Compute orientation matrix
ITRF> ICRF at a given time or in real time
updated : January 2008

N.B: bug in the program related to leap second has been corrected, however
some suplementary check have to be done before to confirm the validity
of the computation of the rotation matrix from ITRF to ICRF. Thank you
for any coments.

Compute time series of the Earth orientation matrix or derived parameters between two dates:
Time scale for civil gregorian date : UTC Step in seconds
First date: year
month
day
hour
min
second
Last date: year
month
day
hour
min
second

Include combined EOP C04 (1962  today + 6 months prediction) when
available :
celestial pole offsets
UT1  UTC
Polar motion
Include diurnal and semidiurnal variations produced by ocean tides
(IERS conventions 2000)


Orientation matrix
output for one line : Modified Julian Date in TAI ; civil date in UTC
; matrix elements a_{11}, a_{12}, a_{13}, a_{21},
a_{22}, a_{23}, a_{31}, a_{32}, a_{33}

Projection of the geographic axis on the equatorial plane J2000.0
OXY (unit : arcsecond)
Draw
N.B.: by taking
UT1UTC and the polar motion to zero one obtains the equatorial celestial
coordinates of the Celestial Intermediate Pole

Components (ω_{1},ω_{2},ω_{3})
of the instantaneous rotation vector ω:
in the international terrestrial frame Oxyz
in the local frame Ox'y'z' : Oz'=vertical (either geographic or astronomical), Ox' tangent to the meridian, towards South, Oy' in the horizontal plane, directly orthogonal to Ox':
Latitude (degree)
longitude (degree)
in the International Celestial Reference Frame (ICRF) OXYZ in nanorad/s
(ω_{1}/Ω,ω_{2}/Ω) in arcsec (Ω=7.292115 e5 rad/s)

do not draw
draw (date,ω_{1})
draw (date,ω_{2})
draw (date,ω_{3})
draw (ω_{1},ω_{2}) 
Precessionnutation matrix 
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 )  We use the FORTRAN CODE of the VLBI analysis Software GLORIA
developped by AnneMarie Gontier (Paris Observatory),
and compatible with the IAU 2000 resolutions
 from 1962 to the current week
the matrix can include the whole EOP set of the IERS combined series
C04 (daily step, 0hUTC, time resolution for such EOP fluctuations
is about 6 days), as well as diurnal and semidiurnal effects produced
by ocean tides, which amount about 0.001". Accuracy is 0.0001",
corresponding to 5 10^{10 }rad. In turn the time resolution
of the matrix can reach approximatively 6 hours. Bewteen two dates
at 0hUTC the EOP are interpolated according to a cubic spline.
 from the current
week to 6 months after
the matrix is computed from the prediction of the polar motion and
UT1UTC.
 outside the range [1962, current week+
6 months prediction] the rotation
matrix is restricted to the diurnal rotation and the precessionnutation
model IAU 2000.
 The last digit (12) of the matrix
element corresponds to the pico radian level.
Corresponding time resolution for the matrix variation is 14 nano
seconds.
 Components of the instantaneous
rotation vector are deduced from
the orientation matrix and its time derivative.
We are grateful to J.C. Marty (CNES, France), Markus Nitshke, Dr.
Feipeng Zhang (GFZ, Germany), Luca Cerri (CNES, France), Dr. Jim Beaupre
(Teledyne Solutions, USA), Hervé Manche (IMCCE, Observatoire
de Paris), Josef Slavicek (Prague, January 2008) for their worthful
comments, which allow us to improve/correct the computation of the
Earth rotation matrix.
