Correction due to finite speed of light in absolute gravimeters

Correction due to finite speed of light is among the most inconsistent ones in absolute gravimetry. Formulas reported by different authors yield corrections scattered up to 8 $\mu$Gal with no obvious reasons. The problem, though noted before, has never been studied, and nowadays the correction is rather postulated than rigorously proven. In this paper we make an attempt to revise the subject. Like other authors, we use physical models based on signal delays and the Doppler effect, however, in implementing the models we additionally introduce two scales of time associated with moving and resting reflectors, derive a set of rules to switch between the scales, and establish the equivalence of trajectory distortions as obtained from either time delay or distance progression. The obtained results enabled us to produce accurate correction formulas for different types of instruments, and to explain the differences in the results obtained by other authors. We found that the correction derived from the Doppler effect is accountable only for $\frac23$ of the total correction due to finite speed of light, if no signal delays are considered. Another major source of inconsistency was found in the tacit use of simplified trajectory models

Search for geodynamic signals in time series of astrometric observations

Since 1963 astronomical observations are conducted at Borowa Gora Geodetic-Geophysical Observatory of the Institute of Geodesy and Cartography with the use of transit instrument. Instrumental, technological and methodical improvements in acquiring and pre-processing of rotational time observations make the time series inconsistent over the whole period of operation of the instrument. The rotational time determined was initially referred to the FK5 catalogue system; starting from the data of 1986 it is also referred to the Hipparcos catalogue system. Data series from last almost 25 years is particularly valuable for the analysis. Complex spectral analysis of a long-standing rotational time data series from 1986.0-2010.6 was performed. A number of periodic terms were separated from the series investigated and the numerical model of the series has been formed. The effects of beat observed in the numerical model were discussed. The existence of a distinguished weekly term in the data investigated has been observed. The results obtained were compared with the spectra of EOP from the analysis of IERS data