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The use of LLR observations (1969-2006) for the determination of the GCRS coordinates of the pole. Inertial mean ecliptic of J2000.0. [CRF] = Q.R.W [TRF]. ε (CIP). ‘ CIP equator. ү I 2000(CIP ). P N (Bias Precession Nutation matrix based on the coordinates X,Y of the CIP). O (CIP). Ф.
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The use of LLR observations (1969-2006) for the determination of the GCRS coordinates of the pole Inertial mean ecliptic of J2000.0 [CRF] = Q.R.W [TRF] ε(CIP) ‘ CIP equator үI2000(CIP) P N (Bias Precession Nutation matrix based on the coordinates X,Y of the CIP) O (CIP) Ф Wassila Zerhouni (1), Nicole Capitaine (1), Gerard Francou (1) (1) Observatoire de Paris / SYRTE , 61 Avenue de l’Observatoire 75014 Paris Wassila.zerhouni@obspm.fr,Nicole.capitaine@obspm.fr,Gerard.francou@obspm.fr The principle of Lunar Laser Ranging is to fire laser pulses from a telescope on the Earth toward a reflector on the Moon, to receive back localised and recognizable signals and to measure the duration of the round trip travel of the light. 2 3 1 The Lunar motion defines intrinsically a dynamical system. It allows in particular the positionning of the dynamical mean ecliptic of J2000.0 with respect to the CIP (Celestial Intermediate Pole) and to the ICRS (International Celestial Reference System) using this transformation : Q : Matrix transformation for the motion of the celestial pole in the celestial system R : Matrix transformation for the Earth rotation W : Matrix transformation for the polar motion In previous work (IUGG 2007), we determined the position of the dynamical mean ecliptic of J2000.0 with respect to the CIP with this classical transformation : [CRF] = A.PN.R.W [TRF] W = R1(yp)R2(xp) P N (Precession Nutation matrix based on Δψ and Δε) A = R1(ε)R3(Ф) R = R3(-GST) Ф, ε : cf. fig 1 GST : Greenwitch Sideral Time xp, yp : pole coordinates in the TRF Using LLR observations from McDonald 1969-2006 and Cerga 1984-2005, the P03 Precession of Capitaine et al. (2003) and MHB 2000 for the nutation, we have found : Ф (arcsecond) = -0.01453±0.00010 and ε (arcsecond) =84381.40379±0.00009 In this work, we have done the same investigation with including the conventional model (precession, nutation and frame bias) for the coordinates X and Y of the CIP (Celestial Intermediate Pole) in the GCRS (Geocentric Celestial Reference System) instead of the classical precession nutation parameters. It implies : Figure 1 R = R3(-ERA) ERA : Earth Rotation Angle • With the same data as in the previous study (LLR observations from 1969 until 2006) and the new transformation, we obtained these residuals • (cf. Fig. 2, Fig. 3). • Normal points : • Figure 2 : • Top : 1183 • Bottom : 8361 • Figure 3 : Top : 3546 Bottom : 2870 Figure 2 Figure 3 In a second step, we made a new analysis with fitting the X and Y parameters. Figure 4 represents the preliminary results obtained with fitting the X, Y parameters and their formal errors . In this preliminary study, we have derived the X, Y coordinates of the CIP at J2000.0 from LLR observations spanning the period 1969-2006. In a further study, we will use such determinations at appropriate intervals for deriving corrections to the precession-nutation model. References : Capitaine et al. 2003, Astron. Astrophys., 412, 567-586. Chapront et al. 2002, Astron. Astrophys., 387, 700-709. Mathews et al.2002, J.Geophys. Res, 107(B4), 10.1029/2001JB00390. McCarthy, D. D. 1996, IERS technical Note 21: IERS Conventions (1996). Williams, J.G.1994,AJ, 108, 2. Figure 4
