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The most accurate current methods for determining the ages of open starclusters, stellar associations and stellar streams are based on isochronefitting or the lithium depletion boundary. We propose another method for datingthese objects based on the morphology of their extended tidal tails, which havebeen recently discovered around several open star clusters. Assuming that theearly-appearing tidal tails, the so called tidal tails I, originate from thestars released from the cluster during early gas expulsion, or that they formin the same star forming region as the cluster (i.e. being coeval with thecluster), we derive the analytical formula for the tilt angle $\beta$ betweenthe long axis of the tidal tail and the orbital direction for clusters orstreams on circular trajectories. Since at a given Galactocentric radius,$\beta$ is only a function of age $t$ regardless of the initial properties ofthe cluster, we estimate the cluster age by inverting the analytical formula$\beta = \beta (t)$. We illustrate the method on a sample of $12$ objects,which we compiled from the literature, and we find a reasonable agreement withprevious dating methods in $\approx 70$% of the cases. This can probably beimproved by taking into account the eccentricity of the orbits and byrevisiting the dating methods based on stellar evolution. The proposedmorphological method is suitable for relatively young clusters (age $\lesssim300$ Myr), where it provides a relative age error of the order of $10$ to $20$%for an error in the observed tilt angle of $5 ^\circ$.

Estimating the ages of open star clusters from properties of their extended tidal tails