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The Necessary Procedures to Reach an Agreeable Reference Frame: Counterproposal to the Circular Letter no. OF Kovalevsky
Abstract
The procedures are summarized in order to obtain a reference system which is available at the present moment and in the near future for the astronomical purposes. The target of the present discussions is the IAU General Assembly to be held in the summer of year 1991, in order to find out an agreeable result there. Discussions beyond this are postponed to a further occasion.
Present observations using modern astrometric techniques are supposed to
provide the Earth orientation parameters, and therefore UT1, with an
accuracy better than ±1 mas.
In practice, UT1 is determined through the intermediary of Greenwich
Sidereal Time (GST), using both the conventional relationship between
Greenwich Mean Sidereal Time (GMST) and UTl (Aoki et al. 1982) and the
so-called "equation of the equinoxes" limited to the first order terms
with respect to the nutation quantities. This highly complex relation
between sidereal time and UT1 is not accurate at the milliaresecond
level which gives rise to spurious terms of milliaresecond amplitude in
the derived UTl.
A more complete relationship between GST and UT1 has been recommended by
Aoki & Kinoshita (1983) and Aoki (1991) taking into account the
second order terms in the difference between GST and GM ST, the largest
one having an amplitude of 2.64 mas and a 18.6 yr-period. This paper
explains how this complete expansion of GST implicitly uses the concept
of "nonrotating origin" (NRO) as proposed by Guinot in 1979 and would,
therefore, provide a more accurate value of UTl and consequently of the
Earth's angular velocity. This paper shows, moreover, that such a
procedure would be simplified and conceptually clarified by the explicit
use of the NRO as previously proposed (Guinot 1979; Capitaine et al.
1986).
The two corresponding options (implicit or explicit use of the NRO) are
shown to be equivalent for defining the specific Earth's angle of
rotation and then UT1. The of the use of such an accurate procedure
which has been proposed in the new IERS standards (McCarthy 1992a)
instead of the usual one are estimated for the practical derivation of
UT1.
Very long baseline interferometry (VLBI) observations of compact extragalactic radio sources collected in North America and Europe between July 1980-December 1984 are analyzed. The nutations derived from VLBI data are compared with the nutations in the Wahr series (1981). Good correlation of the data is observed; however, it is detected that a correction of -1.80 + or - 0.18-i(0.42 + or - 0.18) is required for the amplitude of the retrograde annual nutation in the Wahr series. The change in free core nutation resonance frequency is calculated to explain the derivation in the retrograde annual nutation. It is concluded that VLBI earth nutation measurements have sufficient accuracy to be sensitive to core-mantle boundary properties.
Minimum requirements for a kinetic study of earth's rotation are
considered for the case where observations are referred directly to a
nonrotating frame given by the directions of stars. Fundamentals of
earth-rotation measurements are discussed, along with the nonrotating
reference system, the terrestrial reference system, earth's rotation in
the nonrotating reference system, and the definition of UT1. Proposals
are made concerning the definition of the pole, expressions for certain
corrections, the definition and realization of the space reference
system, the instantaneous equatorial reference system, the definitions
of Universal Time, and the orientation of earth in space.
The relation between the units and readings of time and space coordinates of terrestrial and barycentric reference frames is discussed from the viewpoint of general relativity. Attention is paid to the unit of space coordinates since the International Astronomical Union (IAU) regulates only the unit of time in the above two frames. Two definitions of unit of length are examined and their effects on the numerical expression of coordinate transformation, equations of planetary motions, and those for light propagation time are discussed. A clear conflict is found between the IAU (1976) recommendation on the definition of the time-scales in different frames of reference and the statement that all constants in the IAU (1976) new system of astronomical constants are defined in terms of the Internationsl System of units (SI units). One of the above two definitions is proposed to resolve this conflict by the least alteration to current procedures for analysing the recent astrometric observations such as the radar/laser rangings, the range and range-rate, and the very long baseline interferometric observations. Also, an interpretation of numerical values in the IAU (1976) new system of astronomical constants is presented. It is stressed that the definition proposed in this paper requires that a formula slightly different from that in current use be employed in the numerical transformation of readings of coordinates between the terrestrial and barycentric reference frames.
An instantaneous plate-motion model, Relative Motion 2 (RM2), is obtained by inverting a data set comprising 110 spreading rates, 78 transform fault azimuths, and 142 earthquake slip vectors. RM2 is compared with angular velocity vectors which best fit the data along individual plate boundaries and, while the model performs close to optimally in most regions, attention is directed to those regions which are not suitably described by the model. Reasons for the discrepancies between RM2 and observations for the India-Antarctica plate boundary, the Pacific-India plate boundary, and the east-west trending transform fault azimuths observed in the French-American Mid-Ocean Undersea Study area are discussed.
Observations from 600 Mark III VLBI experiments from 1979 to 1988, resulting in 237,681 acceptable pairs of group delay and phase delay rate observations, have been used to derive positions of 182 extragalactic radio sources with typical formal standard errors less than 1 mas. The sources are distributed fairly evenly above delta = -30 deg, and 70 sources have delta greater than 0 deg. Analysis with different troposphere models, as well as internal and external comparisons, indicates that a coordinate frame defined by this set of radio sources should be reliable at the 1 mas level. The right ascension zero point of this reference frame has been aligned with the FK5 by using the optical positions of 28 extragalactic radio sources whose positions are on the FK5 system. Because of known defects in the knowledge of astronomical constants, daily nutation offsets in longitude and obliquity were determined relative to an arbitrary reference day in the set of experiments.
In an attempt of a realization of the radio reference frame a compilation catalogue of positions is derived from independent observation catalogues of extragalactic objects the coordinates of which had been determined by means of Very Long Baseline Interferometry. The compilation catalogue comprises 209 objects which are divided into a core consisting of 50 objects having mean positional accuracies of 0.5 milliseconds of arc (mas) and an extension with positional accuracies better than 2 mas. Comparison of this catalogue with an independent compilation catalogue led to confidence limits at the 1 mas level. — The compilation catalogue is supposed to represent a static reference frame of fixed extragalactic points. As the epochs of the contributing observations span nearly 10 years it was tried to interpret the apparent motion of the fixed points recognizable in the observation catalogues as an effect of luni-solar precession. The pilot study points at a reduction of the conventional value of about 2 mas per year.
A distinction is made between a conventional reference system and
conventional reference frame. It is pointed out that celestial reference
systems may be defined kinematically or dynamically. The geodynamic
requirements for reference systems may be discussed in terms of global
or regional problems. The former are necessary for monitoring the
earth's rotation, whereas the latter are mainly associated with crustal
motion studies where the predominant interest is in strain or strain
rate, quantities that are directly related to stress and rheology. Two
kinds of quasi-inertial systems are discussed: conventional kinematical
systems and ideal reference systems.
A relation between the Celestial Reference System (CRS) and the Terrestrial Reference System is established theoretically by solving the equations of motion of a rigid Earth under the influence of the Sun and the Moon up to the second order perturbation. The solutions include not only nutation including Oppolzer terms but also the right ascension of the dynamical departure point (DP), as well as the wobble matrix.
We have found that the kinematical definition of the Non-Rotating Origin NRO (for which our term is DP) given by Capitaine, Guinot and Souchay (1987) is not entirely equivalent to that included in the solutions of the equations of motion but shows perturbation, in particular when this is taken on the instantaneous equator. Besides this serious fault, we feel little merit in taking the DP as reference: (1) Unnecessary spurious mixed secular terms appear which come from the geometrical configuration that the DP leaves far and far from the ecliptic. (2) the DP moves secularly as well as oscillating with respect to space; this literally contradicts the term ‘NRO’, or is at least misleading. (3) It does not free us from the precession uncertainty to adopt DP as reference, since we cannot avoid virtual proper motions in terms of the current CRS. (4) No terms ignored hitherto are introduced, even if we take the DP properly chosen, i.e., on the equator of the celestial ephemeris pole. The transformation is only mathematical. There is no sufficient reason to take it instead of the equinox, which is observable in principle, as reference at the cost of the labor of changing all the textbooks, ephemerides, data and computer software now existing.
The exact description of the Earth's rotation raises the problem of the choice of a reference point on the instantaneous equator both in space and in the Earth. We propose to use, as the reference point in space, a 'non-rotating origin' (Guinot 1979) such that its hour angle, reckoned from the origin of the longitudes (or 'non-rotating origin' in the Earth), represents strictly the sidereal rotation of the Earth. Such an origin on the instantaneous equator depends only on the motion of the pole of rotation; it is practically realizable from a chosen fixed reference and we give the formulae to obtain it in space and in the Earth. We show that the estimation of the sidereal rotation is not critically affected by the precision with which the trajectory of the pole is known. We therefore propose a definition of the Universal Time which will remain valid even if the adopted model for the precession and the nutation is revised. We show that the use of the non-rotating origin also simplifies the transformation of coordinates between the terrestrial and celestial reference systems. An additional simplification of this transformation would be obtained when using, in the precession and nutation matrixes the development of the celestial coordinates of the pole as function of time in place of the various usual equatorial and ecliptic parameters. The use of the non-rotating origin instead of the equinox would thus have advantages for both conceptual and practical reasons.
In 1979 the Seventeenth General Assembly of the International Astronomical Union (IAU) in Montreal, Canada, adopted the 1979 IAU Theory of Nutation upon the recommendation of this Working Group. Subsequently the International Union of Geodesy and Geophysics (IUGG) passed a resolution requesting that this action be reconsidered in favor of a theory based on a different Earth model. As a consequence of that reconsideration the 1980 IAU Theory of Nutation was adopted. The details of that theory and the history of its adoption are described here in the Final Report of the IAU Working Group on Nutation. A summary of these events and the essence of our recommendations is provided first while the body of the report discusses these matters in greater detail. The theory itself is contained in Table I.
We show that the non-rotating origin introduced by Guinot is nothing but a departure point on the movable equatorial plane, and discuss that, even if this is introduced, the uncertainty of determining the equinox correction cannot be avoided. A difficulty still remains, furthermore, when we take into account nutational effect, since the (true) departure point is not fixed but moves in RA direction on the equator secularly and periodically with respect to space. We discuss thoroughly the interrelation between old and new concepts, and propose an exact treatment sufficient enough for the precise requirements.