What can bring LLR observations in determining the position of the celestial pole

1. What can bring LLR observations in determining the position of the celestial pole W.Zerhouni, N.Capitaine, G.Francou Observatoire de Paris , SYRTE Journées 2008

2. PLAN 1- Earth orientation 2- Lunar Laser Ranging (LLR) 3- Analysis of LLR data 4- Results and conclusion

3. Earth orientation parameters Polar motion Length of day Precession nutation

4. + PRECESSION - NUTATION

5. PRECESSION - NUTATION

6. num. values of the precession rates (error of -3mas/yr longi. -0.25mas/yr obliq. determined by VLBI). • Based on the IAU76 value for the obliquity • num. values of the coef. in the expressions are given • with a resolution of 0.1 mas after 1 century (MHB 0.1 μas). • Develop. of the expressions are limited to degree 3 in t • Rigid Earth • Only lunisolar effect • Non rigid Earth • Planetary + lunisolar effects • Accuracy of 0.2 mas • Cor. to the IAU 76 precession • Cor. to the obliquity of the equator on • the ecliptic • Cor. to the general precession in longitude • Improved expressions for the motion of the ecliptic • MHB values for the dynamical flattening • Analytical expressions are developed to the order 5 PRECESSION - NUTATION IAU 1976-1980 model of precession nutation : IAU 2000A model of precession nutation (MHB 2000) : IAU 2006-2000A model of precession nutation (P03 + MHB 2000)

7. Dpsi / IAU 1980 model DX / IAU2000 model Deps / IAU 1980 model DY / IAU 2000 model PRECESSION - NUTATION New transformation (DX,DY) IAU 2000model (MHB 2000 + cor. to the precession) IAU 2006 model(MHB 2000 and P03) better accuracy

8. LUNAR LASER RANGING

9. 2 3 1 LUNAR LASER RANGING « ALunar Laser Ranging observation » is, at a time t0 , the duration Δt (averaged on about ten minutes) between : (1) – A laser transmission by a station on the Earth (2) – reflectors on the Moon and (3) its detection on the way back on Earth

10. Cerga Lunar Laser Ranging station McDonald Lunar Laser Ranging station LUNAR LASER RANGING OBSERVATION 1- A telescope on Earth

11. 2- A laser impulsion 3- A reflector on the Moon

13. LUNAR LASER RANGING OBSERVATION Factors that affect the precision of the measurements : Atmosphere Time delay between 50 and 100 ps Orientation of the reflectors 200 ps Divergence of the outgoing beam of 3’’ or 4 ’’ after crossing the earth atmosphere. Angular divergence of the reflected beam 12’’ . One photon detected out of 1020 emitted in the Initial pulse

14. LUNAR LASER RANGING OBSERVATION Normal point on 10 minutes Theoretical precision of a normal point (60 echos) σPN = σ Total /√Nechos = 220 / √60 = 28 ps (4 mm) Observed precision of a normal point (60 echos) σ PN(obs) = 170ps (2.5 cm)

15. LUNAR LASER RANGING McDonald (1969 – 2006) LLR data Haleakala (1987 – 1990) Number of observations Cerga (1984 – 2005) 1- Calculation of the residuals using the IAU 2006-2000A model of precession nutation based on the CIO procedure and the SOFA 2007 routines. 2- Determination of the corrections to the X,Y celestial pole coordinates with respect to the IAU 2006-2000A model of precession nutation (P03 and MHB 2000), every 70 days.

16. Observed value Calculated value TDB UTC Relativistic cor. TDB UTC TAI TT ( TAI + 32.184s) CALCULATION OFTHE RESIDUALS O – C = ΔTo - ΔTc R M B t2 ΔTc = t3 – t1 – ΔT1 (t3) + ΔT1(t1) G t1 ΔTo expressed in TAI t3 O E

17. Lunar ephemeris Planetar ephemeris ELP JPL Reflectors coordinates Rotation (libration) CALCULATION OFTHE RESIDUALS Coord EM Coord TO Coord BG Corrections (relativists,tides, atmo pressure..) Precession nutation pole UT1 Coord MR

18. FITTED PARAMETERS The fitted parameters from LLR observations : • 1- Orbital parameters of the Moon and of the Earth-Moon • barycenter • Mean motion of the Moon and the Earth-Moon barycenter • Tidal secular acceleration of the Moon 2- Libration parameters of the Moon 3- Coordinates of the reflectors 4- Coordinates of the stations 5- Parameters UT0-UTC 6- Position angles of the dynamical ecliptic frame with respect to various systems of axes (ε, Φ, ψ) 7- Corrections to the celestial pole coordinates (DX, DY)

19. RESULTS 1- Residuals

20. RESULTS 2- Corrections to the celestial pole coordinates

21. ANALYSIS OF THE RESULTS Fitted corrections to the terms : model= constant + linear + 18.6-yr term + 9.3-yr term

22. ANALYSIS OF THE RESULTS Fitted corrections to the terms : model= constant + linear + annual + semi-annual term

23. ANALYSIS OF THE RESULTS (LLR) Fitted corrections to the terms : model= constant + linear + 18.6-yr term

24. ANALYSIS OF THE RESULTS Coefficients of correlations : From LLR observations, it is possible to determine corrections to the celestial pole coordinates but not with the same accuracy as from VLBI. Advantage Totally independant from VLBI observations Comparison with VLBI

25. ANALYSIS OF THE RESULTS (VLBI) Fitted corrections to the terms : IVS combined solution (ivse08q1.eops) Residuals calculated with respect to IAU 2006 using the eq. from Capitaine et al. ‘’high precision methods for locating the celestial intermediate pole and origin’ DIF_DX_IAU2000-2006 = 155t-2564t2+2t3+54t4 DIF_DY_IAU2000-2006 = -514t-4t2+58t3-1t4-1t5

26. CONCLUSION It is possible to determine the celestial pole coordinates LLR Due to the imperfect distribution of the data the precision of the results is not at the same level as with VLBI Next step Combine LLR results with VLBI celestial pole offsets in order to benefit from both techniques