CE5The trigonometric parallax of a star, expressed by the angle θ, is a measure of its apparent motion against the background of more distant stars as a result of the earth's motions in its orbit around the sun. Measurements are made at two points six months apart.
parallax [key], any alteration in the relative apparent positions of objects produced by a shift in the position of the observer. In astronomy the term is used for several techniques for determining distance. Trigonometric parallax is the apparent displacement of a nearby star against the background of more distant stars resulting from the motion of the earth in its orbit around the sun. Formally, the parallax of a star is the angle at the star that is subtended by the mean distance between the earth and the sun. A shift in the angular position of a star will be greatest when observed at intervals of six months (see accompanying diagram); this makes the parallax equal to the value of one half of the semiannual displacement of the star. If a star's parallax can be measured, it then determines the distance to the star. A unit of stellar measurement is the parsec; it is the distance at which a star would have a parallax of one second of arc and is equivalent to 206,265 times the distance from the earth to the sun, or about 3.3 light-years. A star's distance d in parsecs is the reciprocal of its parallax p (or d = 1/p). The first stellar parallax was measured in 1838 by Friedrich Bessel for the star 61 Cygni. Its parallax of 0.3 places it at a distance of 3.3 parsecs or about 11 light-years. The technique of stellar parallax is useful for stars within 100 parsecs. Spectroscopic parallax is the most widely used technique for determining the distances of stars that are too distant for their stellar parallaxes to be measured. From the analysis of a star's spectrum, its position on the Hertzsprung-Russell diagram is determined. This diagram correlates the spectral class of the star with its absolute magnitude. By comparing the absolute magnitude to its apparent brightness, the star's distance is calculated. Dynamical parallax is a method for determining the distance to a visual binary star. The angular diameter of the orbit of the stars around each other and their apparent brightness are observed. By applying Kepler's laws and the mass-luminosity relation, the distance of the binary star can be determined. Geocentric parallax is a technique similar to stellar parallax, which uses the diameter of the earth rather than the diameter of its orbit as a baseline. Because this baseline is relatively small, the technique is useful only for close celestial objects such as the moon or the asteroids.
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