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Local objects are usually related in terms of proper motion and radial velocity, that is the amount an object appears to move across the sphere of the sky, and the measured speed at which it travels towards or away from us, respectively. Proper motion and radial velocity can be combined through vector addition to produce the object's motion relative to the Sun. For "peculiar" motion, the rest frame used is not usually the Sun but the local standard of rest (LSR), the average local motion of material in the galaxy. Translating between the LSR and heliocentric rest frames requires the calculation of the Sun's peculiar velocity in the LSR.
According to Hubble's law, galaxies recede from us at a speed proportional to their distance. The relationship between speed and distance would be exact in the absence of other effects.
Galaxies are not distributed evenly throughout observable space, but typically found in groups or clusters, ranging in size from fewer than a dozen to several thousands. All these nearby galaxies have a gravitational effect, to the extent that any one galaxy can have a velocity of over 1,000 km/s in an apparently random direction. This velocity can therefore add to, or subtract from, the radial velocity that one would expect from the Hubble flow. This change in recessional velocity effects the observed redshift of objects via the Doppler effect. Redshift-space distortions can cause the spacial distributions to appear elongated or flattened out, depending on the cause of the peculiar velocities.
The main consequence is that, in determining the distance of a single galaxy, a possible error must be assumed. This error becomes smaller, relative to the total speed, as distance increases. An estimate can be refined by taking the average velocity of a group of galaxies.
- Schönrich, Ralph; Binney, James (2010). "Local kinematics and the local standard of rest". Monthly Notices of the Royal Astronomical Society. 403 (4): 1829–1833. arXiv: . Bibcode:2010MNRAS.403.1829S. doi:10.1111/j.1365-2966.2010.16253.x.
- Kaiser, N. (1 July 1987). "Clustering in real space and in redshift space". Monthly Notices of the Royal Astronomical Society. 227 (1): 1–21. doi:10.1093/mnras/227.1.1.