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 clusters. 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 The moving-cluster method is now largely superseded by other, usually more accurate distance measures.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 motions 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
space velocity, they will appear to move towards a point of common convergence ("
vanishing point
A vanishing point is a point on the image plane of a perspective drawing where the two-dimensional perspective projections of mutually parallel lines in three-dimensional space appear to converge. When the set of parallel lines is perpendicul ...
") on the sky. This is essentially a
perspective effect.
Using the moving-cluster method, the distance to a given star cluster (in
parsecs) can be determined using the following equation:
:
where "θ" is the angle between the star and the cluster's apparent convergence point, "μ" is the proper motion of the cluster (in
arcsec/year), and "v" is the star's
radial velocity (in
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
The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to or (au), i.e. . The parsec unit is obtained by the use of parallax and trigonometry, an ...
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 and the
Pleiades
The Pleiades (), also known as The Seven Sisters, Messier 45 and other names by different cultures, is an asterism and an open star cluster containing middle-aged, hot B-type stars in the north-west of the constellation Taurus. At a distance ...
. 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
Brown dwarfs (also called failed stars) are substellar objects that are not massive enough to sustain nuclear fusion of ordinary hydrogen ( 1H) into helium in their cores, unlike a main-sequence star. Instead, they have a mass between the most ...
2M1207
2M1207, 2M1207A or 2MASSW J12073346–3932539 is a brown dwarf located in the constellation Centaurus; a companion object, 2M1207b, may be the first exoplanet, extrasolar planetary-mass object, planetary-mass companion to be directly image ...
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.
See also
*
Astrometry
*
Parallax
*
Parallax in astronomy
The most important fundamental distance measurements in astronomy come from trigonometric parallax. As the Earth orbits the Sun, the position of nearby stars will appear to shift slightly against the more distant background. These shifts are ang ...
*
Stellar parallax
*
Cepheid Stars
*
RR Lyrae Variable Stars
References
Astrometry
Galactic astronomy
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