## TYz Tcf WSN PH11

The transformation matrices W, S', N, and P account for the following effects:

W = the offset of the Earth's angular velocity vector with respect to the z axis of the ECF (see Section 2.4.2)

S' = the rotation of the ECF about the angular velocity vector (see Sections 2.3.3 and 2.4.2)

N = the nutation of the ECF with respect to the ECI (see Section 2.4.1) P = the precession of the ECF with respect to the ECI (see Section 2.4.1).

The ECI and ECF systems have fundamental characteristics described in Chapter 2. The realization of these reference systems in modern space applications is usually through the International Celestial Reference Frame (ICRF) for the ECI and the International Terrestrial Reference Frame (ITRF) for the ECF. These realizations infer certain characteristics for highest accuracy and consistency. For example, the ICRF is defiled using the coordinates of extragalactic radio sources, known as quasars, where the coordinates are derived from observations obtained on the surface of the Earth with a set of large antennas known as the Very Long Baseline Interferometry (VLBI) network. The coordinates of the quasars are then linked with visible sources to an optical star catalog and the coordinates of the celestial bodies in the solar system. In a similar manner, the ITRF is realized with ground networks of SLR, LLR, GPS, and DORIS (see Chapter 3), which establish the center of mass origin of the ITRF, as well as the reference meridian.

The following sections summarize the content of the matrices required for the transformation from an ECI system to an ECF system. This discussion follows the classical formulation and it will be assumed that the ECI is realized through J2000, which is not precisely the same as the actual ICRF adopted by the International Astronomical Union. If observed values of polar motion (xp, yp) and A(UT1) are used, the transformation matrix has an accuracy of better than one arc-sec. The satellite motion is especially sensitive to polar motion and the rate of change in UT1, which is related to length of day. This sensitivity enables the estimation of these parameters from satellite observations.

The International Earth Rotation Service (IERS) distributes Earth Orientation Parameters (EOP) derived from VLBI and satellite observations. The main EOP are (xp, yp), A(UT1) and corrections to the precession and nutation parameters. These parameters are empirical corrections derived from satellite and VLBI observations which account for changes resulting from tides and atmospheric effects, for example. The EOP are regularly distributed by the IERS as Bulletin B. Consult the IERS publications and web page for additional information. As the models adopted by the IERS are improved, they are documented in new releases of the IERS Standards (or 'Conventions').

For the most part, the following discussion follows Seidelmann (1992) and McCarthy (1996). A comprehensive summary is given by Seeber (1993). A comparison of different implementations of the matrices, including a detailed review of the transformations, has been prepared by Webb (2002).

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