VAX

The parallax is the incidence of the change of position of the observer on the observation of an object.

This word appears at the 16th century, borrowed from the Greek παράλλαξις , who means “contiguous displacement; parallax”.

Metrology

The error of parallax is the Angle between the direction of the glance of an observer and the perpendicular with the graduation of a measuring device, bringing to a misreading of taken measurement.

In order to practically remove this error, the observer must be placed so as to confuse the needle or the index with the image that a mirror located in background gives some.

Psychology

In psychology, the parallax is a modification of the Subjectivité, the difference in perception of the same reality.

One says of a subject that it makes a parallax when it manages to perceive a reality or a state in a different direction, and that it manages to decentre its own perception to build a new direction of this same reality. The gasoline even of the psychological therapy consists in helping the subject to create a parallax of the reality which combines the common direction and its serenity.

Photographs

The parallax of aiming is the difference in framing between the image given by a sight and the image passing in the objective of a Camera. A dual lens camera is an apparatus in which the aiming is carried out through an objective located above the objective of catch of sight. The inaccuracy due to the parallax does not exist of course with a camera reflex camera mono-objective (of which the aiming is done through the lens of catch of sight thanks to a mirror).

Astronomy

In Astronomy, the parallax is the Angle under which since a Astre a reference length can be seen:

for the stars of the Solar system, it is the ray of the Ground which was selected; it is about the diurnal parallax ;
for the stars external with the solar system, the reference is the Equatorial radius of the terrestrial Orbite, that is to say a astronomical Unité; it is about the annual parallax .

Determination of the lunar parallax (between 52" and 62"), is due to Nicolas-Louis de Lacaille and Joseph Jerome Lefrançois de Lalande (1732-1807), simultaneously operating in two points of the surface of the Earth very distant one from the other.

One confuses the arc and the tangent

L = D \ cdot \ beta; \ beta = \ alpha_1 + \ alpha_2

measured by the O1 observers and distant O2 of L

D = \ frac {L} {\ alpha_1 + \ alpha_2}

The closer the star considered is, the more its apparent change of direction related to the displacement of the observer is important. The astronomers of the XVIIème century and the beginning of the XVIIIème lengthily sought to highlight this geometrical effect as confirmation of the heliocentric system of Copernic. The first measurement of the parallax of a star was published in 1838 by German Friedrich Wilhelm Bessel.

Diurnal parallax

One calls diurnal parallax of a star the angle under which one would see since this star the terrestrial ray (R) leading instead of observation (A). This angle is negligible for stars. On the other hand, it is of him that it acts when one speaks about the parallax of a star of the solar system.

When the star is with the horizon place (in A), this angle reaches a maximum, the horizontal parallax . The latter reaches itself its maximum value for a place located at the equator, the equatorial horizontal parallax . For example, the equatorial horizontal parallax of the Sun is worth 8,794". The report/ratio of the average equatorial horizontal parallax of the Sun and the horizontal parallax of a star provides an approximate value of the distance from a star of the solar system, in astronomical units.

Annual parallax

One calls annual parallax of a star the angle under which one would see since this star (E) the equatorial radius of the terrestrial orbit (R).

Measure of distance from the stars by the annual parallax

The annual parallax of closest stars makes it possible to calculate the distance, this distance of it being proportional to the cotangent of the angle of parallax, that is to say roughly the reverse of this angle; between the distance D of star to the Sun - expressed in astronomical units - and the value θ of its annual parallax - expressed in Radian S - exists the relation θ = 1/D.

Friedrich Wilhelm Bessel used this method for the first time in 1838 for binary the 61 of the Cygne.

With the use of this method of measurement of distance, a specific unit of length was defined: the Parsec, which is the distance from a star whose annual parallax is one second of arc (all the annual parallaxes are lower than the second of arc - fraction 1/3600 of a degree -, and are usually expressed in milliseconds of arc).

This unit facilitates calculations; for example, for Proxima Centauri, the star nearest to the Solar system, the parallax is of 760 milliseconds, which corresponds to a distance is of 1/0,760 = 1,32 PC.

At the end of the Years 1980, the annual parallaxes of approximately 8000 stars had been obtained starting from direct measurements ( trigonometrical parallaxes ), the measurements taken starting from the instruments built on the surface of the Earth being affected inaccuracies related to the atmospheric disturbances.

Thanks to the European satellite of Astrometry Hipparcos, annual parallaxes of approximately 100 000 stars are now known with a precision of 0,001".

Spectroscopic parallax

A certain number of more remote star parallaxes are determined by the spectroscopic analysis of their radiation. This spectral analysis makes it possible to consider their magnitude absolute, and thus their distance starting from their apparent magnitude; this method is indicated by parallax spectroscopique' or photometric parallax .

These denominations are only abuses language, this vague method not having any relationship with those described previously (for close stars, of the differences of about a 20% between trigonometrical parallax and spectroscopic parallax are not rare).

The parallax in the debate heliocentrisme/geocentrism

In the lawsuit of Galileo, Inquisiteur St Robert Bellarmin made the objection that, if the Earth were driven, one should observe a parallax (according to the definition above). But no parallax not having been measured, this fact became an argument against the Héliocentrisme. Galileo answered that the stars were too remote so that the parallax can be seen and measured with the instruments of then.

Tycho Brahé had also employed this argument in favor of the immobility of the Earth: but it largely underestimated the distance from closest stars.

The parallax measured by Bessel corresponds to that foreseeable by admitting the heliocentric theory. Of course, presentation of the parallax as a proof of the heliocentrism means that one supposes that the movements of other stars compared to the Sun like negligible in front of the movements of the objects of the Solar system.

See too

site of ESA: allows to measure the progress brought by the automation of measurements of parallax per satellite.
Hipparcos and the Pleiads

Reference

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