Celestial pole offsets | UT1/Length of day | Polar motion

Available EOP series | EOP modelling

The Earth's orientation is defined as the rotation from the Earth crust (the terrestrial system) to a geocentric set of axes tied to the quasars (geocentric celestial system, to be distinguished from the reference celestial system having for origin the barycenter of the solar system). This rotation is split into three components :

  • The precession-nutation of the figure axis in space. It is specified through the conventional precession-nutation model (presently that recommended by the IAU 2000 General Assembly) and corrections determined by the VLBI observations : the celestial pole offsets (dψ,dε) or (dX, dY) according to the parameterisation which has been adopted. The precession-nutation model and its corrections (up to 1 mas / IAU 2000 model) define a fictitious axis, the Celestial Intermediate Pole or CIP.

    N.B.: The CIP was called before 2003 celestial ephemeris pole or CEP. This change of terminology corresponds to the non-ambiguous frequency splitting between diurnal/subdiurnal polar motion and nutation for this axis : by definition the precession-nutation of the CIP does not have spectral components of which the period is smaller than 2 days.

  • The diurnal rotation around the celestial intermediate pole (this one remains close to the instantaneous rotation axis in a tolerance of 20 milliarcseconds) : ΩN UT1. It can be decomposed into an angle uniformly varying with TAI, ΩN TAI, (with the nominal Earth rotation rate ΩN , see useful constants) and corrections showing variations of the Earth angular velocity. These corrections are given by the difference (UT1-UTC) or (UT1-TAI).

  • The polar motion of the celestial intermediate pole with respect to the terrestrial crust. The CIP has for terrestrial coordinate (x,-y,1). As a first approximation, for periods greater than 10 days (x,-y,1) are also the coordinates of the instantaneous rotation axis. It is not possible to confuse both axes at diurnal time scale.

    See on the WEB page of Obseratoire Royal de Belgique, simulated movies of these Earth rotation irregularities

    The five Earth orientation parameters , derived from the observations, bring corrections to the uniform diurnal rotation and modelled precession-nutation :
    • The celestial pole offsets (dψ,dε) or (dX,dY) with a maximum temporal resolution of 2 days.
    • UT1-UTC or UT1-TAI (from which we can derive the variations of the length of the mean solar day, ΔLOD, with respect to its nominal value of 86400 s TAI)
    • The polar motion (x,y)

The Earth orientation is then obtained by inserting those parameters in the coordinate transformation between the Celestial Reference Frame and the Terrestrial Reference Frame :
  • for the classical way : [CRF]=PN(dψ,dε) R3(UT1-TAI) W(x,y) [TRF]
  • for the "non rotating origin" formalism :

    [CRF]=PN(dX,dY,s) R3(UT1-TAI) W(s',x,y) [TRF] (s are s' are practically independent from the EOP)
The description of this matrix can be found in the IERS conventions, chapter 5. For more insight on the meaning of the EOP, read the following page.

We propose two kind of EOP series :
  • the individual series (most often up-dated routinely) as determined from the observations of a given astro-geodetic technique VLBI, LLR, SLR, GPS, DORIS) by various organisations all over the world.
  • the IERS combined series:
    • C04: since 1962, daily
    • C01: since 1840, 0.05 year sampling
    • C02: since 1830 for LOD & UT1 - TAI after 1958 and UT - TE before 1958, 100 day sampling
as well as: