_{1}

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It will show, a recent extension of special relativity on the grounds of a novel concept of velocity, which also predicts the speed of transversal motions on the plane of the sky to increase with enduring observation time, to fully explain the differences of the observational results of the former experiments referring to the distance of the Pleiades from Earth.

It is widely known that the orbiting observatory Hipparcos (High-Precision Parallax Collecting Satellite), launched in 1989 by ESA, among others also measured the distance to the open cluster Pleiades with 118.3 ± 3.5 pc (later publications e.g.: 120.2 ± 1.5 pc), where pc denotes parsec (e.g. [

But very recently a new measurement by using radio interferometry has been published by a cooperation of ten radio telescopes ranging over the whole Earth such that this VLBI (Very Long Base-Line Interferometry) array acts equivalently to a telescope the size of Earth (e.g. [

On the other hand, VLBI referenced to an essentially stationary quasar and using the above array of widely separated radio telescopes this gives the resolution of a telescope the size of Earth―as already mentioned. Thus, the latter global telescope essentially simultaneously could observe the apparent motion of oppositely positioned stars of the cluster. Furthermore, one should notice that to derive the cluster’s absolute parallax the uncertainties of each target star’s position with respect to the center of the cluster have been included, i.e. the binary orbit distances have been converted into a single cluster distance or to rephrase this: the apparent motions of the target stars obviously have been referenced to the stationary center of the Pleiades cluster. This implies that all measured apparent motions at opposite positions of Earth’s orbit are referenced to the center of the cluster. In contrast to this very special VLBI method, Hipparcos referenced the apparent motion of each target star to some “fixed” star individually such that the measured parallaxes are absolute, i.e. the result of a global solution over the whole sky.

The above mentioned novel concept of special relativity and the associated modification of the Lorentz transformation among others propose the existence of an absolute rest frame of nature Σ_{oo} in the form of the space- fabric of symmetric Minkowski-space, indicated through the CMB, implying a duality of the speed of light as well as of inertial velocity in dependence on one-way or two-way measurement, respectively [_{0} along length d on the plane of the sky be observed as the vector product of the diverging coordinate differences of space and time, respectively, in the order of

where by angular dimension π/2 is referred to the angle enclosing the reverse of the vector of the light reaching the observer along the line of sight and d and, furthermore, the angle of the vector of the motion along d relative to the line of sight is running backwards from π/2 to zero (derivation see [_{01} = 1, whereas velocity v_{0} and Lorentz factor γ_{0} denote the respective value relative to the absolute rest frame of nature or the CMB, i.e. in this case v_{o(CMB)} = 370 km∙s^{−}^{1} of the Sun. In [

But from the previous it is obvious that only one of the parallax measurements fulfills the requirements of the coordinate difference of observation time Δt_{d} in the right-hand square root of Equation (1), that is motion from a point at rest relative to the observer alongside distance d transversal to the latter. With the parallax measurements referenced to the Pleiades center the VLBI time of observation clearly fulfills the above demand. Note that other than VLBI centered at the Pleiades, Hipparcos’ four years lasting parallax measurements cover the whole cluster and, thus, also the parallaxes at the opposite sides of Earth’s orbit. This implies observation time of VLBI either to be doubled or of Hipparcosless by half, to make both measurements equivalent in the sense of

of the different distance estimations of both parallax measurements, where Δt in the mid-ratio denotes the respective observation time. This leads in accord with Equation (1) to the further ratio

(y in the right-hand ratio denotes year), whereas the respective ratio of the observationally derived VLBI-dis- tance 136.2 ± 1.2 pc and Hipparcos-distance 118.3 ± 3.5 pc delivers:

Hence, the latter experimental ratio 1.1513 ± 0.0232 of the above derived distances from measurements of the trigonometric parallax of Earth’s orbit at the distance of the Pleiades cluster with differently long observation times seems to be in good accordance with the theoretically derived value 1.1547 of Equation (2a), implying the above discussed discrepancies in distance measurements to owe their existence the relativistic effect Equation (1).

The above introduced extension of special relativity [