Information about Parallax
Parallax, or more accurately motion parallax (Greek: παραλλαγή (parallagé) = alteration) is the change of angular position of two stationary points 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 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. It is most commonly used in astronomy.
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.
However an approximation of the distance error can be computed by means of the following:
where d is the distance and p is the parallax. The approximation is far more accurate for relatively small values of the parallax error when compared to the parallax.
Also in non-optical measurements the thickness of a ruler can create parallax in fine measurements. One is always cautioned in science classes to "avoid parallax." By this it is meant that one should always take measurements with one's eye on a line directly perpendicular to the ruler, so that the thickness of the ruler does not create error in positioning for fine measurements. A similar error can occur when reading the position of a pointer against a scale in an instrument such as a galvanometer. To help the user to avoid this problem, the scale is sometimes printed above a narrow strip of mirror, and the user positions his eye so that the pointer obscures its own reflection. This guarantees that the user's line of sight is perpendicular to the mirror and therefore to the scale.
In photography, one also talks about the parallax of a camera viewfinder: for nearby objects, a viewfinder mounted on top of the camera will show something different from what the lens 'sees', and people's heads may be cut off. The problem does not exist for the single lens reflex camera, where the viewfinder looks (with the aid of a movable mirror) through the same lens as is used for taking the photograph.
Lunar parallax involves the arithmetic of parallel stars between two inverted axis which rotate in angles that are only visible by the moon.
Jules Verne, in From the Earth to the Moon, wrote:
A primitive way to determine the lunar parallax from one location is by using a lunar eclipse. The full shadow of the Earth on the Moon has an apparent radius of curvature equal to the difference between the apparent radii of the Earth and the Sun as seen from the Moon. This radius can be seen to be equal to 0.75 degree, from which (with the solar apparent radius 0.25 degree) we get an Earth apparent radius of 1 degree. This yields for the Earth-Moon distance 60 Earth radii or 384,000 km. This procedure was first used by Aristarchus of Samos and Hipparchus, and later found its way into the work of Ptolemy.
Another way to use parallax to determine the distance to the Moon would be to take two pictures of the Moon at exactly the same time from two locations on Earth, and compare the position of the Moon relative to the visible stars. Using the orientation of the Earth, and those two points, and a perpendicular displacement, a distance to the Moon can be triangulated.
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 asteroids, 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 annual parallax 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 parsecs or about 4.22 light years (±.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.
in arc seconds
where
Picking a good unit of measure will cancel the constants. Derivation:
Measurements 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 on other planets).
In 1989 , a satellite called "Hipparcos" was launched with the main purpose of 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 bit more than one percent of the diameter of our galaxy.
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.
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 Cepheids — 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 lensing 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.
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 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 am also in the picture." [1]
1 Žižek, Slavoj (2006). The Parallax View. The MIT Press, 17. ISBN 0262240513.
Introduction
)
Figure 1: A simplified example of parallax
Use in distance measurement
By observing parallax, measuring angles and using geometry, one can determine the distance to various objects. When this is in reference to stars, the effect is known as stellar parallax. 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.
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" 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:
where d is the distance and p is the parallax. The approximation is far more accurate for relatively small values of the parallax error when compared to the parallax.
Parallax error in photography
Parallax error can be seen when taking photos with many types of cameras, such as twin-lens reflex cameras, and those including viewfinders such as rangefinder cameras. In these cameras, the eye sees the subject through different optics (the viewfinder, or a second lens) than the one through which the photo is taken. As the viewfinder is usually found above the lens of the camera, photos with parallax error are characterized as being slightly lower than intended, the classic example being the image of person with his/her head cropped off. This problem is addressed in single-lens reflex cameras, where the viewfinder sees through the same lens through which the photo is taken, thus avoiding parallax error.Parallax and measurement instruments
If an optical instrument — telescope, microscope, theodolite — is imprecisely focused, the cross-hairs will appear to move with respect to the object focused on if one moves one's head horizontally in front of the eyepiece. This is why it is important, especially when performing measurements, to carefully focus in order to 'eliminate the parallax', and to check by moving one's head.Also in non-optical measurements the thickness of a ruler can create parallax in fine measurements. One is always cautioned in science classes to "avoid parallax." By this it is meant that one should always take measurements with one's eye on a line directly perpendicular to the ruler, so that the thickness of the ruler does not create error in positioning for fine measurements. A similar error can occur when reading the position of a pointer against a scale in an instrument such as a galvanometer. To help the user to avoid this problem, the scale is sometimes printed above a narrow strip of mirror, and the user positions his eye so that the pointer obscures its own reflection. This guarantees that the user's line of sight is perpendicular to the mirror and therefore to the scale.
In photography, one also talks about the parallax of a camera viewfinder: for nearby objects, a viewfinder mounted on top of the camera will show something different from what the lens 'sees', and people's heads may be cut off. The problem does not exist for the single lens reflex camera, where the viewfinder looks (with the aid of a movable mirror) through the same lens as is used for taking the photograph.
Photogrammetric parallax
Aerial pic pairs, when viewed through a stereo viewer, offer a pronounced stereo effect of landscape and buildings. High buildings appear to 'keel over' in the direction away from the centre of the photograph. Measurements of this parallax are used to deduce the height of the buildings, provided that flying height and baseline distances are known. This is a key component to the process of photogrammetry.Lunar parallax
)
Example of lunar parallax: Occultation of Pleiades by the Moon
Lunar parallax involves the arithmetic of parallel stars between two inverted axis which rotate in angles that are only visible by the moon.
Jules Verne, in From the Earth to the Moon, wrote:
"Up till then, many people had no idea how one could calculate the distance separating the Moon from the Earth. The circumstance was exploited to teach them that this distance was obtained by measuring the parallax of the Moon. If the word parallax appeared to amaze them, they were told that it was the angle subtended by two straight lines running from both ends of the Earth's radius to the Moon. If they had doubts on the perfection of this method, they were immediately shown that not only did this mean distance amount to a whole two hundred thirty-four thousand three hundred and forty-seven miles (94,330 leagues), but also that the astronomers were not in error by more than seventy miles (— 30 leagues)."
A primitive way to determine the lunar parallax from one location is by using a lunar eclipse. The full shadow of the Earth on the Moon has an apparent radius of curvature equal to the difference between the apparent radii of the Earth and the Sun as seen from the Moon. This radius can be seen to be equal to 0.75 degree, from which (with the solar apparent radius 0.25 degree) we get an Earth apparent radius of 1 degree. This yields for the Earth-Moon distance 60 Earth radii or 384,000 km. This procedure was first used by Aristarchus of Samos and Hipparchus, and later found its way into the work of Ptolemy.
Another way to use parallax to determine the distance to the Moon would be to take two pictures of the Moon at exactly the same time from two locations on Earth, and compare the position of the Moon relative to the visible stars. Using the orientation of the Earth, and those two points, and a perpendicular displacement, a distance to the Moon can be triangulated.
Solar parallax
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 asteroids, 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.
Stellar parallax
)
Stellar parallax motion
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 annual parallax 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 parsecs or about 4.22 light years (±.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.
Computation
The parallax in arc seconds
where
- 1 AU = 1 astronomical unit = Average distance from the Sun to earth = 1.4959 · 1011 m
- d = distance to the star
Picking a good unit of measure will cancel the constants. Derivation:
- right triangle
- small angle approximation
-
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
Measurements 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 on other planets).
In 1989 , a satellite called "Hipparcos" was launched with the main purpose of 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 bit more than one percent of the diameter of our galaxy.
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 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.
The scale of the Universe
All these various astronomical parallax methods allow us to establish the first rungs on the cosmic scale ladder, out to a few hundred light years. Beyond that, other methods must be taken into use: e.g., "spectroscopic 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 Cepheids — 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 lensing 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.
Parallax in computer graphics
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 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 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 am also in the picture." [1]
References
See also
- Disparity
- Triangulation, wherein a point is calculated given its angles from other known points
- Trilateration, wherein a point is calculated given its distances from other known points
- Trigonometry
External links
- Instructions for having background images on a web page use parallax effects
- Actual parallax project measuring the distance to the moon within 2.3%
- Java applet demonstrating stellar parallax
- BBC's Sky at Night programme: Patrick Moore demonstrates Parallax using Cricket. (Requires RealPlayer)
- Parallax Error in Digital Panoramas - Illustrated diagrams of why this happens, what it does to the photograph, and how to prevent it from occurring
- Definition of "parallax" at http://reference.dictionary.com
- "What is parallax?
Greek}}}
Writing system: Greek alphabet
Official status
Official language of: Greece
Cyprus
European Union
recognised as minority language in parts of:
European Union
Italy
Turkey
Regulated by:
..... Click the link for more information.
Writing system: Greek alphabet
Official status
Official language of: Greece
Cyprus
European Union
recognised as minority language in parts of:
European Union
Italy
Turkey
Regulated by:
..... Click the link for more information.
In physics, displacement is the vector that specifies the position of a point or a particle in reference to an origin or to a previous position. The vector directs from the reference point to the current position.
..... Click the link for more information.
..... Click the link for more information.
stationary point is an input to a function where the derivative is zero (equivalently, the gradient is zero): where the function "stops" increasing or decreasing (hence the name).
..... Click the link for more information.
..... Click the link for more information.
Observation is an activity of a sapient or sentient living being (e.g. humans), which senses and assimilates the knowledge of a phenomenon in its framework of previous knowledge and ideas.
..... Click the link for more information.
..... Click the link for more information.
Measurement is the estimation of the magnitude of some attribute of an object, such as its length or weight, relative to a unit of measuremnt. Measurement usually involves using a measuring instrument, such as a ruler or scale, which is calibrated to compare the object to some
..... Click the link for more information.
..... Click the link for more information.
angle (in full, plane angle) is the figure formed by two rays sharing a common endpoint, called the vertex of the angle. The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept
..... Click the link for more information.
..... Click the link for more information.
Geometry (Greek γεωμετρία; geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. Geometry is one of the oldest sciences.
..... Click the link for more information.
..... Click the link for more information.
Distance is a numerical description of how far apart objects are at any given moment in time. In physics or everyday discussion, distance may refer to a physical length, a period of time, or an estimation based on other criteria (e.g. "two counties over").
..... Click the link for more information.
..... Click the link for more information.
STAR is an acronym for:
Organizations:
..... Click the link for more information.
Organizations:
- Society for Telescopy, Astronomy, and Radio, a non-profit astronomy club in New Jersey
- Special Tasks and Rescue or Special Tactics and Response, synonyms for SWAT
..... Click the link for more information.
Friedrich Bessel
Friedrich Wilhelm Bessel
Born July 22 1784
Minden, Westphalia, now Germany
..... Click the link for more information.
Friedrich Wilhelm Bessel
Born July 22 1784
Minden, Westphalia, now Germany
..... Click the link for more information.
61 Cygni, sometimes called Bessel's Star,[10] is a binary star system in the constellation Cygnus. It consists of a pair of orange dwarf stars—called a visual binary—that orbit (or revolve around) each other with a period of about
..... Click the link for more information.
..... Click the link for more information.
triangulation is the process of finding coordinates and distance to a point by calculating the length of one side of a triangle, given measurements of angles and sides of the triangle formed by that point and two other known reference points, using the law of sines.
..... Click the link for more information.
..... Click the link for more information.
Error refers to a difference between actual behavior or measurement and the norms or expectations for the behavior or measurement. The concrete meaning of the Latin word error
..... Click the link for more information.
..... Click the link for more information.
twin-lens reflex camera (TLR) is a type of camera with two objective lenses of the same focal length. One of the lenses is the photographic objective (the lens that takes the picture), while the other is used for the waist-level viewfinder system.
..... Click the link for more information.
..... Click the link for more information.
viewfinder is what the photographer looks through to compose, and in many cases to focus, the picture.
Viewfinders are widely used in cameras of different types: still and movie, film, analog and digital.
Viewfinders can be optical or electronic.
..... Click the link for more information.
Viewfinders are widely used in cameras of different types: still and movie, film, analog and digital.
Viewfinders can be optical or electronic.
..... Click the link for more information.
rangefinder camera is a camera fitted with a rangefinder: a range-finding focusing mechanism allowing the photographer to judge the focusing distance and take photographs that will be in focus.
..... Click the link for more information.
..... Click the link for more information.
single-lens reflex (SLR) camera is a photographic imaging instrument that currently uses an automatic moving mirror system and viewing pentaprism, which is situated between the lens and the film plane to direct the light reflected from the subject's image, then passing
..... Click the link for more information.
..... Click the link for more information.
A telescope is an instrument designed for the observation of remote objects and the collection of electromagnetic radiation. The earliest known telescopes are credited to three individuals, Hans Lippershey and Zacharias Janssen, spectacle-makers in Middelburg, and Jacob Metius of
..... Click the link for more information.
..... Click the link for more information.
Editing of this page by unregistered or newly registered users is currently disabled due to vandalism.
If you are prevented from editing this page, and you wish to make a change, please discuss changes on the talk page, request unprotection, log in, or .
..... Click the link for more information.
If you are prevented from editing this page, and you wish to make a change, please discuss changes on the talk page, request unprotection, log in, or .
..... Click the link for more information.
theodolite is an instrument for measuring both horizontal and vertical angles, as used in triangulation networks. It is a key tool in surveying and engineering work, but theodolites have been adapted for other specialized purposes in fields like meteorology and rocket launch
..... Click the link for more information.
..... Click the link for more information.
galvanometer is a type of ammeter — an instrument for detecting and measuring electric current. It is an electromechanical transducer that produces a rotary deflection, through a limited arc, in response to electric current flowing through its coil.
..... Click the link for more information.
..... Click the link for more information.
mirror is an object with a surface that has good specular reflection; that is, it is smooth enough to form an image. The most familiar type of mirror is the plane mirror, which has a flat surface.
..... Click the link for more information.
..... Click the link for more information.
Eyes are organs of vision that detect light. Different kinds of light-sensitive organs are found in a variety of organisms. The simplest eyes do nothing but detect whether the surroundings are light or dark, while more complex eyes can distinguish shapes and colors.
..... Click the link for more information.
..... Click the link for more information.
single-lens reflex (SLR) camera is a photographic imaging instrument that currently uses an automatic moving mirror system and viewing pentaprism, which is situated between the lens and the film plane to direct the light reflected from the subject's image, then passing
..... Click the link for more information.
..... Click the link for more information.
Photogrammetry is a remote sensing technology in which geometric properties about objects are determined from photographic images. For example, the three-dimensional coordinates of points on an object are determined by measurements made in two or more photographic images taken from
..... Click the link for more information.
..... Click the link for more information.
Jules Verne
Jules Verne. Photo by Félix Nadar.
Born: January 8 1828
Nantes, France
Died: March 24 1905 (aged 77)
Amiens, France
Occupation: Novelist
Nationality: French
..... Click the link for more information.
Jules Verne. Photo by Félix Nadar.
Born: January 8 1828
Nantes, France
Died: March 24 1905 (aged 77)
Amiens, France
Occupation: Novelist
Nationality: French
..... Click the link for more information.
From the Earth to the Moon
Author Jules Verne
Original title De la Terre à la Lune
Country France
Language French
Genre(s) Science Fiction
Publisher
Publication date 1865
..... Click the link for more information.
Author Jules Verne
Original title De la Terre à la Lune
Country France
Language French
Genre(s) Science Fiction
Publisher
Publication date 1865
..... Click the link for more information.
Aristarchus (Greek: Ἀρίσταρχος; 310 BC - ca. 230 BC) was a Greek astronomer and mathematician, born on the island of Samos, in ancient Greece.
..... Click the link for more information.
..... Click the link for more information.
Hipparchus (Greek Ἵππαρχος; ca. 190 BC – ca. 120 BC) was a Greek astronomer, geographer, and mathematician of the Hellenistic period.
..... Click the link for more information.
..... Click the link for more information.
Claudius Ptolemaeus (Greek: Κλαύδιος Πτολεμαῖος; after 83 – 161 AD), known in English as Ptolemy, was a Greek[1] or Egyptian
..... Click the link for more information.
..... Click the link for more information.
This article is copied from an article on Wikipedia.org - the free encyclopedia created and edited by online user community. The text was not checked or edited by anyone on our staff. Although the vast majority of the wikipedia encyclopedia articles provide accurate and timely information please do not assume the accuracy of any particular article. This article is distributed under the terms of GNU Free Documentation License.
Herod_Archelaus
