Introduction

I would like to see a set of definitions, notations as well as a model which would be declared as a reference model in the future recommendation . It is not important whether it would be the "best" model, it is important only that it would be defined as clear as possible in order to avoid ambiguities in interpretation. I think that the purpose of the recommendations is to facilitate communication and comparisons, to establish a set of notions and reference models which will be (can be) used for future development.

But it seems to me that the questions formulated in the newsletters of working group T5 "Computational Consequences" leads discussion in a bit different way. I think the problems how to estimate EOP are beyond of authority of IAU or any other union. I believe that IAU and any other scientific bureaucratic organizations can not take functions of judgment which way of parameterization of the Earth rotation is the best, no organizations can order how an analyst should analyze observations...

I would like to come back to the set of definitions concerning parameterization of the Earth rotation. It is a common opinion that the IAU 1980 definitions are unsatisfactory and should be revised. When we consider definitions we use the following criteria:

• A definition should not contain internal logical contradictions.
• A definition (a set of definitions) should be complete.
• A definition should not contradict to another adopted definitions.

Proposals

1. The Earth rotation is defined as a spatial three-dimensional rotation of TRF with respect to CRF.
2. CRF is considered as kinematically non-rotating.
3. TRF defines positions and secular velocities of observing stations.
4. Canonical Earth orientation parameters are the parameters which relate TRF and CRF in the following form:

   [TRF] = R_x( E_x(t) ) * R_y( E_y(t) ) * R_z( E_z(t) )   [CRF]

   where R is a rotation matrix, E is a function of time. Time scale is TCG, units should comply SI.

5. It is recommended to provide an expression describing dependence of non-canonical parameters of the Earth orientation with canonical for any theoretical models or series obtained from observations which use a set of non-canonical Earth orientation parameters.
6. Nutation is a constituent of the Earth rotation caused by tidal forces.
7. Prograde polar motion is a component of the Earth rotation which is parameterized as ...
8. Prograde nutation is a component of the Earth rotation which is parameterized as ...

Comments

1. There are no objects on the sky as "celestial pole", "point of the equinox", "Earth's equator" and so on. I propose to avoid mentioning in the definitions the objects which cannot be observed. There are observing stations and there are natural or artificial objects which they observe. We are able to measure angles between the observing stations which represent "the Earth" and the artificial objects which represent "the sky". Let's call them the Earth orientation parameters. In practice we already follow this way. Since rotation is non-transitive in general relativity we should say explicitly which system is rotating. (i.e. if the object A is rotating with respect to the object B with an angular velocity f_AB then we can say that the object B is rotating wrt A with an angular velocity f_BA, but f_AB is not equal to -f_BA !)

2. I thought that the question what is rotating: the Earth or heavens has been resolved by Copernicus but having read newsletters of the working group on nutation I realized that I was too naive and this question is not considered as firmly established in the 21-st century. I would like also to remind that the definition of ICRF clearly says that ICRF does not have rotation. The adjective "kinematically" is important since there are dynamically non-rotating reference systems and kinematically non-rotating reference systems in the framework of general relativity.

3. It is assumed that other non-secular motions, f.e. tidal displacements are taken into account in the model of reduction and subtracted. The fact that EOP are defined as a rotation of TRF wrt to CRF imposes restrictions of observability of EOP. Since station's secular velocities are allowed in TRF results in impossibility to observe secular drift of the canonical Earth orientation parameters since a secular drift of EOP is equivalent to a linear transformation of velocity field of TRF.

4. I think it is the simplest form of the representation of the rotation of any physical body. The vector functions E(t) is a complicated function of time in this representation. In principle it is possible to find such a parameterization (to add more rotation matrices) which would do E more simple but we cannot get substantial simplification in the framework of modern theories.

5. It is a crucial point of my proposals. We allow non-canonical representation. It means that we don't need to revise nutation theories which already exists, we don't need to re-compute series of observations. We don't assume that new theories will be formulated directly in the canonical parameters or the values of E as a function of time will be determined from observations directly. Authors have a freedom of choice to use that parameterization which they believe is the best. But we recommend them to provide a relationship between the set of parameters which they use and canonical EOP. It is not a heavy burden. I believe this strategy would have substantial advantages for our consumers who are not experts in ephemerides astronomy. Everybody is able to program relationship (4) between TRF and CRF. If an author of nutation theory would write an expression which relates the parameters of the theory (f.e., expansions of nutation in longitude and obliquity) then it would be rather easy to implement new theories for computations. A user of nutation theories will build his algorithm of implementation not on the base of how he understands a notion of CEP or mean ecliptic but on the basis of the explicit expressions which an author of the theory (who must have understand it the best) has written. Analogously, an interpretation of observation results would be much facilitated if an author would provide a relationship between the parameters which he/she adjusted to a canonical representation, especially in the case of using a new parameterization like that which P. Mathews proposed.

Thus, canonical parameterization is proposed for facilitating communication. We need some label for a reference parameterization. And that reference parameterization should be specified by such a manner which would guarantee that everybody understand it correctly. If two authors use the different sets of parameters they will be able to compare their results provided each author wrote how his set of parameters is related to the canonical parameterization.

6. This definition unites precession + nutation + high frequency variations in EOP + variations in the UT1 caused by zonal tides. The problem is that the word nutation was used in the past in narrower sense. Alternative is to invent a new termine, f.e. "tidal variations in EOP" and to abandon a termine nutation entirely. I don't know what is the best decision.

Periodic variations of geodetic precession known also as "geodesic nutation" is not a nutation in according with this definition.

7-8. Since different authors use notions "prograde" and "retrograde" motion in opposite meanings it is hard to understand what is what (refer P. Defraigne et al (1995) ). I see a necessity to include a clear definition in the recommendations. Analogous situation was some time ago with notions "right circular polarization" and "left circular polarization". Then IEEE adopted a resolution and now authors writes "right circular polarization in according with IEEE recommendation". I propose to include definition prograde polar motion and retrograde polar motion as well as prograde and retrograde nutations in the terms of canonical EOP in order to allow to authors to refer to this recommendation.

Last update: 13-MAR-2000 10:03:36