# parallax

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In the reflection in the water, the sun seems to be much closer to the lantern than in direct view.

As parallax (from ancient Greek παράλλαξις parallaxis "change, reciprocating") refers to the apparent change in position of an object when the observer moves his own position.

## Definition as a parallactic angle

Simplified representation of the parallax of an object against a distant background, which is caused by a shift in perspective.

The parallax is defined as the angle between two straight lines that are directed from different locations (“baseline”) to the same point (an object). This is also the angle at which this baseline appears from the observed point.

If you hold z. B. the thumb up and looks at it alternately with the left and right eye, so his image shifts against the more distant background. The basis here is the eye relief , the method is called a jump of the thumb . The angle is about 6 degrees with an average arm length. The closer the observed object is and the longer the baseline, the greater the parallax.

The phenomenon of parallax, which is hardly conscious in everyday life, allows the free-eyed estimation of distances and is the basis of spatial vision . If the parallax is determined with a sensor or a measuring telescope and the baseline is known, the distance to the target point can be calculated precisely. This will u. a. Used in cameras and with the highest measuring accuracy in geodesy and astronomy .

## Parallax in Astronomy

### Daily parallax, altitude parallax

For distance measurements to the Earth's moon and nearby planets , the Earth's radius can serve as a base line. For example, the parallax of Venus appears between two observation locations on the globe in a slightly different position in front of the star background . During the rare passages of Venus in front of the sun, the parallax was measured relative to the edge of the sun and in this way brought initial values ​​for the radius of the earth's orbit (the astronomical unit ).

With the moon, the parallax is a maximum of 2 ° due to its short distance (see horizontal parallax ), i.e. H. the moon moves z. B. viewed from Europe past completely different stars than in South Africa. The lunar parallax is also responsible for the different sights an eclipse offers from different geographical latitudes . One can experience an eclipse that only occurs partially at home, north or south, as total eclipse . When the moon's shadow touches the earth in the polar regions , there is in principle only a partial eclipse . For a total eclipse experience, the solar eclipse tourist would have to travel into space (artificially increase the lunar parallax).

A second measuring principle is the use of the earth's rotation : A parallax arises even from a single location, because the location reaches different positions simply by rotating the earth. The application of this effect is called height parallax . Conversely, with precise astrometry, this influence on the measurements must be applied (corrected) as a reduction .

### Annual parallax, star parallax

Principle of star parallax: Due to the annual movement of the earth around the sun, a nearby star moves against the distant background in a half-yearly rhythm (here strongly exaggerated)

Parallax is used to measure the distance of stars near the sun . The mean radius of the earth's orbit , which corresponds to the major semi-axis, serves as the base line . The orbit of the earth changes the apparent star positions in the form of a small ellipse , the shape of which depends on the angle at which the star protrudes from the ecliptic (plane of the earth's orbit). Parallax is the angle at which the radius of the earth's orbit appears from the star. If the parallax is one arc second (1/3600 of a degree), this corresponds to a distance of 3.26 light years or around 31 trillion kilometers. This distance is also known as a parallax second (1 parsec ).

The star parallax is the basis for the unit of length parsec (parallax second). This is the distance from the sun to an astronomical object that has exactly a parallax angle of 1 arcsec (1  AU and 1  pc are not scaled: 1 pc ≈ 206,265 AU)

The parallax is so small, even with nearby fixed stars , that it has not been observed for a long time. In the early modern period this was used as the most important scientific argument against the new heliocentric worldview . In the search for parallax, a completely different effect, aberration , was first discovered. It was not until 1838 that Friedrich Wilhelm Bessel succeeded in measuring parallax: he selected the fast runner (star with large annual movement ) 61 Cygni and, after lengthy analyzes, was able to determine the half-yearly change in angle to be 0.31 ″ (0.00008 degrees); the modern value is 0.29 ″. Even the closest star to the Sun, Proxima Centauri (4 light years from Earth), the parallax is only 0.772 ″. In the 1990s, the European astrometry satellite Hipparcos made accurate parallax measurements for 118,000 stars. The successor Gaia was launched in December 2013 and began at the beginning of 2014 to carry out 40 times more precise measurements on around 1 billion stars.

### Stern current parallax

In the case of star clusters that move together, such as the Hyades , a purely geometric determination of the distance related to parallax is possible. The movement of the stellar current accumulated over the years serves as the baseline . To do its radial velocity and proper motion and the convergence point ( vanishing point ) must be known in the sky, the strive for the cluster stars apparently.

### Expansion parallax

In the case of astronomical objects that expand rapidly, such as planetary nebulae and supernova remnants , direct observation of this expansion can be used to determine the distance by determining the absolute expansion speed (e.g. by Doppler shift ) and the corresponding angular distance (the expansion parallax) on the distance is closed.

A similar procedure is used for the range finding of binary stars that are both visual and spectroscopic; H. From the visual observation of the movement one obtains an angle and from the shift of the spectral lines an absolute speed, from which the distance is then calculated.

### Parallax in the sense of distance

In the older language of astronomy, the term parallax was also used for distance or length , because in the early days of astronomy, the distance to astronomical objects could only be reliably determined on the basis of parallax. This also applied when the distance measurement was carried out by other - e.g. B. photometric - method used.

The use of parallax as a synonym for distance is preserved in that the distance to stars is given in parsecs (pc, approx. 3.26 light-years ), the reciprocal of the semi-annual parallax in arcseconds. Parsec is an abbreviation of the English parallax arcsecond (' arcsecond at the parallactic angle').

## Parallax in photography

 Parallax error in viewfinder cameras, schematic Parallax markings in a bright line viewfinder

In photography , a parallax error occurs with two -lens cameras, both with viewfinder cameras and two-lens reflex cameras : the image detail in the viewfinder and the resulting photographic image do not match. This error naturally increases the closer the object is. Simple cameras with bright line viewfinder often have an additional, fixed marking for the close range, more complex models have automatic parallax compensation : The distance setting of the camera is not only used to focus the lens (sharpness), but also changes the angle between viewfinder and lens or the viewfinder field limitation and so compensates for most of the parallax error. All cameras that use the same optics to generate the viewfinder image that are used for later image recording are free of parallax errors .

In photogrammetry (image measurement), the parallax between the images from two locations is used as a measure of the distance and is evaluated using stereoscopy . When vertical parallax contrast, misalignment of the images is called, in which the visual axes must look into something different heights. It leads to eye fatigue and should be consciously controlled and put away.

Mirror scale ; the mirror helps with vertical reading

For precise measurements on scales - for example on a folding rule or a thermometer - the reading must be perpendicular to the scale ( parallax error ). A mirror behind the scale, as is often found in electrical pointer measuring devices, makes this easier: the pointer and its mirror image must be in congruence at the time of reading.

But the correct eye position can also be found without aids if you pay attention to the scale parallax: the mean value from two extreme positions is usually more accurate than an uncontrolled reading when reading from a linear scale. With conventional outdoor thermometers , the accuracy can be improved from 1 ° C to 0.5 ° C.

Expansion and centrifugal thermometers can be read most accurately if you let them hang vertically and look horizontally while reading (although the reflection of your own head on an outer pane can be helpful).