Everything about Parallax totally explained
Parallax, more accurately
motion parallax, is the change of angular
position of two observations of a single object relative to each other as seen by an observer, caused by the motion of the observer. Simply put, it's the apparent shift of an object against the background that's caused by a change in the observer's position. The term is derived from the Greek παραλλαγή (
parallagé), meaning "alteration".
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
Viewpoint A, 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.
In
astronomy, parallax is the only direct method by which distances to objects beyond the
Solar System can be measured. The
Hipparcos satellite has used the technique for over 100,000 nearby
stars. This provides the basis for all other distance measurements in astronomy, the
cosmic distance ladder.
Use in distance measurement
By observing parallax,
measuring angles and using
geometry, one can determine the
distance to various objects. When the object in question is a
star, the effect is known as
stellar parallax. The first successful measurements of 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, 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 (the other two being close to 90 degrees), the length of the long sides (in practice considered to be equal) can be determined.
Parallax error
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" doesn't 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:
» 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.
Measurement of the annual parallax as the earth goes through its orbit was the first reliable way to determine the distances to the closest
stars. 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 of other planets).
In 1989, the satellite
Hipparcos was launched primarily for obtaining parallaxes and
proper motions 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 more than one percent of the diameter of
our galaxy. The
European Space Agency's
Gaia mission, due to launch in 2011 and come online in 2012, will be able to measure parallax angles to an accuracy of 1 micro-arc second, thus mapping nearby stars (and potentially planets) up to a distance of tens of thousands of light years from earth.
Dynamic 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.
Dynamic 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.
In computer graphics
In many early graphical applications, such as video games, the scene was constructed of independent layers that were scrolled at different speeds when the player/cursor moved. 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 was moving. Now, most games are based on much more comprehensive three-dimensional graphic models, although portable game systems (DS, PSP) still often use parallax.
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 also invoked in the magnum opus of Slovenian philosopher
Slavoj Žižek in his work 'The Parallax View'. "The philosophical twist to be added ((to parallax)), of course, is that the observed distance isn't simply subjective, since 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
Lacanese- 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'm also in the picture
Further Information
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