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\def\aa {{\it Astron. Astrophys.}}
\def\aj {{\it Astron. J.}}
\def\ba {{\it Bull. Astron.}}
\def\cm {{\it Celest. Mech.}}
\def\cmda {{\it Celest. Mech. Dyn. Astr.}}
\def\gjras {{\it Geophys. J. R. Astron. Soc.}}
\def\jgr {{\it J. Geophys. Res.}}
\def\mnras {{\it Mon. Not. R. Astr.Soc.}}

\begin{document}

\vspace*{1.2cm}

\noi {\Large ESTIMATION OF NUTATION USING THE GPS}

\vspace*{1cm}
\noi\hspace*{1.5cm} Robert WEBER\\
\noi\hspace*{1.5cm} Dep. of Advanced Geodesy, TU-Vienna\\ 
\noi\hspace*{1.5cm} Gusshausstr. 27-29, A-1040 Vienna\\ 
\noi\hspace*{1.5cm} e-mail: rweber@luna.tuwien.ac.at\\ 

\vspace*{2cm}

\noi {\large 1. INTRODUCTION}
\ssk
\\ 
GPS measurements obtained from the global IGS network are undoubtedly a 
valuable source for the determination of ERP series. 
This series are at the one hand of high quality ($\sigma_{xp, yp} \approx 0.1 mas$;
$\sigma_{LOD} \approx 0.02 msec/day$) because of the more or less
regular distribution of the active IGS tracking sites (curently about 140 stations).
Moreover the 
uninterrupted coverage of almost 10 years with daily estimates is also 
of importance for detailed studies.

In February 1994 CODE, one of the seven Analysis centers of the IGS started 
to derive nutation rates in addition to polar motion and the routinely estimated
UT1-UTC rates. In 1999, a set of nutation amplitude corrections for 34
periods with respect to the IERS96 model as well as the IAU1980 model was
presented by (Rothacher et al.,1999) based on 3.5  years of data. It has been 
demonstrated that GPS is especially sensitive to periods up to about 20 days.
This overview deals with preliminary results of the most recent update
of the published nutation amplitude corrections by taking into account 6 years 
of observation data and focusing on the 13.66 days term.

\vspace*{1cm}

\noi {\large 2. ESTIMATION OF NUTATION RATES}
\ssk
\\
Contrary to polar motion, offsets in the three remaining earth orientation
components ($\Delta \varepsilon$, $\Delta \psi$,
UT1-UTC) are fully correlated with the orbital parameters describing the
orientation of the orbital planes of the satellites (ascending node,
inclination, and argument of latitude). Nevertheless, an almost 'perfect' 
force model would describe the satellite orbits accurately enough, at least over
an interval of a few days (3 days arcs at CODE) to allow for the
determination of EOP-drift parameters. In reality major biases in the rate
estimates show up at the satellites revolution period or at annual and
semi-annual periods due to solar radiation pressure. 

Daily nutation rates in longitude and obliquity estimated from GPS data
over the past 6 years are available now. All rates are corrections to the 
IAU 1980 Theory of Nutation. 
The series seems to become somewhat noisier at the end of 1996,
caused by a change of the orbit model in October 1996. The formal errors
of the estimates grow by a factor of about 2-3 because of correlations to
the newly added orbit parameters. Nevertheless, (Rothacher et al.,1999) 
have shown in a thorough discussion, that nutation corrections of similar
quality can be obtained with both orbit models.

\vspace*{1cm}
\clearpage
\noi {\large 3. ESTIMATION OF NUTATION AMPLITUDES}
\ssk
\\
To decribe amplitude corrections $A_{ij}$, $A_{oj}$ to nutation terms from a series 
of nutation rates $\delta \Delta \varepsilon'$ and $\delta \Delta \psi'$ we use the
following formulation (e.g. Weber, 1999)
%
\begin{eqnarray}
\delta \Delta \varepsilon(t) ' & = & -\sum_{j=1}^n A_{ij}^\varepsilon \sin \theta_j (t)\frac{\partial \theta_j}{\partial t}+
      \sum_{j=1}^n A_{oj}^\varepsilon \cos \theta_j (t)\frac{\partial \theta_j}{\partial t}     \\
\delta \Delta \psi(t) ' & = & -\sum_{j=1}^n A_{oj}^\psi \sin \theta_j (t)\frac{\partial \theta_j}{\partial t}+
      \sum_{j=1}^n A_{ij}^\psi \cos \theta_j (t)\frac{\partial \theta_j}{\partial t}     
\end{eqnarray}
%
The angles $\theta_j$ denote a linear combination of the Delauny variables and 
n is the number of nutation terms taken into account. The $A_{ij}$, $A_{oj}$ are
usually called in-phase and out -of-phase components, which can be obtained
by a least squares adjustment using the GPS nutation rates as
pseudo-observations.
\vspace{1cm}  \\
                           Figure 
\\ \vspace{1cm}

The diagram presents the first results in evaluating this new enlarged nutation
rate series. A comparison of the nutation in-phase and out-of-phase components
for the 13.66 days period given in various well-known models with the most
recent model by Souchay/Kinoshita (1997.2;SKV972) shows the excellent agreement
and the increasing convergence of the GPS solutions with SKV972.

We may conclude that even now GPS allows an independent check of present-day
nutation models and VLBI results at the high frequency end of the spectrum.
In future a combination of the VLBI and the GPS series at the postprocessing
or even at the observation level might be extremely promising. 

\vspace*{1cm}

\noi {\large 4. REFERENCES} \\
{\leftskip=5mm
\parindent=5mm

\ssk 

Rothacher M., G. Beutler, T.A. Herring, R. Weber, 1999: Estimation of Nutation
using the Global Positioning System, JGR Vol.104, No.B3, pp.4835-4859. 

Souchay J., M. Feissel, C. Bizouard, N. Capitaine, M. Bougeard, 1995,
Precession and Nutation for a non-rigid Earth: Comparisons between Theory
and VLBI Observations, Astronomy and Astrophysics, 299,pp. 277-287. 

Springer T.A., G. Beutler, M. Rothacher, 1998: Improving the Orbit Estimates
of the GPS Satellites, Journal of Geodesy, Vol.73, pp.147-157.

Weber R., 1999: The Ability of the GPS to Monitor Earth Rotation Variations,
Acta Geodetica et Geophysica Hungarica, Vol. 34, Nr.4, pp.457-473, Budapest.



}

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