In the present study, the Lomb–Scargle Scargle (L–S) method was employed for the analysis of brightness measurements from multiple observatories as published in the Minor Planet Center (MPC) circulars, as well as brightness measurements from the Baldone Observatory, to determine the periods of asteroids. The periods of fifteen asteroids were determined. The research yielded results for both asteroids with previously known periods and those without listed periods in the ALCDEF lightcurve database. The results revealed the potential for this approach to be used in the subsequent identification of yet-unknown periods of asteroids. This was demonstrated by the confirmation of periods for four of the five asteroids with known periods from the ALCDEF lightcurve database, namely 1951, 1963, 2134 and 2150. In the case of the fifth asteroid, 2174, for which a previously determined rotation period had been provided, an additional, possible shorter rotation period was identified. As has been shown, the use of the L–S method in conjunction with independent analysis of many series of brightness measurements from different observatories is a suitable approach, even for a small series of samples of brightness observations unevenly spread over a long time, for the determination of periods. Furthermore, this approach is effective even when there are significant intervals between measurements, which is not the case with the classical Fourier method. Additionally, the exclusion of observations that deviate significantly from the linear relationship of the phase diagram, by the three-sigma criterion, markedly enhanced the efficacy and precision of the method. As a result, periods were identified for the first time for asteroids 1779, 1818, 2128, 2318, 2497, 2503, 2538, 2539, and 2583.
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