Earth’s rotation: observations and theory - Earth Dynamics: Deformations and Oscillations of the Rotating Earth - page 275

P

P

O

C

B

B

D

E

E

Figure 4.1 The e ff ects of polar motion on the sidereal time and latitude of an

observatory.

ranging (LLR) and satellite laser ranging (SLR), began with the formation of the
International Earth Rotation Service (IERS) in 1987 as the successor to both the
BIH and IPMS. In contrast with the classical astronometric techniques used by the
IPMS and BIH, which often yielded pole positions di

eringbyasmuchasten
centiseconds of arc (one centisecond of arc is close to one foot, or 30 cm, of pole
displacement), modern space measurement techniques yield pole positions with
error levels decreased by at least three orders of magnitude.
Polar motion changes both the sidereal time and latitude of an observer. These

ff

e ects of a shift in the pole of rotation are illustrated in Figure 4.1. C is the point

at the Earth's centre of mass and O is the position of an observatory on the sur-
face. The meridian circle, through the initial pole position P and the observatory,
intersects the equator at the point E , while B is the point on the equator directly
below the vernal equinox. Then, the initial latitude of the observatory is given by
the angle OCE , and the initial sidereal time is given by the angle BCE .
If the pole of rotation moves from its initial position P to a new position P on
the surface of the Earth, the equator then pivots about an axis through the surface
point D on the equator and the centre of mass C , orthogonal to the plane contain-
ing PCP . After the polar shift, the latitude becomes the angle OCE , measured
along the new meridian circle through O , intersecting the new equator at E .The
new sidereal time is given by the angle B CE , where B is the point on the new
equator directly below the vernal equinox. Changes in the spin rate, or speed of
axial rotation, also a

ff

ect sidereal time.
It is usual to adopt a geocentric Cartesian co-ordinate system in which the origin
is placed at the centre of mass, the x 3 -axis is taken through a fixed reference pole,
the x 1 -axis is taken toward the Greenwich meridian at 0 ◦ longitude, and the x 2 -axis

ff