Editing Open cluster (section)

==Astronomical distance scale==
[[File:Messier11.jpg|left|thumb|[[Wild Duck Cluster|M11]], also known as 'the Wild Duck Cluster', is a very rich cluster located towards the center of the [[Milky Way]].]]

Determining the distances to astronomical objects is crucial to understanding them, but the vast majority of objects are too far away for their distances to be directly determined. Calibration of the [[cosmic distance ladder|astronomical distance scale]] relies on a sequence of indirect and sometimes uncertain measurements relating the closest objects, for which distances can be directly measured, to increasingly distant objects.<ref name=keel09/> Open clusters are a crucial step in this sequence.

The closest open clusters can have their distance measured directly by one of two methods. First, the [[parallax]] (the small change in apparent position over the course of a year caused by the Earth moving from one side of its orbit around the Sun to the other) of stars in close open clusters can be measured, like other individual stars. Clusters such as the Pleiades, Hyades and a few others within about 500&nbsp;light years are close enough for this method to be viable, and results from the [[Hipparcos]] position-measuring satellite yielded accurate distances for several clusters.<ref name=rmaa11/><ref name=aaa400/>

The other direct method is the so-called [[moving cluster method]]. This relies on the fact that the stars of a cluster share a common motion through space. Measuring the proper motions of cluster members and plotting their apparent motions across the sky will reveal that they converge on a [[vanishing point]]. The radial velocity of cluster members can be determined from [[Doppler shift]] measurements of their [[electromagnetic spectrum|spectra]], and once the radial velocity, proper motion and angular distance from the cluster to its vanishing point are known, simple [[trigonometry]] will reveal the distance to the cluster. The [[Hyades (star cluster)|Hyades]] are the best-known application of this method, which reveals their distance to be 46.3&nbsp;[[parsec]]s.<ref name=aj80/>

Once the distances to nearby clusters have been established, further techniques can extend the distance scale to more distant clusters. By matching the [[main sequence]] on the Hertzsprung–Russell diagram for a cluster at a known distance with that of a more distant cluster, the distance to the more distant cluster can be estimated. The nearest open cluster is the Hyades: The stellar association consisting of most of the [[Ursa Major Moving Group|Plough stars]] is at about half the distance of the Hyades, but is a stellar association rather than an open cluster as the stars are not gravitationally bound to each other. The most distant known open cluster in our galaxy is [[Berkeley 29]], at a distance of about 15,000&nbsp;parsecs.<ref name=aaa429/> Open clusters, especially [[super star clusters]], are also easily detected in many of the galaxies of the [[Local Group]] and nearby: e.g., [[NGC 346]] and the SSCs [[R136]] and [[NGC 1569|NGC 1569 A and B]].

Accurate knowledge of open cluster distances is vital for calibrating the period–luminosity relationship shown by [[variable star]]s such as [[Cepheid]] stars, which allows them to be used as [[standard candle]]s. These luminous stars can be detected at great distances, and are then used to extend the distance scale to nearby galaxies in the Local Group.<ref name=ssr48_1_2/> Indeed, the open cluster designated NGC 7790 hosts three [[classical Cepheids]].<ref name=sa1958>Sandage, Allan (1958). [http://adsabs.harvard.edu/abs/1958ApJ...128..150S ''Cepheids in Galactic Clusters. I. CF Cass in NGC 7790.''], AJ, 128</ref><ref name=ma2013>Majaess, D.; Carraro, G.; Moni Bidin, C.; Bonatto, C.; Berdnikov, L.; Balam, D.; Moyano, M.; Gallo, L.; Turner, D.; Lane, D.; Gieren, W.; Borissova, J.; Kovtyukh, V.; Beletsky, Y. (2013). [http://adsabs.harvard.edu/abs/2013A%26A...560A..22M ''Anchors for the cosmic distance scale: the Cepheids U Sagittarii, CF Cassiopeiae, and CEab Cassiopeiae''], A&A, 260</ref>  [[RR Lyrae variables]] are too old to be associated with open clusters, and are instead found in [[globular clusters]].