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The moving cluster method is a method of determining the distance to a group of stars that are moving at the same velocity and are sufficiently close to us that their proper motion can be determined. Open clusters are so-grouped and generally moving as a group, so this applies to them if they are not too distant.
The method consists of determining a convergent point, a point in the celestial sphere to or from which the stars appear to be moving. The method uses the fact that a line between us and that convergent point is virtually parallel to the stars' direction of motion. This is analogous to the situation of a nearby straight railroad track: the direction of a point on the horizon where the rails appear to meet is virtually parallel to the track, and a train on the track appears to be moving toward or away from that point. Given this determination of the stars' direction of motion, the ratio of their transverse velocities and radial velocities can be worked out, and with the radial velocity measured by Doppler shift, the transverse velocity can be calculated. From this determined transverse velocity and the measured proper motion, the distance can be determined.
I've seen the phrase convergent point method described as synonymous, but one source calls them "closely related" and I've seen convergent point method described as a means to determine which stars are in a cluster; basically, their velocity appears similar and they have such a convergent point.
The moving cluster method's accuracy is improved by probability analysis of measurements of numerous stars in the cluster, given random measurement errors and the stars' individual peculiar velocities. The method lost favor as other distance-determination methods improved, such as parallax using the modern precise astrometry of Hipparcos. However, it has more recently sparked some interest because the improvement in astrometry also improves this method's results.