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According to the statistical law of large numbers, the expected mean ofidentically distributed random variables of a sample tends toward the actualmean as the sample increases. Under this law, it is possible to test theChandrasekhar's relation (CR), <V>=(\pi/4)^{-1}<Vsini>, using a large amount of<Vsini> and V data from different samples of similar stars. In this context, weconducted a statistical test to check the consistency of the CR in the Keplerfield. In order to achieve this, we use three large samples of V obtained fromKepler rotation periods and a homogeneous control sample of <Vsini> to overcomethe scarcity of <Vsini> data for stars in the Kepler field. We used thebootstrap-resampling method to estimate the mean rotations (<V> and <Vsini>)and their corresponding confidence intervals for the stars segregated byeffective temperature. Then, we compared the estimated means to check theconsistency of CR, and analyzed the influence of the uncertainties in radiimeasurements, and possible selection effects. We found that the CR with<Vsini>=\pi/4 is consistent with the behavior of the <V> as a function of<Vsini> for stars from the Kepler field as there is a very good agreementbetween such a relation and the data.

Chandrasekhar's relation and the stellar rotation in the Kepler field