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

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

star cluster A star cluster is a group of stars held together by self-gravitation. Two main types of star clusters can be distinguished: globular clusters, tight groups of ten thousand to millions of old stars which are gravitationally bound; and open 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 The moving-cluster method is now largely superseded by other, usually more accurate distance measures.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 Proper motion is the astrometric measure of changes in the apparent places of stars or other celestial objects as they move relative to the center of mass of the Solar System. It is measured relative to the distant stars or a stable referenc ...

s and

Doppler shift The Doppler effect (also Doppler shift) is the change in the frequency of a wave in relation to an observer who is moving relative to the source of the wave. The ''Doppler effect'' is named after the physicist Christian Doppler, who described t ...

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 (geometry), point on the projection plane, image plane of a graphical perspective, perspective rendering where the two-dimensional perspective projections of parallel (geometry), parallel lines in three-dimensional ...

") 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, and ...

) 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 of a target with respect to an observer is the rate of change of the vector displacement between the two points. It is formulated as the vector projection of the target-observer relative 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, 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 and distances of ...

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

Pleiades The Pleiades (), also known as Seven Sisters and Messier 45 (M45), is an Asterism (astronomy), asterism of an open cluster, open star cluster containing young Stellar classification#Class B, B-type stars in the northwest of the constellation Tau ...

. 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 are substellar objects that have more mass than the biggest gas giant planets, but less than the least massive main sequence, main-sequence stars. Their mass is approximately 13 to 80 Jupiter mass, times that of Jupiter ()not big en ...

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.

References

{{DEFAULTSORT:Moving Cluster Method Astrometry Galactic astronomy

Introduction

Usage

See also

References