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Subsections
This section is dedicated to the global comparison
of H96NUT with existing nutation series.
First of all one has to choose the most
suitable model for a comparison.
Obviously, the older nutation models (like
K77, ZG89 or KS90) have  although they are
well established  a threshold which is not
comparable to that of H96NUT.
The recent theories of the nutation for the rigid Earth model
SK96.2, RDAN97, SMART97 as already mentioned in Sect. 1 have
a threshold smaller than our model and therefore we have only to
decide which of them is the most convenient one for comparison.
Unfortunately, there is no suitable benchmark nutation series,
that is the total nutation angles computed over
some time interval at discrete times,
in contrast to the situation with tidal models
where at least two reference series exist.
The benchmark RDNN97 mentioned in
Roosbeek & Dehant (1997)
is
still under testing and not
yet prepared for public use.
What makes the comparison more complicated
is that in the particular nutation models different
variables in the arguments are used.
We use in H96NUT the mean longitude of planets referred to the mean
dynamical ecliptic and equinox of date.
Roosbeek & Dehant (1997)
use the mean longitude referred to the mean dynamical
ecliptic and equinox J2000. In both theories the values are taken from
Simon et al. (1994)
and differ by the value of the general
precession in longitude .
Williams (1995),
Kinoshita & Souchay (1990),
Souchay & Kinoshita (1996, 1997a,b),
use the mean
longitude referred
to the mean dynamical ecliptic and equinox J2000 and moreover, the
general precession as an additional fundamental argument.
In
Bretagnon et al. (1998)
the mean longitudes of planets
are
reckoned from the equinox of date. Their values differ from those of
Simon et al. (1994)
due to modifications of the tidal model in
the lunar theory and the new inertial ecliptic and dynamical
equinox defined by DE403/LE403
(Standish et al. 1995).
It must be mentioned that also the precession theories
used in the computations sometimes differ:
Lieske et al. (1977),
Williams (1994)
or
Simon et al. (1994)
are commonly in use.
Therefore, the scaling factor also takes
different values but in recent works the agreement
is better than the relative uncertainty (about 10^{5})
due to that of the precession constant .It is also doubtful whether a simple rescaling
of the nutation amplitudes makes much sense.
To close these general remarks it should be noted
that little is said about the consistency
of the various nutation models,
i.e. whether all theories and numerical constants
(e.g. ) used in the computations are
compatible with each other or not.
Except for the older expression of
Aoki et al. (1982)
used in the computation of the tidal potential HW95
and the relationship between and
taken from KS90, everything else is compatible here.
=.4
Table 11:
Differences larger than 5 as
in longitude and obliquity (in as) between H96NUT and RDAN97 (t in J cy)

For the term by term comparison we have chosen the model RDAN97 of
Roosbeek & Dehant (1997)
which appeared recently.
This model employed a threshold of 0.1 as and contains 1553
terms with similar arguments to that used in H96NUT.
While the expressions of Delaunay's arguments D, F, l, and are the same in both theories, different expressions for the mean
longitudes of the planets were used.
The mean longitude
referred to the mean dynamical ecliptic and equinox of date is used in
H96NUT in comparison with the mean longitude referred to the mean
dynamical ecliptic and equinox J2000 used in RDAN97. Both systems
were taken from
Simon et al. (1994)
and they differ by the value of
the general precession in longitude . This difference appears
in the direct and indirect planetary terms only and is vanishing for
J2000 when the longitudes are the same in both systems.
The compensation of the difference in the arguments should appear in the
secular term of amplitude in the other phase. For example, for the largest of
concerning terms in
having in argument with an amplitude close to 300
as and period 91505.1 days the difference between the
series should appear
in with amplitude about 50 as
(for t not too large) as we can see in the first term of
Table 11. In the
comparison we have found
27 terms of H96NUT which are not involved in
RDAN97. 14 of them are indirect planetary terms coming from the
lunisolar potential, one is a direct planetary term of Venus and remaining
12 ones are lunisolar terms coming from the Moon.

Figure 2:
Comparison in time domain H96NUT  SMART97 for
shortperiodic terms only
a) b):
values in as 
The nutation model SMART97
(Bretagnon et al. 1998)
is not
convenient for the
term by term comparison with H96NUT in spite of having the threshold
more than one order smaller because of the different fundamental
nutation arguments. To take advantage of the quality of this model we
have utilized it for the comparison in the time domain.
Table 12:
Overall and short period only comparison in time domain:
H96NUT  SMART97,
values in as

First, a term by term comparison for the nutation of the figure
axis between H96NUT and RDAN97 has been carried out.
The maximum difference, the sum of all absolute differences
and the rms value are given in Table 9.
The percentage distribution of the differences in the various
intervals is shown in the Table 10. The list of the
differences which are bigger than 5 as in longitude and
obliquity is presented in Table 11. These three tables
clearly demonstrate that more than 90% of the terms can be computed
with comparable accuracy as in other nutation series.
However significant differences
occur for the largest nutation terms (with periods
18.6 y, 9.3 y, 365 d, 182 d, 13 d) and for the
longperiodic nutation terms, say above 18.6 years.
Both should be expected due to the reasons explained in
Sect. 4.
Next, a comparison between H96NUT and SMART97 in time domain was performed.
Thus the nutation angles and were evaluated numerically starting at JED = 2396931.666
with a time step of 20 hours and a total step number
of 131072 (2^{17}) covering approximately 300 years.
It follows from Table 9
that the largest difference of about 5500 as
at 6786 days would dominate the comparison in time domain.
Therefore, instead of showing the figures in that case
another comparison in time domain was carried out where all
nutation terms with periods larger than 6700 days were
omitted in order to compare in a better manner
the shortperiodic terms.
Indeed, the differences in time domain drop
by one order of magnitude (see Table 12).
They are shown for the time interval 18502150
in Fig. 2.
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