#
Empirical Earth Rotation model

## Introduction

Empirical Earth Rotation Model is an alternative to the traditional
method for modeling kinematics of the Earth's rotation. The empirical
Earth rotation model represents the transformation of a vector from
the terrestrial coordinate system **r**_{T} to the celestial
**r**_{C} as
**r**_{c} =
*M*_{a} ⋅
**r**_{T}
+ **q**_{e} × **r**_{T}
where *M*_{a} is the a priori
rotation matrix accurate to a level of 2⋅10^{-6} rad,
**q**_{e} — the vector of small perturbational rotation
determined from analysis of observations. The vector **q**_{e}
is sought in the form of expansion over two bases: the Fourier basis and
the basis of B-splines. Thus, the Empirical Earth Rotation Model determines
a continuous, differentiable function which defines the matrix of
transformation from the terrestrial coordinate system to the celestial
coordinate system at any given moment of time within
the interval of observations.

This approach is discussed in details in
**L. Petrov, "The empirical Earth rotation model from VLBI observations",**
*Astronomy and Astrophysics*, vol. **467**, pp. 359-369, 2007;
http://arxiv.org/abs/astro-ph/0611781

Full text:
http://astrogeo.org/petrov/papers/erm.pdf.

**NB:** Printed version of the paper **has several
typos** in equations.
Please refer to Erratum.

## Empirical Earth orientation model from analysis of VLBI observations

Numerical tables of the results of analysis of VLBI observations from
1984.0 through 2006.7, discussed in the paper are here:
- Variations of the vector of small Earth rotation expanded into
Fourier basis
heo_10d3.heo
- Variations of the vector of small Earth rotation expanded into
B-spline basis
heo_10d3.erm

## Latest full ERM from VLBI observations

Numerical tables of the results of analysis of VLBI observations from
1984.01.04 through 2007.03.06 are here:
- Variations of the vector of small Earth rotation expanded into
Fourier basis
heo_14b_int.heo
- Variations of the vector of small Earth rotation expanded into
B-spline basis
heo_14b_int.erm

## Latest restricted ERM from VLBI observations

Numerical tables of the results of analysis of VLBI observations from
1984.01.04 through 2013.04.02 are here:
- Expansion of the vector of small perturbations of the Earth rotation
with respect to the empirical nutation series MHB and empirical
precession expression Capitaine_2003 into Fourier series as well
as sub-daily variations in UT1 and polar motion
heo_20141202.heo

- Plots of parts of the spectrum of the variations in the Earth rotation
from VLBI solution are available here.

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*
This page was prepared by Leonid Petrov
() *

Last update: 2014.12.06_21:17:44