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radial velocity(ray -dee-ăl) (line-of-sight velocity) Symbol: v r. The velocity of a star along the line of sight of an observer. It is calculated directly from the doppler shift (see Doppler effect) in the lines of the star's spectrum: if the star is receding there will be a redshift in its spectral lines and the radial velocity will be positive; an approaching star will produce a blueshift and the velocity will be negative. Most stars have values lying between +40 and –40 km s–1. Radial velocity is usually given in terms of the Sun's position so that the Earth's orbital motion has no effect.
The velocity and direction of motion of the Sun relative to the local standard of rest can be determined from a statistical analysis of the observed radial velocities of nearby stars: stars in the region of the solar apex have predominantly positive velocities while those around the antapex have predominantly negative ones.
A star's velocity in space relative to the Sun – its space velocity – is a vector quantity and can be split into two components: its radial velocity and its tangential velocity, v t, along the direction of proper motion. Measurements of these components give both the magnitude, V , and direction, θ, of the star's space velocity (see illustration).
(in astronomy), line-of-sight velocity, the projection of the velocity of a star or other celestial object on the direction from the object to the observer, that is, along the line of sight. The Doppler effect, whose applicability to light waves was demonstrated in 1900 by A. A. Belopol’skii, is used in determining the radial velocity. According to this effect, the wavelength of light emitted or absorbed by a moving body increases or decreases depending on whether the body is receding from or approaching the observer. If the wavelength emitted by a source of light that is stationary relative to the observer is λo and that emitted by a moving source is λ, then the difference λ — λ0 depends on the velocity v of the source relative to the observer according to the following formula, which takes relativistic effects into account:
where c is the velocity of light. When v is much less than c, this equation can be written in the approximate form
Since stellar velocities in our galaxy do not exceed several hundred kilometers per second, this approximate formula is used in studying the motions of stars. The exact formula is used, for example, in studying the velocity of matter ejected from stars.
The radial velocity is determined by measuring the difference between the wavelengths of emission or absorption lines in the spectrum of the celestial object and the wavelengths in the spectrum of a stationary laboratory source of light. The line shifts are small for ordinary stellar velocities. Thus the difference λ — λ0 for λ0 = 4,500 Å amounts to 0.15 Å for a radial velocity of 10 km/sec. The difference in the position of the lines on the spectrogram amounts to only about 0.004 mm if the dispersion of the spectrograph used is 40 Å/mm. Therefore, in order to measure accurately the radial velocity it is necessary to have a specially constructed apparatus that minimizes instrumental and other errors.
Radial velocities of stars have been determined for many years at a number of observatories equipped with large telescopes, including those in the USSR (at the Crimean Astrophysical Observatory of the Academy of Sciences of the USSR). Measurements of the radial velocities of stars in galaxies have made it possible to detect the rotation of galaxies and to determine the kinematic characteristics of the rotation of galaxies, including our own. Periodic variations in the radial velocity of some stars led to the detection of the orbital motion of these stars in binary and multiple systems and, when the angular dimensions of the orbit are known, also led to the determination of the linear dimensions of the orbit and the distance to the star. Periodic variations in the radial velocity are sometimes explained by the pulsation of the outer layers of the star. In a number of cases, a difference in the radial velocities determined from spectral lines originating in different atmospheric layers of the star makes it possible to study the motion of stellar matter. A common radial velocity for a group of stars permits us to identify the group as a cluster of genetically related stars, which is of great importance for studying stellar evolution.
REFERENCEKurs astrofiziki i zvezdnoi astronomii, vol. 1. Moscow-Leningrad, 1951. Chapters 18-21.
V. L. KHOKHLOVA