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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 parsecparsec
[parallax + second], in astronomy, basic unit of length for measuring interstellar and intergalactic distances, equal to 206,265 times the distance from the earth to the sun, 3.26 light-years, or 3.08 × 1013 km (about 19 million million mi).
..... Click the link for more information. ; 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 spectrumspectrum,
arrangement or display of light or other form of radiation separated according to wavelength, frequency, energy, or some other property. Beams of charged particles can be separated into a spectrum according to mass in a mass spectrometer (see mass spectrograph).
..... Click the link for more information. , its position on the Hertzsprung-Russell diagramHertzsprung-Russell diagram
[for Ejnar Hertzsprung and H. N. Russell], graph showing the luminosity of a star as a function of its surface temperature. The luminosity, or absolute magnitude, increases upwards on the vertical axis; the temperature (or some temperature-dependent
..... Click the link for more information. is determined. This diagram correlates the spectral classspectral class,
in astronomy, a classification of the stars by their spectrum and luminosity. In 1885, E. C. Pickering began the first extensive attempt to classify the stars spectroscopically.
..... Click the link for more information. of the star with its absolute magnitudemagnitude,
in astronomy, measure of the brightness of a star or other celestial object. The stars cataloged by Ptolemy (2d cent. A.D.), all visible with the unaided eye, were ranked on a brightness scale such that the brightest stars were of 1st magnitude and the dimmest stars
..... Click the link for more information. . 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 starbinary star
or binary system,
pair of stars that are held together by their mutual gravitational attraction and revolve about their common center of mass. In 1650 Riccioli made the first binary system discovery, that of the middle star in the Big Dipper's handle, Zeta
..... Click the link for more information. . The angular diameter of the orbit of the stars around each other and their apparent brightness are observed. By applying Kepler's lawsKepler's laws,
three mathematical statements formulated by the German astronomer Johannes Kepler that accurately describe the revolutions of the planets around the sun. Kepler's laws opened the way for the development of celestial mechanics, i.e.
..... Click the link for more information. and the mass-luminosity relationmass-luminosity relation,
in astronomy, law stating that the luminosity of a star is proportional to some power of the mass of the star. More massive stars are in general more luminous.
..... Click the link for more information. , 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.
parallax(pa -ră-laks) The angular displacement in the apparent position of a celestial body when observed from two widely separated points. It is thus the angle that the baseline connecting two viewpoints would subtend at the object (see illustration). It is very small in value and is usually expressed in arc seconds. If the baseline is of a fixed length then as the distance to the celestial object decreases, its parallax will increase accordingly. If the parallax can be measured then so can the distance.
The observer's position on Earth changes with the daily rotation of the Earth, the annual revolution of the Earth around the Sun, and the long-term motion of the Sun and Solar System relative to the background stars. Each motion produces a different measure of parallax: diurnal parallax, annual parallax, and secular parallax, respectively. The continual change in the apparent position of a celestial object, produced by the observer's changing position, is termed parallactic motion and must be distinguished from the star's own peculiar motion in space.
Methods used to determine the parallax and hence the distance of celestial bodies require an accurate knowledge of the baseline length. The baseline for diurnal parallax – the Earth's radius – can be used for distance measurements only within the Solar System. The baselines used in annual parallax – the semimajor axis of the Earth's orbit – and secular parallax are sufficiently great for stellar distances to be measured. Other methods based on the concept of parallax and used in distance determination include dynamical parallax, moving-cluster parallax, and statistical parallax.
Distances determined indirectly from stellar brightness are also sometimes called parallaxes: in spectroscopic parallax the absolute magnitude of a main-sequence star is deduced from the spectral type of the star using the Hertzsprung–Russell diagram and this together with the apparent magnitude gives the distance modulus and hence the distance. See also distance determination.
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
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.
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.
REFERENCEParenago, P. P. Kurs zvezdnoi astronomii [3rd ed.]. Moscow, 1954.
N. P. ERPYLEV
ii. The difference in the direction of a celestial object as seen by an observer from two widely separated points. The measurement of parallax is used directly to find the distance of the body from the earth and from the sun.
iii. The phenomenon in radar imagery when a tall object is imaged and the top of the object is nearer the aircraft. In this case, the slant range to the top of the object is less than that to the base. The object appears to lie toward the aircraft flight path. This is known as radar parallax.