USNO Circular 179 - U.S. Naval Observatory

38 PRECESSION & NUTATION
Figure 5.2 Observed values of celestial pole offsets from VLBI data. Offsets in
longitude have been multiplied by the sine of the obliquity to allow the same scale
to be used for both components. Circled points with error bars represent the offset
of the observed pole with respect to the computed pole, and the solid line in each
plot is a curve fitted to the data. The computed pole is given by the Lieske et al.
(1977) precession expressions and the 1980 IAU Theory of Nutation. These plots
are from Ma et al. (1998).
The VLBI observations of dψ and dɛ indicate the error in the computed position of the pole
with respect to a space-fixed system defined by the positions of extragalactic objects. However,
the conventional expressions for precession and nutation have used angles measured with respect
to the ecliptic, a plane to which VLBI is not sensitive. The ecliptic plane has a slow precessional
movement of its own due to planetary perturbations on the heliocentric orbital motion of the
Earth-Moon barycenter. 3 In the theoretical developments it is necessary to distinguish between
precession of the equator and precession of the ecliptic, which were formerly called, respectively,
lunisolar precession and planetary precession. Both types of precession are measured with respect
to a space-fixed system. The algorithms for precession and nutation provide the motion of the
3 The mean ecliptic is always implied. This is the smoothly moving plane that does not undergo the periodic
oscillations of the instantaneous orbital plane of the Earth.