**Bulletin of Taras Shevchenko National University of Kyiv. Astronomy, no. 67, p. 15-19 (2023)**

**COSMIC DISTANCE LADDER AND RELATED PROBLEMS**

**Serge PARNOVSKY, DSc (Phys. & Math.), Prof.
**

**Taras Shevchenko National University of Kyiv**

**, Kyiv, Ukraine**

**Abstract**

A brief description of the methods of determining the distances to celestial bodies in the Solar System, the Galaxy and beyond is given; the concept of the “distance ladder” is described. The problems that arise when moving from one level to another are shown. A bias in the determination of distances and a systematic error in the Hubble constant occur if we use distances estimated using statistical dependencies to calibrate ones obtained by another method. This is a consequence of statistical data processing when approximating any dependence based on a set of measurement data. Random errors in the values of the ordinate lead to random errors in the parameters of the dependence. However, random errors in the values of the abscissa lead additionally to systematic errors in the dependence parameters. This gives a systematic error when estimating the value based on the obtained dependence.

When astronomers calibrate distances to the stars in the Galaxy estimated by Cepheid or main-sequence star luminosities, the abscissa is the distance to nearby stars determined by parallaxes, which have small errors that can be reduced as measurement accuracy improves. A spread in ordinate for fixed abscissa is related to the statistical nature of dependence. When moving to the next rung of the ladder, astronomers compare the distances obtained for a sample of nearby galaxies by other methods (Tully-Fisher-type dependencies, surface brightness fluctuations, etc.), which are ordinate, and the ones obtained from Cepheid, etc, which are the abscissa. It is the errors in the abscissas that lead to the appearance of the bias of the calibration and all the distances estimated by the obtained dependence. This bias increases when moving to the next rungs of the distance ladder. The consequences of it and ways to reduce the bias impact are discussed. Appropriate corrections could be done using the error estimation obtain from the Monte Carlo simulations. This bias can be the source of the Hubble tension.

**Key words
**Galaxies, star formation, statistical methods.

**References
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