Parallax (redirected from parallactic)

parallax (pâr`əlăks), 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; 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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parallax

Difference in the direction of a celestial object as seen by observers from two widely separated points, a measurement used to find a body's distance. The two positions of the observers and that of the object form a triangle; its apex angle (at the object) is twice the parallax, which becomes smaller with increasing distance. Observations for calculating the Sun's parallax can be made simultaneously from two different places on Earth's surface; that value reaches a maximum of 8.794 seconds of arc for observers at points separated by Earth's diameter. Observing the difference in an object's position as seen from Earth at points six months apart in its orbit (stellar, or annual, parallax) allows measurements of distances (e.g., of stars) too large to be made from two places on Earth's surface. The nearest star system, Alpha Centauri, has a stellar parallax of 0.76 second of arc. Highly precise parallaxes, and thus the positions, of more than 100,000 stars in the Sun's vicinity were determined from data collected by the European Space Agency's Hipparcos satellite (launched 1989).

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parallax

1. an apparent change in the position of an object resulting from a change in position of the observer

2. Astronomy the angle subtended at a celestial body, esp a star, by the radius of the earth's orbit. Annual or heliocentric parallax is the apparent displacement of a nearby star resulting from its observation from the earth. Diurnal or geocentric parallax results from the observation of a planet, the sun, or the moon from the surface of the earth

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parallax [′par·ə‚laks]

(optics)

The change in the apparent relative orientations of objects when viewed from different positions.

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Parallax 

the apparent change in the relative position of an object as a result of movement of the observer’s eye. Parallax can cause errors in the reading of a scale that is not in direct contact with an object whose length is being measured or whose position

Figure 1

is being determined (see Figure 1). In optical instruments, such as telescopes or microscopes, parallax results from the observer’s eye movement in front of the eyepiece when the graticule or cross hair used for measurement is not in the same plane as the image produced by the objective. The concept of parallax plays an important role in astronomy.

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Parallax 

in astronomy, the apparent displacement of bodies on the celestial sphere as a result of the movement of the observer in space. The earth’s rotation about its axis is the cause of diurnal parallax, the earth’s revolution about the sun is responsible for annual parallax, and the solar system’s motion in the Galaxy causes secular parallax. Given accurate measurements of the parallactic shifts of celestial bodies or groups of bodies, the bodies’ distances can be determined.

Diurnal parallax. The diurnal parallax of a celestial body is the angle whose vertex is at the center of the body and whose sides are directed toward the earth’s center and the observer’s location on the earth’s surface. The magnitude of the diurnal parallax depends on the zenith distance of the celestial body and varies with a period of 24 hours. The parallax of a body located on the horizon of the observer is called the horizontal parallax; if the observer is on the equator, the horizontal parallax is referred to as the equatorial horizontal parallax and is constant for bodies located at a constant distance from the earth. The relation between the equatorial horizontal parallax p₀ of a celestial body and the body’s geocentric distance r is given by the formula

where R is the radius of the earth’s equator. The distance to the sun, moon, or other bodies within the solar system can be expressed in terms of the body’s equatorial horizontal parallax. Thus, the value 8.79” is taken for the mean distance to the sun, and 57’ 2.6” is taken for the mean distance to the moon. Because the stars are very distant from the earth, diurnal parallax has practically no effect on their positions.

Annual parallax. The annual parallax of a celestial body is the small angle in the right triangle whose hypotenuse is the distance from the sun to the star and whose small leg is the semimajor axis of the earth’s orbit. Annual parallax can be used to determine the distances to stars. Because they are very small, these parallaxes can be regarded as inversely proportional to the distances to the stars; a parallax of 1 “corresponds to a distance of one parsec. The parallax of the nearest star, Proxima Centauri, is 0.76”. Parallaxes determined from the direct measurement of the apparent displacements of stars against a background of considerably more distant stars are called trigonometric. Because of their small value, trigonometric parallaxes have been successfully measured for only the nearest stars. The comparison, however, of the stars’ absolute magnitudes, which can be computed from the stars’ parallaxes, with certain properties of the stars’ spectra has permitted the discovery of relationships that can be used to estimate the distances to other, more remote stars, for which trigonometric parallaxes cannot be determined. Parallaxes computed in this way are called spectroscopic parallaxes.

Secular parallax. The secular parallax of a star is the star’s angular displacement in a year as a result of the motion of the solar system; the displacement is relative to a direction perpendicular to this motion. In contrast to diurnal and annual parallaxes, which are connected with periodic shifts of stars on the celestial sphere, secular parallax is determined by a parallactic shift that increases continuously over time. Because of the proper motions of the stars, secular parallaxes can be determined only statistically, that is, with respect to a sufficiently large group of stars; the peculiar motions of the stars in the group are assumed to average zero. Secular parallaxes are made use of in stellar astronomy, since they permit the estimation of distances that are considerably larger than the distances that can be obtained by measurements of annual parallaxes. The distances corresponding to secular parallaxes, however, are only averages that hold for the entire group of stars involved in the measurements; the distances may differ considerably from the actual distances for individual stars.

REFERENCE

Parenago, P. P. Kurs zvezdnoi astronomii [3rd ed.]. Moscow, 1954.

N. P. ERPYLEV