, or more accurately '''motion parallax''' ( of two Stationary Point s relative to each other as seen by an observer, caused by the motion of an observer. Simply put, it is the shift of an object against a background caused by a change in observer position. If there is no parallax between two objects then they are side by side at the exact same height.
This parallax is often thought of as the 'apparent motion' of an object against a distant background because of a perspective shift, as seen in Figure 1. When viewed from , the object appears to be closer to the blue square. When the viewpoint is changed to '''Viewpoint B''', the object ''appears'' to have moved in front of the red square. It is most commonly used in astronomy.
By Observing parallax, Measuring Angle s and using Geometry , one can determine the Distance to various objects. When this is in reference to Star s, the effect is known as . The first successful measurements of a stellar parallax were made by Friedrich Bessel in 1838 , for the star 61 Cygni .
Distance measurement by parallax is a special case of the principle of Triangulation , where 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 only ''one'' side has been measured. Thus, the careful measurement of the length of one baseline can fix the scale of a triangulation network covering the whole nation. In parallax, the triangle is extremely long and narrow, and by measuring both its shortest side and the small top angle (the other two being close to 90 degrees), the long sides (in practice equal) can be determined.
Precise parallax measurements of distance usually have an associated Error . Thus a parallax may be described as some angle ± some angle-error. However this "± angle-error" will not translate directly into a ± error for the range, 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 means of the following:
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After
Copernicus proposed his heliocentric system, with an Earth in revolution around the Sun, it was possible to build a scale model of the whole solar system, but without the scale. To ascertain the scale, it is necessary only to measure one distance within the solar system, e.g., the mean distance from the Earth to the
Sun or
Astronomical Unit (AU). When done by
Triangulation , this is referred to as the ''solar parallax'', the difference in position of the Sun as seen from the Earth's centre and a point one Earth radius away, i.e., the angle subtended at the Sun by the Earth's mean radius. Knowing the solar parallax and the mean Earth radius allows one to calculate the AU, the first, small step on the long road of establishing the size — and thus, according to
Big Bang theory, the minimum age — of the visible Universe.
A primitive way of determining the distance to the Sun in terms of the distance to the Moon was already proposed by
Aristarchus Of Samos in his book
On The Sizes And Distances Of The Sun And Moon . He argued that the Sun, Moon, and Earth form a right triangle at the moment of
First Or Last Quarter Moon . He then estimated that the Moon, Earth, Sun angle was 87°. Using correct
Geometry , but inaccurate observational data, Aristarchus concluded that the Sun was slightly less than 20 times farther away than the Moon. The true value of this angle is close to 89° 50', and the Sun is actually about 390 times farther away. He pointed out that the Moon and Sun have nearly equal
Apparent Angular Sizes and therefore their diameters must be in proportion to their distances from Earth. He thus concluded that the Sun was around 20 times larger than the Moon; which, although wrong, follows logically from his incorrect data. It does suggest that the Sun is clearly larger than the Earth, which can be taken to support the heliocentric model. Although his results were incorrect due to observational errors, they were based on correct geometric principles of parallax, and became the basis for estimates of the size of the solar system for almost 2000 years, until the
Transit Of Venus was correctly observed in 1761 and 1769.
This method was proposed by
Edmond Halley in 1716 , although he did not live to see the results.
The use of Venus transits was less successful than had been hoped due to the
Black Drop Effect , but the resulting estimate, 153 million kilometers, is just 2% over the currently accepted value, 149.6 million kilometers.
Much later, the solar system was 'scaled' using the parallax of
Asteroid s, some of which, like
Eros , pass much
closer to Earth than Venus. In a favourable opposition, Eros can approach the Earth to within 22 million kilometres. Both the
opposition of 1901 and that of 1930/1931 were used for this purpose, the calculations of the latter determination being completed by
Astronomer Royal Sir
Harold Spencer Jones .
Also
Radar reflections, both off Venus (1958) and off asteroids, like
Icarus , have been used for solar parallax
determination. Today, use of
Spacecraft Telemetry links has solved this old problem completely.
On an interstellar scale, parallax created by the different orbital positions of the Earth causes nearby stars to appear to move relative to the more distant stars. However, this effect is so small it is undetectable without extremely precise measurements.
The is 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. Given two points on opposite ends of the orbit, the parallax is half the maximum parallactic shift evident from the star viewed from the two points. The
Parsec is the distance for which the annual parallax is 1
Arcsecond . A parsec equals 3.26 light years.
The distance of an object (in parsecs) can be computed as the
Reciprocal of the parallax. For instance, the
Hipparcos satellite measured the parallax of the nearest star,
Proxima Centauri , as .77233 seconds of arc (±.00242"). Therefore, the distance is 1/0.772=1.29
Parsec s or about 4.22
Light Year s (±.01 ly).
The angles involved in these calculations are very small. For example, .772 arcseconds is roughly the angle
Subtended by an object about 2 centimeters in diameter (roughly the size of a
U.S. Quarter Dollar ) located about 5.3 kilometers away.
The parallax
in arc seconds
where
: 1 AU = 1
Astronomical Unit = Average distance from the
Sun to
Earth = 1.4959 · 10
11 m
: d = distance to the star
Picking a good unit of measure will cancel the constants.
Derivation:
:
:
:
:
arcseconds
: parallax
: If the parallax is 1", then the distance is
= 206,265 AU = 3.2616 lyr = 1 parsec (This ''defines'' the parsec)
: The parallax
arcseconds, when the distance is given in parsecs
The fact that stellar parallax was so small that it was unobservable at the time was used as the main scientific argument against
Heliocentrism during the early modern age. It is clear from
Euclid's Geometry that the effect would be undetectable if the stars were far enough away; but for various reasons such a gigantic size seemed entirely implausible.
Measurements of the annual parallax as the earth goes through its orbit was the first reliable way to determine the distances to the closest
Star s. This method was first successfully used by
Friedrich Wilhelm Bessel in 1838 when he measured the distance to
61 Cygni with a
Heliometer , and it remains the standard for calibrating other measurement methods (after the size of the orbit of the earth is measured by
Radar reflection on other planets).
In 1989 , a satellite called "
Hipparcos " was launched with the main
purpose of obtaining parallaxes and
Proper Motion s of nearby stars, increasing the reach of the method tenfold. Even so, Hipparcos is only able to measure parallax angles for stars up to about 1,600 light-years away — a little bit more than one percent of the diameter of
Our Galaxy .
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 us to estimate the distance of the cluster (151 light years) and its member stars in much the same way as using annual parallax.
Dynamic parallax has sometimes also been used to determine the distance to a supernova, when the optical wave front of the outburst was seen to propagate through the surrounding dust clouds at an apparent angular velocity, when we know its true propagation velocity to be the
Speed Of Light .
All these various astronomical parallax methods allow us to establish the first rungs on the cosmic scale ladder, out to a few hundred parallaxes" — not really parallaxes at all. It is a prototype of a "standard candle" method, where we observe the apparent brightness of an object we know, based on some physical theory, the true brightness of. For groups of stars we have the
Hertzsprung-Russell Diagram which allows us to derive a star's
Absolute Brightness or magnitude
from its spectral type. The observed
(apparent) Brightness or magnitude being
, we can then derive its parallax
by
:
called "spectroscopic parallax".
Further methods, mostly of the
Standard Candle variety, are the variable stars called
Cepheid s — the
absolute brightness of which depends on their observed period of variation —,
Supernova brightnesses,
Globular Cluster sizes and brightnesses, complete
Galaxy brightnesses etc. These are all much more uncertain as they are not based on simple geometry. Yet, parallaxes are the basis of everything, as they allow the calibration of these more uncertain methods in the Solar neighbourhood.
A very modern method which is not a traditional parallax method but also geometric in nature, is "
Gravitational Lens ing parallax". It depends on observing the differential time delay of brightness variations from a remote
Quasar reaching us by two different paths through the gravitational field or "lens" of a foreground galaxy. If the redshifts of both the quasar and the foreground galaxy are known, one can show that the absolute distances of both are proportional to the differential delay, and can in fact be calculated given also the geometry of the gravitational lens on the celestial sphere.
All these independent techniques aim at determining
Hubble's Constant , the constant describing how the
Redshift of galaxies, due to the Universe's expansion, depends on these galaxies' distance from us. Knowing Hubble's constant again allows us to determine, by simply running the film of the cosmic expansion backwards, how long ago it was when all these galaxies were collected in a single point -- the
Big Bang . Current knowledge puts this at some 13.7 billion years ago, but with considerable uncertainty and dependence on various model assumptions.
See Also: Parallax scrolling
In many early graphical applications, such as video games, the scene would be constructed of independent layers that are scrolled at different speeds when the player/cursor moves. Some hardware had explicit support for such layers, such as the
Super Nintendo Entertainment System . This gave some layers the appearance of being farther away than others and was useful for creating an illusion of depth, but only worked when the player is moving. Now, most games are based on much more comprehensive three-dimensional graphic models, although portable game (DS, PSP) systems still often use parallax.
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 a 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 of "parallax" feature prominently in
James Joyce 's 1922 novel, ''
Ulysses ''.
Orson Scott Card also used this term when referring to
Ender's Shadow as compared to
Ender's Game .
The metaphor is also invoked in the magnum opus of Slovenian philosopher
Slavoj Žižek in his work The Parallax View. "The philosophical twist to be added ((to paralllax)), of course, is that the observed distance is not simply subjective, due to the fact that the same object which exists "out there" is seen from two different stances, or points of view. It is rather that, as
Hegel would have put it, subject and object are inherently mediated so that an "epistemological" shift in the subject's point of view always reflects an ontological shift in the object itself. Or -to put it in
Lacan ese- the subject's gaze is always-already inscribed into the perceived object itself, in the guise of its "blind spot," that which is "in the object more than object itself", the point from which the object itself returns the gaze. Sure the picture is in my eye, but I am also in the picture."
Slavoj Žižek, The Parallax View, 17
