Geology Reference
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with σ
W
denoting the angular wobble frequency. Then, the angular wobble fre-
quency is
plus the signed angular nutation frequency. For the PFCN, the
associated wobble has a retrograde period slightly longer than a sidereal day, while
for the RFCN the associated wobble has a retrograde period slightly shorter than a
sidereal day.
In terms of frequencies, equation (4.122) becomes
−Ω
1
T
s
,
f
N
=
f
W
+
(4.123)
with
f
N
,
f
W
denoting the nutation and wobble frequencies and
T
s
representing
the length of the sidereal day. The length of the sidereal day is
T
s
=
2π/
Ω
.For
10
−
5
Ω=
×
/
the adopted mean rate of rotation of the Earth,
7.292115
rad
sand
T
s
=
0.9972696 days. Combining relations (4.120) and (4.122) gives the ratio of
the nutation amplitude to the wobble amplitude for the RFCN as
A
N
A
W
=
σ
W
σ
W
,
(4.124)
+Ω
while combining relations (4.121) and (4.122) gives the ratio of the nutation amp-
litude to the wobble amplitude for the PFCN as
A
N
A
W
=−
σ
W
σ
W
+Ω
.
(4.125)
In the space frame of reference, in which the nutations are observed, the res-
onances are of the form (4.111). To indicate that they refer to nutations, we write
them as
a
N
f
N
0
/
f
N
0
2
.
(4.126)
Q
N
f
N
−
1
+
Of more direct geophysical interest are the resonances of the associated nearly
diurnal wobbles, which we write as
a
2
W
f
W
0
/
f
W
0
2
.
(4.127)
Q
2
W
f
W
1
+
−
Expressing the right sides of equations (4.124) and (4.125) in terms of frequencies
via relation (4.123), we find that
f
N
0
f
N
0
−
A
W
=±
1/
T
s
A
N
,
(4.128)
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