### moving-cluster method

(method of measuring distance to a nearby star cluster)

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. If they are moving away from that point, the method
works on the assumption that
they are moving in a direction parallel to our line of sight toward that point.
This is analogous to the fact that the direction at which
we see the apparent meeting point of the rails of a straight railroad
track is virtually parallel to the direction of the rails.
Given this determination of their direction of motion, the ratio of the
transverse velocity and radial velocity can be worked out,
the radial velocity can be measured by Doppler shift, and the
transverse velocity can be deduced. By knowing this actual 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". I've also seen reference
to *convergent point method* as a means to determine which stars
are in a cluster; basically, their velocity appears similar and
they do have such a convergent point.

The moving cluster method's accuracy is improved by probability
analysis of measurements of numerous stars in the cluster, in light
of random measurement errors and of the stars' individual
peculiar velocities.
The method lost favor as other distance-determination methods
improved, such as with the modern precise astrometry of Hipparcos.
However, it has more recently sparked interest because the improvement
in astrometry also improves this method's results.

(*measurement,star clusters,stars*)
**Further reading:**

http://en.wikipedia.org/wiki/Moving-cluster_method

https://ui.adsabs.harvard.edu/abs/2012A%26A...538A..23G/abstract

https://ui.adsabs.harvard.edu/abs/1950ApJ...112..225B/abstract

https://ui.adsabs.harvard.edu/abs/1999MNRAS.306..381D/abstract

Index