SUPPORT THE WORK

# GetWiki

### parallax

ARTICLE SUBJECTS
news  →
unix  →
wiki  →
ARTICLE TYPES
feed  →
help  →
wiki  →
ARTICLE ORIGINS
parallax
[ temporary import ]
- the content below is remote from Wikipedia
- it has been imported raw for GetWiki
{{other uses}}(File:Parallax Example.svg|thumb|300px|right|A simplified illustration of the parallax of an object against a distant background due to a perspective shift. When viewed from "Viewpoint A", the object appears to be in front of the blue square. When the viewpoint is changed to "Viewpoint B", the object appears to have moved in front of the red square.)(File:Parallax.gif|thumb|300px|right|This animation is an example of parallax. As the viewpoint moves side to side, the objects in the distance appear to move more slowly than the objects close to the camera. In this case, the blue cube in front appears to move faster than the red cube.)Parallax ({{etymology|grc|Ï€Î±ÏÎ¬Î»Î»Î±Î¾Î¹Ï‚ (parallaxis)|alternation}}) is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines.DICTIONARY, Mutual inclination of two lines meeting in an angle, Shorter Oxford English Dictionary, 1968, DICTIONARY, Oxford English Dictionary, 1989, Second, Parallax, Astron. Apparent displacement, or difference in the apparent position, of an object, caused by actual change (or difference) of position of the point of observation; spec. the angular amount of such displacement or difference of position, being the angle contained between the two straight lines drawn to the object from the two different points of view, and constituting a measure of the distance of the object.,weblink Due to foreshortening, nearby objects show a larger parallax than farther objects when observed from different positions, so parallax can be used to determine distances.To measure large distances, such as the distance of a planet or a star from Earth, astronomers use the principle of parallax. Here, the term parallax is the semi-angle of inclination between two sight-lines to the star, as observed when Earth is on opposite sides of the Sun in its orbit.In the past diurnal parallax was also used to measure distances to celestial objects within the Solar System. This method has now been superseded by more accurate techniques. These distances form the lowest rung of what is called "the cosmic distance ladder", the first in a succession of methods by which astronomers determine the distances to celestial objects, serving as a basis for other distance measurements in astronomy forming the higher rungs of the ladder.Parallax also affects optical instruments such as rifle scopes, binoculars, microscopes, and twin-lens reflex cameras that view objects from slightly different angles. Many animals, including humans, have two eyes with overlapping visual fields that use parallax to gain depth perception; this process is known as stereopsis. In computer vision the effect is used for computer stereo vision, and there is a device called a parallax rangefinder that uses it to find range, and in some variations also altitude to a target.A simple everyday example of parallax can be seen in the dashboard of motor vehicles that use a needle-style speedometer gauge. When viewed from directly in front, the speed may show exactly 60; but when viewed from the passenger seat the needle may appear to show a slightly different speed, due to the angle of viewing.

## Visual perception

As the eyes of humans and other animals are in different positions on the head, they present different views simultaneously. This is the basis of stereopsis, the process by which the brain exploits the parallax due to the different views from the eye to gain depth perception and estimate distances to objects.BOOK, Steinman, Scott B., Garzia, Ralph Philip, 2000, Foundations of Binocular Vision: A Clinical perspective, McGraw-Hill Professional, 978-0-8385-2670-5, 2â€“5, harv, Animals also use motion parallax, in which the animals (or just the head) move to gain different viewpoints. For example, pigeons (whose eyes do not have overlapping fields of view and thus cannot use stereopsis) bob their heads up and down to see depth.{{harvnb|Steinman|Garzia|2000|loc=p. 180}}.The motion parallax is exploited also in wiggle stereoscopy, computer graphics which provide depth cues through viewpoint-shifting animation rather than through binocular vision.

## Astronomy

(File:Parallax geo or helio static.PNG|thumb|300px|Parallax is an angle subtended by a line on a point. In the upper diagram, the earth in its orbit sweeps the parallax angle subtended on the sun. The lower diagram shows an equal angle swept by the sun in a geostatic model. A similar diagram can be drawn for a star except that the angle of parallax would be minuscule.)Parallax arises due to change in viewpoint occurring due to motion of the observer, of the observed, or of both. What is essential is relative motion. By observing parallax, measuring angles, and using geometry, one can determine distance. Astronomers also use the word "parallax" as a synonym for "distance measurement" by other methods: see parallax (disambiguation)#Astronomy.

### Stellar parallax

Stellar parallax created by the relative motion between the Earth and a star can be seen, in the Copernican model, as arising from the orbit of the Earth around the Sun: the star only appears to move relative to more distant objects in the sky. In a geostatic model, the movement of the star would have to be taken as real with the star oscillating across the sky with respect to the background stars.Stellar parallax is most often measured using annual parallax, defined as the difference in position of a star as seen from the Earth and Sun, i. e. the angle subtended at a star by the mean radius of the Earth's orbit around the Sun. The parsec (3.26 light-years) is defined as the distance for which the annual parallax is 1 arcsecond. Annual parallax is normally measured by observing the position of a star at different times of the year as the Earth moves through its orbit. Measurement of annual parallax was the first reliable way to determine the distances to the closest stars. The first successful measurements of stellar parallax were made by Friedrich Bessel in 1838 for the star 61 Cygni using a heliometer.{{harvnb|Zeilik|Gregory|1998 | loc=p. 44}}. Stellar parallax remains the standard for calibrating other measurement methods. Accurate calculations of distance based on stellar parallax require a measurement of the distance from the Earth to the Sun, now based on radar reflection off the surfaces of planets.{{harvnb|Zeilik|Gregory|1998|loc=Â§ 22-3}}.The angles involved in these calculations are very small and thus difficult to measure. The nearest star to the Sun (and thus the star with the largest parallax), Proxima Centauri, has a parallax of 0.7687 Â± 0.0003 arcsec.JOURNAL
, Benedict
, Interferometric Astrometry of Proxima Centauri and Barnard's Star Using Hubble Space Telescope Fine Guidance Sensor 3: Detection Limits for Substellar Companions
, The Astronomical Journal
, 1999, 118, 2, 1086â€“1100
, 1999AJ....118.1086B
, 10.1086/300975
, harv, astro-ph/9905318
, vanc
, G. Fritz
, 2
, Chappell
, D.W.
, Nelan
, E.
, Jefferys
, W.H.
, Van Altena
, W.
, Lee
, J.
, Cornell
, D.
, Shelus
, P.J., This angle is approximately that subtended by an object 2 centimeters in diameter located 5.3 kilometers away.

### Distance measurement

File:Stellarparallax2.svg|thumb|175px|right|Stellar parallaxStellar parallaxDistance measurement by parallax is a special case of the principle of triangulation, which states that one can solve for all the sides and angles in a network of triangles if, in addition to all the angles in the network, the length of at least one side has been measured. Thus, the careful measurement of the length of one baseline can fix the scale of an entire triangulation network. In parallax, the triangle is extremely long and narrow, and by measuring both its shortest side (the motion of the observer) and the small top angle (always less than 1 arcsecond, leaving the other two close to 90 degrees), the length of the long sides (in practice considered to be equal) can be determined.Assuming the angle is small (see derivation below), the distance to an object (measured in parsecs) is the reciprocal of the parallax (measured in arcseconds): d (mathrm{pc}) = 1 / p (mathrm{arcsec}). For example, the distance to Proxima Centauri is 1/0.7687={{convert|1.3009|pc|ly}}.

### Diurnal parallax

Diurnal parallax is a parallax that varies with rotation of the Earth or with difference of location on the Earth. The Moon and to a smaller extent the terrestrial planets or asteroids seen from different viewing positions on the Earth (at one given moment) can appear differently placed against the background of fixed stars.BOOK
, P. Kenneth, Seidelmann, 2005
, Explanatory Supplement to the Astronomical Almanac
, University Science Books, 123â€“125
, 978-1-891389-45-0
, BOOK
, Cesare, Barbieri, 2007
, Fundamentals of astronomy, 132â€“135
, CRC Press, 978-0-7503-0886-1,

### Lunar parallax

mathrm{distance}_{mathrm{moon}} = frac {mathrm{distance}_{mathrm{observerbase}}} {tan (mathrm{angle})}
(File:Lunarparallax 22 3 1988.png|thumb|right|Example of lunar parallax: Occultation of Pleiades by the Moon)This is the method referred to by Jules Verne in From the Earth to the Moon: Until then, many people had no idea how one could calculate the distance separating the Moon from the Earth. The circumstance was exploited to teach them that this distance was obtained by measuring the parallax of the Moon. If the word parallax appeared to amaze them, they were told that it was the angle subtended by two straight lines running from both ends of the Earth's radius to the Moon. If they had doubts on the perfection of this method, they were immediately shown that not only did this mean distance amount to a whole two hundred thirty-four thousand three hundred and forty-seven miles (94,330 leagues), but also that the astronomers were not in error by more than seventy miles (â‰ˆ 30 leagues).

### Dynamical or moving-cluster parallax

The open stellar cluster Hyades in Taurus extends over such a large part of the sky, 20 degrees, that the proper motions as derived from astrometry appear to converge with some precision to a perspective point north of Orion. Combining the observed apparent (angular) proper motion in seconds of arc with the also observed true (absolute) receding motion as witnessed by the Doppler redshift of the stellar spectral lines, allows estimation of the distance to the cluster (151 light-years) and its member stars in much the same way as using annual parallax.JOURNAL, 10.1086/307021, A Precision Test of Hipparcos Systematics toward the Hyades, 1999, Vijay K. Narayanan, Andrew Gould, The Astrophysical Journal, 515, 1, 256, harv, astro-ph/9808284, 1999ApJ...515..256N, Dynamical parallax has sometimes also been used to determine the distance to a supernova, when the optical wave front of the outburst is seen to propagate through the surrounding dust clouds at an apparent angular velocity, while its true propagation velocity is known to be the speed of light.JOURNAL, 10.1086/186164, Properties of the SN 1987A circumstellar ring and the distance to the Large Magellanic Cloud, 1991, Panagia, N., The Astrophysical Journal, 380, L23, 4, Gilmozzi, R., MacChetto, F., Adorf, H.-M., Kirshner, R.P., harv, 1991ApJ...380L..23P,

### Derivation

For a right triangle,
tan p = frac {1 text{ AU}} {d} ,
where p is the parallax, {{convert|1|AU|km | abbr=on | sigfig=4 }} is approximately the average distance from the Sun to Earth, and d is the distance to the star.Using small-angle approximations (valid when the angle is small compared to 1 radian),
tan x approx xtext{ radians} = x cdot frac {180} {pi} text{ degrees} = x cdot 180 cdot frac {3600} {pi} text{ arcseconds} ,
so the parallax, measured in arcseconds, is
p'' approx frac {1 text{ AU}} {d} cdot 180 cdot frac{3600} {pi} .
If the parallax is 1", then the distance is
d = 1 text{ AU} cdot 180 cdot frac {3600} {pi} approx 206,265 text{ AU} approx 3.2616 text{ ly} equiv 1 text{ parsec} .
This defines the parsec, a convenient unit for measuring distance using parallax. Therefore, the distance, measured in parsecs, is simply d = 1 / p, when the parallax is given in arcseconds.Similar derivations are in most astronomy textbooks. See, e.g., {{harvnb|Zeilik|Gregory|1998|loc=Â§ 11-1}}.

### Error

Precise parallax measurements of distance have an associated error. However this error in the measured parallax angle does not translate directly into an error for the distance, except for relatively small errors. The reason for this is that an error toward a smaller angle results in a greater error in distance than an error toward a larger angle.However, an approximation of the distance error can be computed by
delta d = delta left( {1 over p} right) =left| {partial over partial p} left( {1 over p} right) right| delta p ={delta p over p^2}
where d is the distance and p is the parallax. The approximation is far more accurate for parallax errors that are small relative to the parallax than for relatively large errors. For meaningful results in stellar astronomy, Dutch astronomer Floor van Leeuwen recommends that the parallax error be no more than 10% of the total parallax when computing this error estimate.BOOK, Floor, van Leeuwen, Hipparcos, the new reduction of the raw data, 350, Astrophysics and space science library, Springer, 2007, 978-1-4020-6341-1, 86,weblink no,weblink" title="web.archive.org/web/20150318002121weblink">weblink 2015-03-18,

### Spatio-temporal parallax

From enhanced relativistic positioning systems, spatio-temporal parallax generalizing the usual notion of parallax in space only has been developed. Then, eventfields in spacetime can be deduced directly without intermediate models of light bending by massive bodies such as the one used in the PPN formalism for instance.JOURNAL, Rubin, J.L., Relativistic Pentametric Coordinates from Relativistic Localizing Systems and the Projective Geometry of the Spacetime Manifold, Electronic Journal of Theoretical Physics, 2015, 12, 32, 83â€“112,weblink no,weblink" title="web.archive.org/web/20150208153753weblink">weblink 2015-02-08,

## {{Anchor|Parallax error}}Metrology

(File:Parallax pointer error.PNG|thumb|The correct line of sight needs to be used to avoid parallax error.)Measurements made by viewing the position of some marker relative to something to be measured are subject to parallax error if the marker is some distance away from the object of measurement and not viewed from the correct position. For example, if measuring the distance between two ticks on a line with a ruler marked on its top surface, the thickness of the ruler will separate its markings from the ticks. If viewed from a position not exactly perpendicular to the ruler, the apparent position will shift and the reading will be less accurate than the ruler is capable of.A similar error occurs when reading the position of a pointer against a scale in an instrument such as an analog multimeter. To help the user avoid this problem, the scale is sometimes printed above a narrow strip of mirror, and the user's eye is positioned so that the pointer obscures its own reflection, guaranteeing that the user's line of sight is perpendicular to the mirror and therefore to the scale. The same effect alters the speed read on a car's speedometer by a driver in front of it and a passenger off to the side, values read from a graticule not in actual contact with the display on an oscilloscope, etc.

## Photogrammetry

Aerial picture pairs, when viewed through a stereo viewer, offer a pronounced stereo effect of landscape and buildings. High buildings appear to 'keel over' in the direction away from the centre of the photograph. Measurements of this parallax are used to deduce the height of the buildings, provided that flying height and baseline distances are known. This is a key component to the process of photogrammetry.

## Photography

File:Contax III IMG 5349-white.JPG|thumb|Contax III rangefinder camera with macro photographymacro photography(File:Parallax detalj-1.jpg|thumb|left|Failed panoramic image due to the parallax, since axis of rotation of tripod is not same of focal point.)Parallax error can be seen when taking photos with many types of cameras, such as twin-lens reflex cameras and those including viewfinders (such as rangefinder cameras). In such cameras, the eye sees the subject through different optics (the viewfinder, or a second lens) than the one through which the photo is taken. As the viewfinder is often found above the lens of the camera, photos with parallax error are often slightly lower than intended, the classic example being the image of person with his or her head cropped off. This problem is addressed in single-lens reflex cameras, in which the viewfinder sees through the same lens through which the photo is taken (with the aid of a movable mirror), thus avoiding parallax error.Parallax is also an issue in image stitching, such as for panoramas.

## Artillery gunfire

Because of the positioning of field or naval artillery guns, each one has a slightly different perspective of the target relative to the location of the fire-control system itself. Therefore, when aiming its guns at the target, the fire control system must compensate for parallax in order to assure that fire from each gun converges on the target.

## Rangefinders

(File:Telemetre parallaxe principe.svg|thumb|right|Parallax theory for finding naval distances)A coincidence rangefinder or parallax rangefinder can be used to find distance to a target.

## As a metaphor

In a philosophic/geometric sense: an apparent change in the direction of an object, caused by a change in observational position that provides a new line of sight. The apparent displacement, or difference of position, of an object, as seen from two different stations, or points of view. In contemporary writing parallax can also be the same story, or a similar story from approximately the same time line, from one book told from a different perspective in another book. The word and concept feature prominently in James Joyce's 1922 novel, Ulysses. Orson Scott Card also used the term when referring to Ender's Shadow as compared to Ender's Game.The metaphor is invoked by Slovenian philosopher Slavoj Å½iÅ¾ek in his work The Parallax View, borrowing the concept of "parallax view" from the Japanese philosopher and literary critic Kojin Karatani. Å½iÅ¾ek notes,
|author= Slavoj Å½iÅ¾ek |title=The Parallax View }}

{{Reflist}}

## References

• BOOK, Hirshfeld, Alan w., Parallax: The Race to Measure the Cosmos, New York, W.H. Freeman, 2001, 978-0-7167-3711-7, harv,
• BOOK, Whipple, Fred L., 2007, Earth Moon and Planets, 978-1-4067-6413-0, Read Books, harv, .
• BOOK, Zeilik, Michael A., Gregory, Stephan A., Introductory Astronomy & Astrophysics, 4th, 1998, Saunders College Publishing, 978-0-03-006228-5, harv, .

- content above as imported from Wikipedia
- "parallax" does not exist on GetWiki (yet)
- time: 6:05pm EDT - Wed, May 22 2019
[ this remote article is provided by Wikipedia ]
LATEST EDITS [ see all ]
GETWIKI 09 MAY 2016
GETWIKI 18 OCT 2015
M.R.M. Parrott
Biographies
GETWIKI 20 AUG 2014
GETWIKI 19 AUG 2014
GETWIKI 18 AUG 2014
Wikinfo
Culture
CONNECT