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This publication presents the results of two studies of astroarchaeological monuments in North Khakassia confirming the existence of Siberia stellar astronomy in the Bronze age (andronovo culture, Khakassia, mid-II millennium BC). It is proved that in the study area ("Sunduki") Arcturus - the brightest star in the northern sky - was purposefully observed in conjunction with the stars of the Orion constellation (in particular Betelgeuse - the brightest star of the constellation). In both investigated monuments of the Bronze Age were found man-made objects specifying astronomically important areas - a kind of tools to monitor these stars. Because there is no any written source the observed stars and epoch of observation were identified by geodetic measurements and astronomical calculations. This era is XIV-XIII centuries BC which corresponds to the archaeological dating of these objects defined in terms of style and semantics of petroglyphic images marking astronomically significant azimuths. The work confirms the hypothesis of tracking the heliacal and acronycal passages of Arcturus by Andronov priests (the first in the morning and the last in the night) in predetermined directions. Arcturus was observed by priests to determine the winter solstice, the middle of the spring and summer seasons. This revealed the specifications of observing of the heliacal and acronychal passages of stars with a naked eye such as a weakening of the apparent brightness of stars near the horizon at dusk and full moon, as well as the loss of light depending on the angular distance from the sun. Because of these features the first and the last star passages of the year through a given direction can be observed in the time interval up to ten days. The conclusion about the features of the observation of Arcturus by andronovo culture priests confirms and explains the perfection and precision of their lunar-solar calendar systems revised in such a way from the observations of the stars. No less important was the fact that figuring out a direct connection of different types of okunev and andronovo anthropomorphic petroglyphs with astronomically significant directions. This allows us to judge more reliably the semantics of certain images of okunev and andronovo cultures. Due to the fact that until recently Arcturus took a very important place in the astral mythology of indigenous peoples of Siberia the problem of reconstruction of stellar components of andronovo mythology in Khakassia becomes more perspective to solve. The obtained results allow us to consider the whole astronomical dating from observations of stars as a reliable and highly accurate (+- 50 years) instrument of ancient man-made structures' dating which was used with different cultures in the cult practice of astronomical observations.