On a modern definition of the Earth orientation parameters

Questions, answers and comments/font>


1. The questions (cf. IAU T5 WG Newsletter 4)

(1) Do you agree that the current parameters in the FK5 system must be abandoned for being consistent with the newly adopted ICRS ?

(2) Do you agree that, for consistency with ICRS, the current formulation combining the motions of the equator and of the ecliptic wrt the CRS has to be abandoned ?

(3) Do you agree that the angle of Earth rotation must no more be reckoned from the true equinox which is moving due to precession and nutation and which is referred to the ecliptic of date ?

(4) Do you agree that new parameters for the orientation of the Earth's axis in the CRS must include both precession and nutation ?

(5) Which parameters (either among the parameters presented previously or new ones) do you propose to use for the EOP referred to the ICRS in place of the current parameters referred to the FK5 ?

(6) Which origin on the moving equator do you prefer ?

(7) Do you agree that in order to provide Earth rotation form the orientation angle around the axis of the CEP, it is necessary to use an origin without any instantaneous rotation wrt the CRS around this axis ?

2. Individual answers and comments (cf. Annex to IAU T5 WG Newsletter 5)

FROM D.D. MCCARTHY, 22 February 2000

Question 1. Yes

Question 2. Yes

Question 3. Yes

Question 4. Yes

Question 5. I favor what is referred to in your Newsletter as alternative (v)

Question 6. Non-rotating origin

Question 7. I don't think it is necessary (strictly) but it is certainly to be preferred.


FROM P. BRETAGNON, 6 March 2000

(1) yes

(2) yes

(3) yes

(4) yes

(5) The equator of date is referred to the ICRS by

\begin{displaymath}\lbrack TRS\rbrack = R_3(\phi).R_2(\omega).R_3(\psi). R_1(\epsilon_0)\ \lbrack CRS\rbrack\ \end{displaymath}

where $ R_1(\epsilon_0).\ \lbrack CRS\rbrack$ define one ``conventional fixed ecliptic'' with $\epsilon_0 = 23^{\circ} 26' 21.409''$ for instance.

It is not possible to directly refer $\lbrack TRS\rbrack$ to $\lbrack CRS\rbrack $ with three Euler's angles (see comments).

(6) the intersection of the moving equator with the fixed ecliptic.

(7) ?

Comments about the newsletter 4 of the subgroup T5

- in 2 (ii), it is written : "- the definition 2) is on the fixed equator of the TRS, ..." No, the origin of the definition 2) is on the moving equator and the fixed ecliptic.

- in 2 (iii) Euler's angles The formula (2) has no sense. When we refer the moving equator to the CRS, the precession-nutation variables $\psi$ and $\theta$ are singular and there are no analytical representations of such variables. It is why we have to use (as Woolard) Euler's angles referred to the fixed ecliptic (see answer 5 above).

- 2 (ix) It seems to me it is no necessary to have an Earth's angle of rotation which includes only the "intrinsic Earth rotation". It is easier to use the third Euler's angle reckoned from the intersection of the moving equator with the fixed ecliptic and this is better than the introduction of new developments ($s$ and $s'$) computed with some approximations.


FROM A. BRZEZINSKI, 8 March 2000

General comment

A basic idea is to make the parameterization of Earth rotation, understood as time dependent transformation between the terrestrial and the celestial reference systems, as simple as possible by removing all the elements which are no more necessary after adoption of the new ICRS. It seems for me that the idea of using the coordinates of the CEP as the transformation parameters (point v of your presentation, or point viii which is a special case of point v - am I right?) together with the use of the "non-rotating origin", is very attractive, particularly from the point of view of interpretation of the observed variations. However, there is one issue which has already been mentioned in the context of adoption the new intermediate celestial pole (point 4 of the preliminary proposals presented in Newsletter 3) but not here, namely about the practical consequences of the change such as continuity of the procedures applied so far by the people deriving the Earth orientation parameters or those using the EOP in reduction of the observations. So my answers given below are from the point of view of somebody who tries to interpret the observed EOP's in terms of different perturbations, but who takes less care of practical aspects.

Answers to your questions

Q.(1) Yes

Q.(2) Yes.

Q.(3) Yes.

Q.(4) Yes.

Q.(5) Celestial and terrestrial coordinates of the intermediate pole.

Q.(6) "Non-rotating origin".

Q.(7) Yes.


(1) Do you agree that the current parameters in the FK5 system must be abandoned for being consistent with the newly adopted ICRS ? YES

(2) Do you agree that, for consistency with ICRS, the current formulation combining the motions of the equator and of the ecliptic wrt the CRS has to be abandoned ? YES

(3) Do you agree that the angle of Earth rotation must no more be reckoned from the true equinox which is moving due to precession and nutation and which is referred to the ecliptic of date ? YES

(4) Do you agree that new parameters for the orientation of the Earth's axis in the CRS must include both precession and nutation ? YES

(5) Which parameters (either among the parameters presented previously or new ones) do you propose to use for the EOP referred to the ICRS in place of the current parameters referred to the FK5 ? THE CELESTIAL POLE COORDINATES X,Y OF THE CEP IN THE CRS

(6) Which origin on the moving equator do you prefer ? THE NON ROTATING ORIGIN (OR "DEPARTURE POINT") ON THE MOVING EQUATOR (8)

(7) Do you agree that in order to provide Earth rotation form the orientation angle around the axis of the CEP, it is necessary to use an origin without any instantaneous rotation wrt the CRS around this axis ? YES


FROM B. GUINOT, 11 March 2000

(1) to (4) Yes.

(5) Direction cosines of the axis of rotation (for the new definition of the Celestial Ephemeris Pole) in the CRS and in the TRS. Notes : 1. UT1 should be proportional to the stellar angle, as defined in Newsletter 4. 2. Question. Should we consider a re-definition of the coordinates of the pole in the TRS so that they correspond to the usual direct trirectangular coordinates in use ?

(6) The non-rotating origin (NRO). Note. It is recalled that, in case of change of model of precession/nutation, quantity s providing the NRO changes by an amount which is much smaller than that of the change of direction of the pole at changeover. In addition, the net effect of such a model change on the stellar angle (and on UT1 defined as being proportional to the stellar angle, with an invariable relationship) is negligible at the microarcsecond level. For these reasons, I do not see the advantage of a purely geometrical definition, since anyway the sidereal rotation of the Earth, which requires the concept of NRO, is needed. However, if a geometrical origin is required, my preference would be the equality of arcs reckoned from the node, as proposed in (6) of 2(ii) of Newsletter 4.

(7). Yes (see above in 6).


FROM L. PETROV, 13 March 2000

Q1) Do you agree that the current parameters in the FK5 system must be abandoned for being consistent with the newly adopted ICRS ?

A1) Yes.

Q2) Do you agree that, for consistency with ICRS, the current formulation combining the motions of the equator and of the ecliptic wrt the CRS has to be abandoned ?

A2) Yes.

Q3) Do you agree that the angle of Earth rotation must no more be reckoned from the true equinox which is moving due to precession and nutation and which is referred to the ecliptic of date ?

A3) No answer. The question has internal logical contradictions.

Q4) Do you agree that new parameters for the orientation of the Earth's axis in the CRS must include both precession and nutation ?

A4) No answer. The question has internal logical contradictions.

Q5) Which parameters (either among the parameters presented previously or new ones) do you propose to use for the EOP referred to the ICRS in place of the current parameters referred to the FK5 ?

A5) Euler angles for definition, any angles for theory or series of results from observations provided authors presented expressions between the set of parameters which they used and Euler angles. Refer to $http://giub.geod.uni-bonn.de/Mitarbeiter/petrov_docs/discussion/eop.html$ for argumentation.

Q6) Which origin on the moving equator do you prefer ?

A6) I prefer to abandon a notion of moving equator at all.

Q7) Do you agree that in order to provide Earth rotation form the orientation angle around the axis of the CEP, it is necessary to use an origin without any instantaneous rotation wrt the CRS around this axis ?

A7) In general this statement is not correct.


FROM J. VONDRAK, 14 March 2000

(1) yes

(2) yes

(3) yes

(4) yes

(5) I propose option (v), i.e. the coordinates of the CEP in the CRS and TRS $(X, Y, x_p, y_p)$.

(6) I prefer the non-rotating origin (small sigma)

(7) yes


FROM V. DEHANT, 15 March 2000

(1) Yes

(2) Yes

(3) Yes

(4) Yes

(5) (6) (7) up to people reducing data


FROM B. KOLACZEK, 15 March 2000

I agree with questions 1-4 of this Newsletter.

In the question 5 I propose to use previous EOP parameters referred to the ICRS. Introduction of the Euler's angels instead of the present EOP parameters needs deep consideration. We have to remember about analysis of long series of EOP parameters and separate analysis of polar motion and nutation corrections.

No opinion about the questions 6 and 7.


FROM S. LOYER, 15 March 2000

Concerning the questions in newsletter 4 concerning the new parameters , I can only give general remarks. (I have no time to investigate the consequences of the different proposals).

Remarks :

a) The number of parameters should be reduced with the suppression of all the non-necesary intermediate axis. The reduction up to 3 parameters only seems very difficult for observational techniques that cannot estimate these parameters at a hight rate. But it could be possible in principle as soon as some techniques can provide hight rate information.

b) After a rapid look I answer yes to questions 1 and 4.

c) the general problem of how we represent the link between terrestrial and celestial frame is poluted by the historical constrains on Time definition. Nowdays the "physical time" is no longer related to Earth rotation and we should definitively abandon the constrain to have GST appearing in the matrix representation we use for orientation.

This is (may be) necessary to have a way of define the "human time" from the motion of the Earth relatively to the Sun.

But this is not necessary at all to have the "human time" (or somathing that looks like human time, like GST) appearing explicitely in the orientation representation.

Any proposition that suppress the intermediates axis that were historically introduced for the time definition is thus interesting...


FROM C. BIZOUARD, 15 March 2000
(1) Do you agree that the c urrent parameters in the FK5 system must be abandoned for being consistent with the newly adopted ICRS ?

YES

(2) Do you agree that, for consistency with ICRS, the current formulation combining the motions of the equator and of the ecliptic wrt the CRS has to be abandoned ?

YES

(3) Do you agree that the angle of Earth rotation must no more be reckoned from the true equinox which is moving due to precession and nutation and which is referred to the ecliptic of date ?

YES

(4) Do you agree that new parameters for the orientation of the Earth's axis in the CRS must include both precession and nutation ?

YES

(5) Which parameters (either among the parameters presented previously or new ones) do you propose to use for the EOP referred to the ICRS in place of the current parameters referred to the FK5 ?

The combined parameters of Aoki and Kinoshita referred to the fixed ecliptic of the epoch J2000 (iv) or the (X,Y) coordinates (v)

(6) Which origin on the moving equator do you prefer ?

the intersection, gamma' of the moving equator with the fixed ecliptic or the non rotating origin.

(7) Do you agree that in order to provide Earth rotation form the orientation angle around the axis of the CEP, it is necessary to use an origin without any instantaneous rotation wrt the CRS around this axis ?

YES


FROM H. SCHUH, 20 March 2000

Your questions:

(1) yes

(2) yes

(3) yes

(4) yes

(5) as I already wrote in my response to your former questionaire I do not see any benefit of the 3-parameter approach from a practitioner's point of view. Thus, the options (iii) and (viii) should be discarded. From the other options number (v) is probably preferable but I have to think about it again.

(6) I haven't come to a final conclusion about the definition of the origin but probably the 'non rotating origin' is the best choice.

(7) yes

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