Earth’s rotation: observations and theory - Earth Dynamics: Deformations and Oscillations of the Rotating Earth - page 309

barycentre of the solar system, displacement of the rotation axis involved in nuta-
tion is described by co-ordinates

x = r cosα =Δ ψsin 0 , y = r sinα =Δ , (4.107)

using (4.106).

4.4.1 VLBI nutation observations
As well as the pole path, the very long baseline interferometry (VLBI) technique
is used to measure motions of the celestial pole or nutations. The observations are
expressed as residuals of longitude and obliquity compared to a specific theoret-
ical model. Two principal nutation models have been developed. The first is the
1980 IAU theory developed by John Wahr (Wahr, 1981). A later nutation model,
the MHB2000 theory, developed by Mathews, Herring and Bu

ff

et (Mathews et al .,
2002), fits a model of known nutations to observations and is therefore not inde-
pendent of the data or the model. Because this procedure might suppress new,
unmodelled signals, we choose to examine residuals with respect to the 1980 IAU
theory.
The residuals in longitude,

Δ , compared to the 1980 IAU
nutation series, and their standard errors, in milliarcseconds, are available on the
Goddard Space Flight Center website (http:

Δ ψ, and obliquity,

// gemini.gsfc.nasa.gov / solutions /

2003b 2003b.eops). The downloadable file 2003b.eops contains 3370 points run-

ning from Julian day 2,444,089.993750 (3 August 1979) to Julian day
2,452,705.270139 (6 March 2003). The time tags are given in Julian days minus
2,400,000. The programme NUT2003B extracts the residuals of longitude and
obliquity with their standard errors and converts them to the Cartesian co-ordinates
given by (4.107) using sin 0

/

0.39777716 for the year 2000.0. The resulting nuta-
tion residuals x ,yand their standard errors, in terms of the time in days from the
beginning of the record, are returned in the file nut2003b.dat.

=

C PROGRAMME NUT2003B.FOR

C
C NUT2003B.FOR extracts residuals of ecliptic longitude and
C obliquity of the ecliptic with their standard errors,
C compared to the 1980 IAU model of Wahr, from the file
C 2003b.eops on the Goddard Space Flight Center website.
C They are then converted to Cartesian co-ordinates of
C the celestial pole before output.
C

IMPLICIT DOUBLE PRECISION(A-H,O-Z)
OPEN(UNIT=1,FILE='2003b.eops',STATUS='OLD')
OPEN(UNIT=2,FILE='nut2003b.dat',STATUS='UNKNOWN')
C Read in extracted residuals of longitude and obliquity.
DO 10,I=1,3369
READ(1,11)DAY,XWOB,YWOB,UT1MC,PSI,EPS,EXWOB,EYWOB,

1 EUT1MC,SEPSI,SEEPS,WMS,C1,C2,C3,C4,N,SC,SD,RX,RY,