The systematic part of the difference between the Hipparcos positions
and positions in an inertial reference system can be described by a rotation.
Whereas, the differences in proper motions are represented by the spin, the
time derivative of the rotation. For the determination of the spin vector
we used the basic equations
and
are the proper motion differences
in the sense Hipparcos minus absolute,
and
are the equatorial
coordinates of the link stars. The indices x to z refer to a
right-handed triad with the x-axis pointing towards the vernal equinox
and the z-axis towards the north equatorial pole.
The were computed from both components of the
proper motion differences, i.e. from the least squares solution of 2n
equations, where n is the number of link stars. This is called the "star
solution''. For three out of 360 stars used in the solution, proper motions
were determined in two fields (M3-Z and M3-IV). In the star solution we used
the average of both proper motion determinations for these stars.
The proper motion differences in a given field may be
correlated due to a systematic error of the extragalactic link in each
field. Therefore, we used the average proper motion differences for each
field in a second least squares solution of 2m equations, where m is the
number of link fields. This is called the "field solution''.
Both, star and field solution should be identical if the stars are homogeneously distributed in the fields with the same weights and if the fields are homogeneously distributed over the sky. This is not the case, therefore the solutions will differ. Formally, the rms error of the star solution is smaller than that of the field solution because of the greater number of equations.
Using H37cr data and the absolute proper motions of all 360 stars
in the whole magnitude interval 6 < B < 13 the following results were
obtained, for the star solution and the field solution, respectively:
preliminary solution with 360 stars in 24 fields | |
referred to the final Hipparcos system (see Sect. 6 (click here)) | |
star solution | field solution |
residual spin parameters [mas/yr] | |
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rms of solution | |
6.9 mas/yr | 3.1 mas/yr |
correlation coefficients | |
rxy = +0.20 | rxy = +0.21 |
rxz = +0.04 | rxz = -0.04 |
ryz = +0.02 | ryz = -0.01. |