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{{Refimprove|date=December 2009}}
In [[astrometry]], the '''moving-cluster method''' and the closely related convergent point method are means, primarily of historical interest, for determining the distance to [[star cluster]]s. They were used on several nearby clusters in the first half of the 1900s to determine distance. The moving-cluster method is now largely superseded by other, usually more accurate distance measures.

==Introduction==
The moving-cluster method relies on observing the [[proper motion]]s and [[Doppler shift]] of each member of a group of stars known to form a cluster. The idea is that since all the stars share a common [[Stellar_kinematics#Space_velocity|space velocity]], they will appear to move towards a point of common convergence ("[[vanishing point]]") on the sky. This is essentially a [[perspective (visual)|perspective]] effect.

Using the moving-cluster method, the distance to a given star cluster (in [[parsec|parsecs]]) can be determined using the following equation:
:<math>\mathrm{distance} = \mathrm{tan}(\theta) \frac {\mathrm{v}} {\mathrm{\mu}}</math>
where "θ" is the angle between the star and the cluster's apparent convergence point, "μ" is the proper motion of the cluster (in [[Minute_and_second_of_arc|arcsec]]/year), and "v" is the star's [[radial velocity]] (in [[Astronomical_unit|AU]]/year).

==Usage==
The method has only ever been used for a small number of clusters. This is because for the method to work, the cluster must be quite close to Earth (within a few hundred [[parsec]]s), and also be fairly tightly bound so it can be made out on the sky. Also, the method is quite difficult to work with compared with more straightforward methods like trigonometric parallax. Finally, the uncertainty in the final distance values are in general fairly large compared those obtained with precision measurements like those from [[Hipparcos]].

Of the clusters it has been used with, certainly the most famous are the [[Hyades (star cluster)|Hyades]] and the [[Pleiades]]. The moving-cluster method was in fact the only way astronomers had to measure the distance to these clusters with any precision for some time in the early 20th century.

Because of the problems outlined above, this method has not been used practically for stars for several decades in astronomical research.

However, recently it has been used to estimate the distance between the [[brown dwarf]] [[2M1207]] and its observed exoplanet [[2M1207b]]. In December 2005, American astronomer Eric Mamajek reported a distance (53 ± 6 parsecs) to 2M1207b using the moving-cluster method.<ref>{{cite journal | bibcode=2005ApJ...634.1385M | author=Mamajek| title= A Moving Cluster Distance to the Exoplanet 2M1207b in the TW Hydrae Association | journal= The Astrophysical Journal| volume=634 | issue=2 | year=2005 | pages=1385–1394| doi= 10.1086/468181 |arxiv = astro-ph/0507416 | s2cid=17162407}}</ref>

==See also==
* [[Astrometry]]
* [[Parallax]]
* [[Parallax in astronomy]]
* [[Stellar parallax]]
* [[Cepheid|Cepheid Stars]]
* [[RR_Lyrae_variable|RR Lyrae Variable Stars]]

== References ==
{{Reflist}}

{{DEFAULTSORT:Moving Cluster Method}}
[[Category:Astrometry]]
[[Category:Galactic astronomy]]

Moving-cluster method - Revision history

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