Earth’s rotation: observations and theory - Earth Dynamics: Deformations and Oscillations of the Rotating Earth - page 321

with the positive sign referring to the RFCN and the negative sign referring to
the PFCN. Comparing the denominators of the resonances expressed by the forms
(4.126) and (4.127), and again using the frequency relation (4.123), the wobble Q W
is found to be related to the nutation Q N by

f N 0 − 1/ T s

f N 0

Q W =± Q N . (4.129)

Again the positive sign refers to the RFCN and the negative sign refers to the
PFCN.
The wobble and nutation frequencies, from expression (4.123), are related by

1
T s .

f W = f N − (4.130)

The wobble period is then related to the nutation period by

1
T W =

1
T N −

1
T s ,

(4.131)

or

T s T N
T s −

T W =

T N .

(4.132)

It is of interest to find the amplitude, period and Q of the nearly diurnal wobbles
associated with each of the two nutation resonances, fitted to the average spec-
tral density, in Figures 4.16 and 4.17. For the nearly diurnal wobble associated
with the PFCN, the amplitude A W = 0.230713 microarcseconds (μas), the period

is T W 2287.20. The nearly diurnal wobble associ-

ated with the RFCN has amplitude A W

=− 0.999838 days and Q W =

=

0.444719 microarcseconds (μas), period

T W = − 0.994893 days and Q W = 2800.50.

The nutation Q N can be recovered from the straight lines fitted to the ring downs
of the PFCN and RFCN, shown in Figures 4.18 and 4.19, using the values of the
nutation periods recovered from the resonances fitted to the average spectral dens-
ity of the nutation residuals, shown in Figures 4.16 and 4.17. The slope of the fitted
straight lines is

=± π log e

log e
τ ,

c

Q N T N =−

(4.133)