Geoscience Reference
In-Depth Information
Celestial Reference Frame
Nutation
Polar motion
Polar motion
-2.0 -1.5 -1.0 -0.5
0
0.5
1.0
1.5
2.0
2.5
3.0
cpsd
-3.0 -2.5
-2.0 -1.5 -1.0 -0.5
0
0.5
1.0
1.5
2.0
cpsd
Polar motion
Nutation
Polar motion
Terrestrial Reference Frame
Fig. 2
Relationship between the frequency of some motion as viewed from the celestial reference
frame (
top
half of figure) and the corresponding frequency of the same motion as observed from
the terrestrial reference frame (
bottom
half of figure) (Gross
2007
)
bands are thus connected by
σ
c
=
σ
t
+
Ω,
(2)
where
signifies the angular velocity of the Earth. Equation (
2
), illustrated in Fig.
2
,
is the basic frequency relation for some motion as observed simultaneously in the
celestial frame
c
and in the terrestrial frame
t
. The separation of polar motion
and precession-nutation based on frequencies represents the current conventional
approach, replacing the traditional distinction between astronomical and geophysical
Earth rotation, for which it is decisive whether external or internal torques are acting
upon the planet.
Ω
1.2 Precession and Nutation
The Earth can be characterized approximately as an oblate spheroid, its rotation axis
inclined by
5
◦
with respect to the ecliptic normal (Schuh and Böhm
2011
).
Subject to the gravitational torques ofMoon and Sun, which try to force the equatorial
plane into the ecliptic, the rotating Earth acts like a gyroscope and swerves bymoving
in space. The resulting motion is a retrograde revolution around the ecliptic pole,
the rotation axis describing a cone with aperture 2
ε
≈
23
.
. This steady or secular motion
(period: 25800yr corresponding to 1 Platonic year) with respect to the space-fixed
reference system is called precession.
Smaller periodic changes of the spin axis with respect to the space-fixed systemare
superimposed on precession. Such motions with periods from a few days to 18.6yr
are summarized as nutation and originate from the gravitational interaction of the
Earthwith other celestial bodies. Those forced parts of precession and nutation can be
modeled and predicted precisely using time-dependent harmonic series expansions
(Schuh and Böhm
2011
). The currently most accurate precession-nutation model
adopted by the latest IAU resolutions (IAU Resolutions
2000
,
2006
) considers both
lunisolar and planetary effects, mantle anelasticity, electromagnetic coupling mech-
anisms between core and mantle as well as between inner and outer core, but also
geophysical effects, like ocean tides, which are characterized as nutation following
ε
