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IAA Transactions, No. 8, ``Celestial Mechanics'', 2002
High­precision numerical theory of the rigid Earth
rotation taking into account the geodetic
perturbations
G. I. Eroshkin, V. V. Pashkevich
Pulkovo Observatory, St. Petersburg, Russia
The present investigation is a development of the previous research (Pashke­
vich, 2000). The equations of the rigid Earth rotation taking into account the
most essential relativistic perturbations -- the geodetic perturbations -- are modi­
fied. As a result, the numerical theory of the rigid Earth rotation is constructed,
which is more adequate to the kinematical solution of the semi--analytical theory
SMART97 [1]. The initial conditions of the numerical theory are determined by
the kinematical solution of the semi--analytical theory SMART97. In the previ­
ous investigation [2] DE403/LE403 ephemeris was used for generating the per­
turbations of the disturbing bodies. In the present investigation by means of the
numerical experiments it is discovered that for constructing a high--precision nu­
merical theory of the Earth rotation the ephemeris DE404/LE404 can be used
instead of the ephemeris DE403/LE403. The ephemeris DE404/LE404 is less
precise than DE403/LE403 but is valid over significantly longer time interval.
The numerical theory based on DE404/LE404 ephemeris and numerical theo­
ry based on DE403/LE403 ephemeris are practically identical over the common
time interval of these ephemerides. The results of the mathematical description
of the behaviour of the residuals between the numerical theory and SMART97
kinematical solution depend essentially on the time interval of comparison. It is
necessary to note that the comparison of these theories over the several thousand
year time interval gives more correct qualitative description of the behaviour of
the residuals.
The possibility of extending the time interval of the semi--analytical theory
of the rigid Earth rotation SMART97 to several thousand year time interval is
discussed.
The results of the present research are as follows.
a) The high--precision (at microarcsecond level accuracy) numerical theory
of the rigid Earth rotational motion dynamically adequate to the ephemeris
DE404/LE404 has been constructed,
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b) The numerical investigation of the rigid Earth rotational motion, taking
into account the geodetic perturbations over long time interval, has been carried
out.
References
1. Bretagnon P., Francou G., Rocher P., and Simon J. L. SMART97: A new
solution for the rotation of the rigid Earth, Astron. Astrophys., 1998, 329,
329--338.
2. Pashkevich V. V. New development of the numerical theory of the earth ro­
tation, In: Journ'ees 2000: J2000, a fundamental epoch for origins of reference
systems and astronomical models, (N. Capitaine, ed.), 2000, 169--176.
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