astrometry Astrometry is a branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. It provides the kinematics and physical origin of the Solar System and this galaxy, the Milky Way. His ...

, the moving-cluster method and the closely related convergent point method are means, primarily of historical interest, for determining the distance to

star cluster Star clusters are large groups of stars. Two main types of star clusters can be distinguished: globular clusters are tight groups of ten thousand to millions of old stars which are gravitationally bound, while open clusters are more loosely clust ...

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 The moving-cluster method is now largely superseded by other, usually more accurate distance measures.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 Proper motion is the astrometric measure of the observed changes in the apparent places of stars or other celestial objects in the sky, as seen from the center of mass of the Solar System, compared to the abstract background of the more dista ...

s and

Doppler shift The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who d ...

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 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 ...

) can be determined using the following equation: :

\mathrm = \mathrm(\theta) \frac

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 The radial velocity or line-of-sight velocity, also known as radial speed or range rate, of a target with respect to an observer is the temporal rate of change, rate of change of the distance or Slant range, range between the two points. It is e ...

(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, and ...

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 ''Hipparcos'' was a scientific satellite of the European Space Agency (ESA), launched in 1989 and operated until 1993. It was the first space experiment devoted to precision astrometry, the accurate measurement of the positions of celestial obj ...

. Of the clusters it has been used with, certainly the most famous are the

Hyades Hyades may refer to: * Hyades (band) *Hyades (mythology) *Hyades (star cluster) The Hyades (; Greek Ὑάδες, also known as Caldwell 41, Collinder 50, or Melotte 25) is the nearest open cluster and one of the best-studied star clusters. Loca ...

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 of ...

. 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 extrasolar planetary-mass companion to be directly imaged, and is the first discovered ...

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.

References

Astrometry Galactic astronomy {{Astronomy-stub

Introduction

Usage

See also

References