The 3D representation of the new transformation from the terrestrial to the celestial system.

1. The 3D representation of the new transformation from the terrestrial to the celestial system. Véronique Dehant, Olivier de Viron Royal Observatory of Belgium Nicole Capitaine Observatoire de Paris, France

2. Content of my talk • (International) Terrestrial Reference System • (International) Celestial reference system • Motions of one with respect to the other • Definition of the Celestial Intermediate pole (CIP) • The classical transformation • The transformation based on the Non Rotating Origins (NROs) • Definition of the NRO and of the Earth Rotation Angle • Conclusions

3. Preface When you see this sign: , it means that there is a movie and that you have to wait until the end of the movie before continuing the slide show (pressing “page down”).

4. The (International) Terrestrial reference system It must be noted that the "Greenwich meridian", is not called like that anymore but rather the "ITRF zero meridian".

5. The (International) Celestial reference system

6. Two systems in an ideal world;the celestial frame is fixed to the stars and the terrestrial frame is fixed to the Earth; the Earth is uniformly rotating X,Y,Z: for CRS x,y,z: for TRS

7. The less ideal world;the Earth orientation is changing in space; the Earth rotation is not uniform; there is polar motion, precession, nutations, and length-of-day changes; the Earth is non-rigid, deformable, there is plate tectonics, there are oceans and atmosphere, …

8. zTRS zIRS= ZIRS = CIP ZCRS • motion of the Celestial • Intermediate Pole (CIP) • in Earth 2. Earth rotation 3. motion of the Celestial Intermediate Pole (CIP) in space IRS = Intermediate Reference System Only the intermediary systems are different when using the new or the classical transformations. The (I)TRS and (I)CRS are not affected. TRS= Terrestrial Reference System (I)TRS= (International) Terrestrial ReferenceSystem CRS= Celestial Reference System (I)CRS= (International) Celestial ReferenceSystem

9. Definition of the CIP Polar motion Higher prograde frequencies Higher retrograde frequencies 0 +1 -2 -1 frequency in TRF in cycle/sidereal day +1 cycle/sidereal day (Earth rotation) Higher retrograde frequencies Higher prograde frequencies 0 +1 -1 +2 frequency in CRF in cycle/sidereal day Precession and nutation

10. The classical transformation

11. 1. From (I)TRS to CIP

12. 2. To the True equinox of date

13. How to go from one equinox another? Z Ecliptic 2 y x g2 Equator 2 Ecliptic 1 Equator 1 g1

14. How to go from one equinox another? rotation 1 (z) y y x x Z Ecliptic 1 Ecliptic 2 gi Equator 1 g1

15. How to go from one equinox another? Z Z Rotation2(x) y y Ecliptic 2 gi Equator 1 x

16. How to go from one equinox another? Rotation3(z) x x y Z Ecliptic 2 g2 gi Equator 1 Equator 2

17. How to go from one equinox another? Z Z Rotation4(x) Ecliptic 2 g2 x Equator 2

18. How to go from one equinox another? Ecliptic 2 g2 x Equator 2 It takes 4 operations…

19. 1 2 3 4 True ecliptic of date Mean ecliptic of date Equator of basic epoch True equator of date Mean equator of date gv g0 Ecliptic of basic epoch In the classicaltransformation, one needs to go from the true equinox of date gv (from which GST is computed) to the equinox of J2000 or even to the equinox g0 (considered in the FK5 celestial reference frame). It must be noted that in addition to these transformations, bias between the ICRF and the equinox-based reference frame must be considered; there exists "frame bias" between the mean equator and equinox of J2000 and the ICRS.

20. Transformation based on NROs

21. 1. From (I)TRS to CIP

22. 2. From CIP to terrestrial NRO

23. 3. From terrestrial NRO (TIO,) to celestial NRO (CIO,s): Earth Rotation Angle (ERA,q) (stellar angle)

24. 4. From CIO (s) to XCRF or S: s

25. 5. From celestial NRO/CIP equator to (X,Y,Z): motion of the CIP in space (precession and nutations)

26. What is the NRO? 1.Characterized by its motion: no rotation around the CIP associated with polar motion or precession/nutation. 2. Not one particular point, any point of the CIP equator is convenient. 3. Allows to get rid of the equinox in the change of reference system and in the definition of Earth rotation.

28. So, can we take any points we want? 1.Yes, it is not the point it-self that matter, but its motion. 2. But, we want the new system to be consistent with the classical one. 3. Thus, the point is chosen to insure continuity (January 2003).

29. Definition of NRO • The NRO is defined by its position at the basic epoch (continuity); its motion (no motion in the CIP equator associated with CIP motion). • The NRO ensures Earth rotation angle being pure rotation (no contamination from CIP motion)

30. Conclusions 1. No change in the definition of precession and nutation and polar motion since CIP definition. 2. The use of the NROs does only change the Intermediate system involved; no change of the ICRS or ITRS; it ensures a good definition of the Earth rotation (no contamination from polar motion of from precession and nutation).