Earth tides affect astronomical observations of the Earth's rotation in the following two ways: (1) verticals are deflected; and (2) the polar moment of inertia of the Earth is changed causing periodic variations in the rotation rate. The diurnal and semidiurnal tides and nutation were examined in periodic variations. Results indicate little change occured in the polar motions. Nutation observations were disturbed rather seriously by the diurnal tides

Sasao, T.

English

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PRECEDING PAGE BLANK NOT FILMED ,
How Do Earth Tides Affect Astronomers?
Tetsuo Sasao'
Cooperative Institute for Research in Environmental Sciences
University of Colorado/NOAA
Boulder, Colorado 80309
N79 21511
Earth tides affect astronomical observations
of the Earth's rotation in two ways. They- de-
flect verticals and change the polar moment of
inertia of the Earth, thus causing periodic
variations in its rotation rate (Table 1). Since
astronomers observe stars usually around midnight
at almost the same local sidereal time 0=1^ +180°
in every station, where Lg is the mean longitude
of the Sun, the diurnal and semidiurnal tides; as
well as nutations, produce apparently common
variations with long "aliased" periods in the
daily mean latitude and time values of different
stations. Therefore, detection of polar motions
is little contaminated by the Earth-tide effects,
because they are largely absorbed in "common" z,
T and n-terms in the conventional observation
equation:
latitude: A<}> = x cos A + y sinX + z
time: co(UTO-UTC) = tan(j>(x sinX - y cosX + T) + n
where x, y are "pole coordinates", <|>, X are lati-
tude and east longitude of a station and to is the
mean rotation rate of the Earth. Nutation ob-
servations, on the contrary, are disturbed rather
seriously by the diurnal tides with the same
arguments and, through the aliasing, by semi-
diurnal and long period tides.
A major concern of astronomers in analysing
the nutations is to detect evidence for the fluid-
core resonance. Observed values contained in the
squares of Figure 1 seemingly follow a theoretical
resonance curve based on a realistic Earth model.
Effects of the diurnal tides in time and latitude
expected in <t>=39°08' (latitude of 5 ILS
stations) are shown by the arrows in Figure 1
under the assumption A= 1 + k -H = 1. 2. It is
evident that Oj and Pj tides may deviate the
observations of the fortnightly and semiannual
nutations noticeably. It does not seem appropri-
ate, however, to correct astronomical data for
the diurnal-tide effects by simply assuming
A=1.2, because ocean-tide effects must hardly be
negligible. The problem may become important in
more detailed studies of the internal constitu-
tion of the Earth by means of nutation observa-
tions.
Consequences of the oscillations of the verti-
cals due to M2-tide can be observed in the astro-
nomical latitude and time data and are regarded
as one of the means for determination of the
A-factor. In order to decide, for example, that
A=1.2 but not 1.1, however, one needs accuracy
higher than 0.001 arcseconds or 3 cm. It does
not seem easy, in general, to attain such accuracy:
by conventional astronomical observations with the
typical error of single observation reaching 0.2
arcseconds or 6m. As a matter of fact, 52
determinations of the A-factor so far obtained
TABLE 1. Effects of Earth Tide on Astronomical Observations
Irregularities in the Earth's-Rotation
Polar motion Nutation Changes in L.O.D.
Latitude
Time
x(t)cosX + y(t)sinX
tanc|>[x(t)sinX-y(t)cosX]
sin[L(t) -a]
tan<j> cos[L(t) - a] n(t)
Earth Tide Effects
Long period tide
Vertical deflection Changes in C
Diurnal tide
Vert. defl.
Semidiurnal tide
vert. defl.
Latitude
Time
Asin2(f>cosL(t)
k sinL(t)
Acos24>sin[L(t) -a] A sin2((>cos[L(t) - 2a]
Atan<j)cos[L(t) - a] A sin[L(t) - 2a]
A = 1 + k - £
L(t): Argument of periodic disturbance due to the Sun and Moon
a : Local sidereal time
Proc. of the 9th GEOP Conference, An International Symposium on the Applications of
Geodesy to Geoitynamirx. October 2-5.197S. Dept. of Geodetic Science Rept. No. 280, The
Ohio State Univ.. Columbus, Ohio 43210.
Permanent address: International Latitude
Observatory of Mizusawa:, Mizusawa, Iwate, Japan)
https://ntrs.nasa.gov/search.jsp?R=19790013340 2020-03-21T23:58:45+00:00Z
0.997
0.996
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NUTATION FREQUENCY
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©
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-MANABE 1978 A
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- MANABE 1978 C
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- Sekiqucbi (553
MANABE 1978 B
= MANABE 1978 0
MANABE I978A
'0.0001 0.0002
1.04
1.03
_ i
_ _ Popov I957
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ako !970 B
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MANABE I978C
Yckcyama I973B
MANABE I978 B
Wako I957A
Wako I970A1 i
0.070 0.075 0.080 0.005 0.010
Fig. 1. Effects of diurnal Eaettv tides on nutation observations. 'Arrows T
and L show the effects of diurnal tides on main nutation components in time
and latitude observations, respectively, calculated for 4>=39°08' with
1.2;an assumption 1 + k-
are scattered from 0.1 to 2.3, as shown in Figure
2. Although some authors have pointed out the
possible secular'change in the A-factor, recent
analysis of past ILS data done by Manabe', Sakai
and Sasao has revealed no firm evidence for the
change (Figure 3). Different values of the A- . ,
factor detected in. different stations are some~
times attributed to the difference between
oceanic and continental stations. However,
deviation of the 18.6-year principal nutation
from'Woolard's value derived by Manabe' et al.
from latitude data of 5 ILS stations shows even
larger station-to-station differences than those
of the M2-tide (Figure 4), though the principal'
nutation must almost be unaffected by ocean-tide
effects. It thus seems ^ necessary to examine
carefully the scale value problem and other
possible sources of instrumental errors before
considering any inverse problems for the ocean-
tide effects "on the basis of the astronomical
M2-tide data.
•Changes in the rotation rate of the Earth due
to zonal deformation,caused by MU and Mf tides
are -analyzed so as to determine Love number k.
It should be noted that one needs 0.001 arcseconds
accuracy again in order'to decide whether k=0.30
or 0.27. Nevertheless, the reported difference
between k^numbers derived from MU and Mf waves
appears- significant (Table 2). It might be
interesting to note here a possibility that the
Mf-wave is disturbed by the aliased "uncorrected"
part of 'the fortnightly nutation arising from the
fluid-core effect, which does not seem to have
been taken into consideration fully.
342
25
20
15
10
5
= 52
. n
0.1 0.3 O.5 O.7 O.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 A
Fig. 2. Histogram of astronomically inferred
values of A=l + k-X, factor.
A
1.4
1.2
1.0
0.8
0.6
0.4 •
I I
—i—
I
I
i
Fig. 3. Values of A=l + k-£ factor estimated
for different periods of ILS observations.
Nl2 - tide (1. k-l )
1935 - 1966
- 1B.6 nutation
070096 •. KOOII
-4:88± 6141
0:0157t 070034
177145 t 12'.24
TABLE 2. Estimation of Love Number k from
Changes in the Earth's Rotation Rate
Due to Mf and Mm Tide
Theoretical Values (in msec)
MJJ -0.77(k/0. 29)sin(L< - r')
Mf -0.71(k/0.29)sin2L{
-0.30(k/0.29)sin(2L( - «)
Observed k
Authors Mf
Guinot (1970)
Pilinik (1970)
Guinot (1974)
Djurovic (1975)
0.331±0.061 0.265±0.068
0.300 + 0.005
k(Mf) -k(Mm) =0.030 + 0.006
0.334 + 0.005 0.295 + 0.011
0.343 0.301
Fig. 4. Amplitude and phase diagram showing
station-to-station differences of the estimated
values of the 1 +'k - £ factor and retrograde
component of "uncorrected" 18.6-year principal
nutation. M, K, C, G, U correspond to 5 ILS
stations: Mizusawa (Japan), Kitab (USSR),
Carloforte (Italy), Gaithersburg (USA) and Ukiah
(USA).
343


How do earth tides affect astronomers?

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