Compute the Earth rotation matrix / quaternion  


updated on November 2021

Include combined EOP C04 (1962 - today + 6 months prediction) :
Celestial pole offsets   UT1 - UTC   Polar motion

Include diurnal and semidiurnal variations produced by ocean tides in polar motion and UT1 (IERS conventions 2000)

Civil date UTC:
year   month   day      h   min   s
Real time
stop   yes 





         2022 5 21   16 h 31 min 29 s   UTC 

Matrix ITRF -> ICRF: 

-0.60018628617256        -0.79985736744006         0.00214793907164 
0.79985923906651        -0.60018763503772         0.00002068252174 
0.00127262340422         0.00173046227731         0.99999769296233 

Quaternion (q1, q2, q3, q4):

         0.44710842414118         0.00095602076770         0.00048943143327         0.89447912415168

Transformation coordinate M from the international terrestrial reference system (ITRF) to the international celestial reference frame (ICRF) : Celestial coordinates ( X Y Z) = M x Terrestrial coordinates ( x y z ) and associated quaternion of rotation. Compution of Celestial Pole coordinates (X,Y), Earth rotation angle, Celestial Intermediate Origin locator, Terrestrial Intermediate Origin locator are performed by FORTRAN programs of the SOFA IAU library, consistent with the IAU 2000/2006 resolutions.
  • from 1962 to the current week the transformation can include the interpolated EOP of the daily IERS combined series C04, as well as diurnal and semidiurnal variations in UT1 and polar motion produced by oceanic tides (IERS 2000 conventions). Accuracy is 0.05 mas (milli-arc-seconds), corresponding to 2.5 10-10 rad.

  • from the current week to 6 months afterthe matrix is computed from the prediction of the polar motion and UT1-UTC.

  • outside the range [1962, current week+ 6 months prediction] the rotation matrix is restricted to the diurnal rotation and the precession-nutation model IAU 2000

  • the last digit (14) of the matrix element corresponds to the 10-14 radian level or 2 10-6 mas or a datation uncertainty of 0.14 nano seconds/1.6 10-15 day (in reason of the diurnal rotation)