Parallax

As parallax ( from Ancient Greek παράλλαξις parallaxis " change back and forth movement " ) refers to the apparent change in position of an object when the observer moves his own position.

Definition as the parallax angle

Defines the parallax as the angle between two straight lines of different locations ( " baseline " ) to the same point (an object ) are directed. This is also the angle at which this base line appears on the observed point.

One lifts such as the thumbs up and looking at it alternately with the left and right eye, then its image moves in front of the distant background. The base here is the eye relief, the method is called thumb jump. The angle is about 6 degrees with average arm length. The parallax is larger, the closer is the observed object, and the longer the base line.

The barely conscious in everyday phenomenon of parallax allows freiäugige estimation of distances and is the basis of spatial vision. By determining the parallax of a sensor or measuring telescope and the baseline is known, the distance to the target point can be precisely calculated. This will, inter alia, applied in cameras, and with high measurement accuracy in geodesy and astronomy.

Parallax in astronomy

Daily parallax Höhenparallaxe

For distance measurements to the Earth's moon and planets near the Earth's radius can already serve as a baseline. For example, the parallax of Venus between two observation sites appear on the globe in a slightly different position in front of the star background. On the rare Venus passages from the sun's parallax was measured relative to the solar limb and applied in this way first values ​​for the astronomical unit.

For the moon, the parallax is because of its small distance more than 2 ° (see horizontal parallax ), that is, the moon pulls Consider, for example, from Europe to completely different than past stars in South Africa. The lunar parallax is also responsible for the different sight which provides a solar eclipse from different geographical latitudes. You can get a home only partially occurring darkness north or south than experience total darkness. If the Moon's shadow touches the Earth in the polar regions, only a partial eclipse takes place there in principle. For a total darkness experience the eclipse tourist would have been traveling into space ( the lunar parallax for artificially enlarge ).

A second measurement principle is the use of the Earth's rotation: Even from a single location creates a parallax because the place reached solely by the rotation of the earth different positions. The application of this effect is called Höhenparallaxe. Conversely, it must at precisely this influence astrometry applied to the measurements as reduction ( corrected).

Annual parallax stellar parallax

The parallax is used to measure distances close to the Sun Star. As a baseline is the mean radius of the orbit of the earth, corresponding to the semi-major axis is used. The orbit of the earth changes the apparent positions of stars in the form of a small ellipse whose shape depends on the angle at which the star of the ecliptic projects (plane of Earth's orbit ). The parallax is the angle at which the radius of the Earth's orbit from the star appear from. If the parallax one arcsecond ( 1/3600 of a degree ), this corresponds to a distance of 3.26 light- years or about 31 trillion kilometers. This distance is also referred to as a parallax (1 Parsecs ).

The parallax is so small that you could not watch it long, even at near- fixed stars. This has been argued as the main scientific argument against the new heliocentric view of the world in the early modern period. In search of the first parallax was a completely different effect, discovered the aberration. It was not until 1838 Friedrich Wilhelm Bessel succeeded in parallax: he chose the high-speed ( star with large annual proper motion ) 61 Cygni and was the biannual angle change after extended analysis on 0.3 " determine ( 0.00008 degrees) Even with the sun nearest star Proxima Centauri. (4 light-years away from Earth ), the parallax of only 0.772 ". In the 1990s, reached with the European astrometric satellite Hipparcos parallax measurements accurate for 118,000 stars. Gaia, as a planned successor (launched December 2013 ) is scheduled to commence in early 2014 so that, even forty times make more accurate measurements at about 1 billion stars.

Star Tromp Aral Laxe

When together moving star clusters like the Hyades one of the parallax is related, purely geometric distance determination possible. As a baseline the years accumulated motion of the star stream is used. For this purpose, the radial velocity and proper motion as well as the convergence point ( vanishing point ) must be known in the sky, the strive towards the cluster stars apparently.

Expansion parallax

For astronomical objects that expand rapidly, such as planetary nebulae and supernova remnants, a direct observation of this expansion can be used for distance determination by from a determination of the absolute rate of expansion (such as Doppler shift ) and the corresponding angular distance ( the expansion parallax ) to the distance is closed.

A similar method is used for determining the distance of binary stars, which are both visually and spectroscopically, i.e., from the visual observation of the movement angle, and obtains a shift of the spectral lines of the absolute velocity, from which the distance is calculated.

Parallax in the sense of distance

In the older language of astronomy, the term ' parallax ' for distance or length was simply used because the distance of astronomical objects could be determined reliably only on the basis of the parallax in the early days of astronomy. This was true even when the distance measurement other - used method - eg photometric.

The use of ' parallax ' as a synonym for ' distance ' is obtained that the distance of stars in pc ( parsecs, about 3.26 light years), the reciprocal of the semi-annual parallax in arc seconds, is specified. ' Parsec ' is an abbreviation of parallax arcsecond ( ' arcsecond at parallactic angle ').

Parallax in photography

In photography occurs in binocular cameras, both rangefinder cameras as well as twin-lens reflex cameras, a parallax: The picture in the viewfinder and the resulting photographic image do not match. This error is, of course, the greater the closer the object is located. Simple cameras with bright-line frame viewfinder often have an additional, fixed marker for close range, more sophisticated models have an automatic parallax: The distance setting on the camera not only serves to focus the lens (focus ), but also changes the angle between the viewfinder and the lens or the viewfinder area limitation and so compensate for the major part of the parallax. Free of parallax are only SLR cameras and digital cameras with which the monitor takes over the function of the viewfinder and the image of the viewfinder comes direct from the image sensor.

In photogrammetry (photogrammetry ) the parallax between the images of two sites is used to measure the distance and is evaluated by means of stereoscopy. A vertical parallax, however, a misalignment of the images is referred to, in which the eye axes must look slightly different in height. It leads to speedy eye fatigue and should be consciously controlled and put away.

Parallax when reading scales

For accurate measurements on scales - such as on a scale or a thermometer - must be made perpendicular to the reading scale ( parallax ). A mirror behind the scale, as it is frequently found in electrical measuring instru-ments, makes this easier: the pointer and its mirror image must be at the time of reading for cover.

However, even without tools, the right eye position are found when paying attention to the Skalenparallaxe: the average of the two extreme positions is generally more precise than an uncontrolled reading, when read by a linear scale. With conventional outdoor thermometers can be improving by 1 ° C to 0.5 ° C accuracy.

Expansion and spin thermometers are the most accurate to read, if you let them hang vertically and horizontally while reading looks (the mirror image of one's head can be helpful at an outer pane ).