaborated in GR only (e.g. DSX). NEVERTHELESS, it is desirable to have some PPN-framework at least the Eddington-Robertson parameters beta and gamma. As Ken Nordtvedt and Marshall Eubanks pointed out, the inclusion of PPN-parameters is important not only for testing GR but also for the understanding of uncertainty budgets and correlations. In the case of choosing a PPN framework as the fundamental theory of gravity a generalization of the theory of reference frames (e.g. DSX) to include the PPN-parameters beta and gamma both a) in the theory of astronomical reference frames and b) in the equations of motion for N arbitrarily composed and shaped bodies should be worked out.

 The full post-Newtonian metric tensor necessary to describe the motion of massive bodies should be specified precisely. This implies that some gauge condition for the metric has to be chosen as being preferred in some sense (to be specified). More precisely, the full post-Newtonian metric tensor in the barycentric reference system (BRS) and in the geocentric reference system (GRS) (and analogously planetocentric reference systems) has to be specified completely.

Corresponding relations between the BRS-coordinates and the GRS-coordinates have to be given.

In analogous manner, topocentric RS should be specified and the relations of TRS-coordinates to the other ones given. For most (if not all) practical purposes in AGR only the time part of this transformation is required (i.e. transformation between TCG/TCB and the proper time of the topocentric observer).

One subtle point is the specification of the time coordinate to order 1/c^4. In the usual understanding of the post-Newtonian framework this is beyond the first post-Newtonian order, so some gauge freedom can be retained at this level of accuracy. The equations of motion of massive bodies to order 1/c^4 and of photons to order 1/c^2 are uneffected by this gauge freedom. Only if time scales are needed to post-post Newtonian precision gauge dependent terms play a role. In the TCG-TCB transformation these terms are of order 10^-16 (U^2/c^4) which is only an order of magnitude smaller than the accuracy of the best atomic clocks at present (df/f < 3 10^-15). Therefore these terms and consequently the choice of a gauge will be needed in the near future.

 Starting from the expressions for the metric tensor the mass, center-of-mass, and the higher mass-multipole moments of a body have to be defined in a useful and physically meaningful manner.

Corresponding spin-multipole moments have to be defined to Newtonian order.

The self-part of the metric of a body has to be characterized uniquely.

Outside this body it has to be skeletonized in terms of these multipole moments. This multipole representation of the self-part of the metric tensor outside the body should look simple because it plays a major role in satellite geodesy. The procedures for obtaining the numerical values of these multipole moments should be specified.

Satellite equations of motion and translational laws of motion (leaving the time dependence of the various multipole open) have to be given explicitly. As a general rule orders of magnitudes should be published and those terms that are really necessary for the near future should be collected separately. User friendly recipes in form of clear mathematical models should be published.

 Post-Newtonian definitions of the spin of a body in its own local frame, of the angular velocity, tensor of inertia etc. have to be given.

 Reanalyse the definitions of the units of the Système International d'Unités (SI units) in the framework of GR. In this context some non-SI units (e.g. the Astronomical unit) should also be examined.

Establish a uniform system of notations for quantities and units and apply it to future official texts and to rewrite past texts if necessary. In this aim, should we use a notation that explicitly distinguishes coordinate quantities (and their scale units) from proper (locally measured) quantities and their units (SI)?

 Define time scales TCG and TCB as time coordinates with the new metric (see section II).

Reexamine the transformations TCB to TCG and proper to coordinate time to accuracy needed by new clocks and new activities (see section VIII).

Reexamine the present definition and realization of TT in the present framework (IAU'1991 metric, geoid) at higher accuracy: role of tides, definition of the geoid.

Examine the case for a new definition and realization of TT, in the new framework and even in the present framework, in particular see if the reference to the geoid can be maintained. Evaluate the consequences for TAI.

In the present framework (IAU'1991):

- Clarify some of the basic concepts and definitions: e.g. meaning of GM_E (two values given by IERS Standards (1992) only one in IERS standards (1996) but not compatible with Resolution A4).... ), definition of the astronomical unit, role of Recommendation IV on TT in the IAU'1991 Resolution.

- The various astronomical concepts useful in the Newtonian framework (ecliptic, equinox, siderial time etc.) have to be analyzed if they are still useful in GR or if they are obsolete and should be abandoned. If some concept should be abondoned it should be clarified how it can be avoided.

- Interpret the results (coordinates, fundamental constants and other parameters) of different realizations of space-time references: One has to check in the software packages if the models are used in a consistent manner. As an example, the effects of various rescalings have to be analyzed further.

In the new framework (section II):

- Define the fundamental constants and quantities (parameters) appearing in the expressions (GM, multipole expansions...) and establish procedures to obtain their numerical value.

- Examine how certain basic concepts can be maintained and define them (e.g. geoid).

 Under this item are specified a number of activities for which general relativity is to be considered. The name "activity" is general and is meant to include measurement techniques as well as all kinds of procedures dealing with space-time coordinates. In all cases, one should consider which kinds of measurements are used, which coordinate transformations are necessary and infer what is the required accuracy of the relativistic modelling. Limitations by nuisance phenomena should be carefully considered in setting the required accuracy. It is possible that an activity is used so as to study the nuisance phenomenon (e.g. radio techniques to study troposphere, ephemerides to study asteroid density) so that the modelling accuracy should be well below the nuisance level.

For each activity, the end-product should be a detailed mathematical model.

- VLBI

- Satellite/Lunar/Probe/Planet Laser Ranging

- Satellite/Lunar/Probe/Planet Radio Ranging

e.g. the practical case of GPS

- Optical astrometry from space

- Satellite/Lunar/Probe/Planet clock synchronization/syntonization

- Pulsar timing

- Solar system ephemerides

As an extension of this task, existing software should be documented and checked for agreement with IAU recommendations.

A post-Newtonian formalism of elastomechanics should be worked out. The role of geodetic precession and nutation for the construction of transfer-functions (describing the ratio of nutational amplitudes for elastic and rigid Earth) should be clarified.