There are 88 constellations, these are:

• Andromeda
• Antlia (the air pump)
• Apus (the bird of paradise)
• Aquila (the eagle)
• Aquarius (the water carrier)
• Ara (the altar)
• Auriga (the charioteer)
• Bootes (the herdsman)
• Caelum (the chisel)
• Camelopardalis (the giraffe)
• Cancer (the crab)
• Canes Venatici (the hunting dogs)
• Canis Major (the greater dog)
• Canis Minor (the lesser dog)
• Capricornus (the sea goat)
• Carina (the keel)
• Cassiopeia (the vain queen)
• Centaurus (the centaur)
• Cepheus (the Ethiopian king)
• Cetus (the whale)
• Chamaeleon (the chamealeon)
• Circinus (the drawing compass)
• Columba (the dove)
• Coma Berenices (berenice's hair)
• Corona Australis (the southern crown)
• Corona Borealis (the northern crown)
• Corvus (the crow)
• Crater (the cup)
• Crux (the southern cross)
• Cygnus (the swan)
• Dorado (the fish)
• Draco (the dragon)
• Delphinus (the dolphin)
• Equuleus (the foal)
• Eridanus (the river)
• Fornax (the furnace)
• Gemini (the twins)
• Grus (the crane)
• Hercules
• Horologium (the pendulum clock)
• Hydra
• Hydrus (the little water snake)
• Indus (the Indian)
• Lacerta (the lizard)
• Leo (the lion)
• Leo Minor (the little lion)
• Lepus (the hare)
• Libra (the scales)
• Lupus (the wolf)
• Lynx (the lynx)
• Lyra (the lyre)
• Mensa (the table mountain)
• Microscopium (the microscope)
• Monoceros (the unicorn)
• Musca (the fly)
• Norma (the carpenter's level)
• Octans (the octant)
• Orion (the hunter)
• Ophiuchus (the serpent bearer)
• Pavo (the peacock)
• Pegasus (the winged horse)
• Perseus
• Phoenix (the phoenix)
• Pictor (the easel)
• Pisces (the fishes)
• Piscis Austrinus (the southern fish)
• Puppis (the stern)
• Pyxis (the mariner's compass)
• Reticulum (the eyepiece graticule)
• Sagitta (the arrow)
• Sagittarius (the archer)
• Scorpius (the scorpion)
• Sculptor (the sculptor)
• Scutum (the shield)
• Serpens (the snake)-divided into Serpens Caput and Serpens Cauda
• Sextans (the sextant)
• Taurus (the bull)
• Telescopium (the telescope)
• Triangulum (the triangle)
• Triangulum Australe (the southern triangle)
• Tucana (the toucan)
• Ursa Major (the great bear)
• Ursa Minor (the little bear)
• Vela (the sails)
• Virgo (the virgin)
• Volans (the flying fish)
• Vulpecula (the fox)

No.Abbrev.ConstellationGenitiveEnglish NameAreaHem.Alpha Star1AndAndromedaAndromedaeAndromeda722NHAlpheratz2AntAntliaAntliaeAir Pump239SH3ApsApusApodisBird of Paradise206SH4AqrAquariusAquariiWater Carrier980SHSadalmelik5AqlAquilaAquilaeEagle652NH-SHAltair6AraAraAraeAltar237SH7AriAriesArietisRam441NHHamal8AurAurigaAurigaeCharioteer657NHCapella9BooBootesBootisHerdsman907NHArcturus10CaeCaelumCaeliChisel125SH11CamCamelopardalisCamelopardalisGiraffe757NH12CncCancerCancriCrab506NHAcubens13CVnCanes VenaticiCanun VenaticorumHunting Dogs465NHCor Caroli14CMaCanis MajorCanis MajorisBig Dog380SHSirius15CMiCanis MinorCanis MinorisLittle Dog183NHProcyon16CapCapricornusCapricorniGoat ( Capricorn )414SHAlgedi17CarCarinaCarinaeKeel494SHCanopus18CasCassiopeiaCassiopeiaeCassiopeia598NHSchedar19CenCentaurusCentauriCentaur1060SHRigil Kentaurus20CepCepheusCepheiCepheus588SHAlderamin21CetCetusCetiWhale1231SHMenkar22ChaChamaleonChamaleontisChameleon132SH23CirCircinusCirciniCompasses93SH24ColColumbaColumbaeDove270SHPhact25ComComa BerenicesComae BerenicesBerenice's Hair386NHDiadem26CrACorona AustralisCoronae AustralisSouthern Crown128SH27CrBCorona BorealisCoronae BorealisNorthern Crown179NHAlphecca28CrvCorvusCorviCrow184SHAlchiba29CrtCraterCraterisCup282SHAlkes30CruCruxCrucisSouthern Cross68SHAcrux31CygCygnusCygniSwan804NHDeneb32DelDelphinusDelphiniDolphin189NHSualocin33DorDoradoDoradusGoldfish179SH34DraDracoDraconisDragon1083NHThuban35EquEquuleusEquuleiLittle Horse72NHKitalpha36EriEridanusEridaniRiver1138SHAchernar37ForFornaxFornacisFurnace398SH38GemGeminiGeminorumTwins514NHCastor39GruGrusGruisCrane366SHAl Na'ir40HerHerculesHerculisHercules1225NHRasalgethi41HorHorologiumHorologiiClock249SH42HyaHydraHydraeHydra ( Sea Serpent )1303SHAlphard43HyiHydrusHydriWater Serpen ( male )243SH44IndIndusIndiIndian294SH45LacLacertaLacertaeLizard201NH46LeoLeoLeonisLion947NHRegulus47LMiLeo MinorLeonis MinorisSmaller Lion232NH48LepLepusLeporisHare290SHArneb49LibLibraLibraeBalance538SHZubenelgenubi50LupLupusLupiWolf334SHMen51LynLynxLyncisLynx545NH52LyrLyraLyraeLyre286NHVega53MenMensaMensaeTable153SH54MicMicroscopiumMicroscopiiMicroscope210SH55MonMonocerosMonocerotisUnicorn482SH56MusMuscaMuscaeFly138SH57NorNormaNormaeSquare165SH58OctOctansOctantisOctant291SH59OphOphiucusOphiuchiSerpent Holder948NH-SHRasalhague60OriOrionOrionisOrion594NH-SHBetelgeuse61PavPavoPavonisPeacock378SHPeacock62PegPegasusPegasiWinged Horse1121NHMarkab63PerPerseusPerseiPerseus615NHMirfak64PhePhoenixPhoenicisPhoenix469SHAnkaa65PicPictorPictorisEasel247SH66PscPiscesPisciumFishes889NHAlrischa67PsAPisces AustrinusPisces AustriniSouthern Fish245SHFomalhaut68PupPuppisPuppisStern673SH69PyxPyxisPyxidisCompass221SH70RetReticulumReticuliReticle114SH71SgeSagittaSagittaeArrow80NH72SgrSagittariusSagittariiArcher867SHRukbat73ScoScorpiusScorpiiScorpion497SHAntares74SclSculptorSculptorisSculptor475SH75SctScutumScutiShield109SH76SerSerpensSerpentisSerpent637NH-SHUnuck al Hai77SexSextansSextantisSextant314SH78TauTaurusTauriBull797NHAldebaran79TelTelescopiumTelescopiiTelescope252SH80TriTriangulumTrianguliTriangle132NHRas al Mothallah81TrATriangulum AustraleTrianguli AustralisSouthern Triangle110SHAtria82TucTucanaTucanaeToucan295SH83UMaUrsa MajorUrsae MajorisGreat Bear1280NHDubhe84UMiUrsa MinorUrsae MinorisLittle Bear256NHPolaris85VelVelaVelorumSails500SH86VirVirgoVirginisVirgin1294NH-SHSpica87VolVolansVolantisFlying Fish141SH88VulVulpeculaVulpeculaeFox268NH

"How to use an oscilloscope."Here's a few notes on how to use an oscilloscope. First off I am going to show you one very important point using my oldest oscilloscope and that is - they haven't changed at all!

If you study the picture below then you'll see that all modern oscilloscopes follow the same basic pattern.

OK these days they have more functions (and are now digital) but the basic method: how to use an oscilloscope remains the same.

Even digital oscilloscopes follow the same basic pattern of the original oscilloscope design.

So looking at them is just as relevant now as it was 20 years ago and its one of the measurement methods that has not changed except for modernizing it into DSPs.

How to use an oscilloscope : Older oscilloscope controls are still relevant today

Tip: For a digital oscilloscope all you need to know is the location of the 'Reset button'!!! - this will get you out of all trouble as you can set up digital oscilloscopes in many different ways and they often have options buried in the depths of the menu system.

Note: Before hitting the reset button - if someone else has been using it - save the settings (and possibly data) to an internal floppy drive or over the network to your hard disk - this will save you getting into trouble if someone else was using it.

How to use an oscilloscope (or CRT) : Find the beam!The cathode ray oscilloscope (above) is the original oscilloscope and uses a high voltage cathode ray tube. Electrons are forced off a plate at one end using very high voltages (1000s of volts) and guided by electric fields to the phosphor screen that fluoresces when hit by an electron.

Note: Never open the oscilloscope as these voltages are extremely dangerous they are high current and high voltage. Even 10mA at 250Vac can kill and voltages in the oscilloscope are far higher.

The first thing you need to know about it is how to find the beam! Unlike a digital scope it does not test the inputs and set itself up for the most appropriate display mode for you - with the CRT you have to do this yourself. Here's the bits that need setting up:

1. Timebase
2. Intensity
3. Input
4. Trigger
5. Level

Note: You have to set all of these appropriately - setting any one incorrectly will result in an invisible beam.

TimebaseThe timebase sets the time that the beam is scanned from left to right on the screen and it's calibrated in horizontal divisions (the black grid on the front of the screen).

The timebase (picture to left) is set to 0.5ms/DIV which means that the beam (ray) is moved through each horizontal division over the period of 0.5ms. So the time for going from left to right covering the whole display is 10x05.ms = 5ms (a frequency of 200Hz - 200 times a second) - for finding the beam this is a reasonable time.

Make sure that X-Y mode is not selected as this disables the timebase - on this oscilloscope it is one of the controls to the right (black button in the green area).

How to use an oscilloscope: Intensity

Sets the amount of electrons hitting the phosphor screen and it can be set it to zero - so you won't see a thing! So set it to about ¾ full brightness.

Note: After you have found the beam turn it down as if you leave it on for a long time at a high intensity the phosphor burns leaving a permanent line in the phosphor.

How to use an oscilloscope: InputEach channel on the oscilloscope is really just a high quality amplifier with low noise, high bandwidth and selectable gain which connects to the vertical deflector in the oscilloscope.

So if there is any input signal it will be amplified possibly moving the beam out of the display! set the channel input switch to ground (this switch is labeled DC, AC, GND). Setting it to ground connects the input of the amplifier to ground and ignores the input signal.

Note: Remember to switch it back to DC or AC after beam finding otherwise you won't see any measurement!

How to use an oscilloscope: TriggerThe trigger detects when to start moving the beam to the right across the display. Setting this to Auto makes the beam trigger continuously.

It triggers continuously using the internal timebase unless there is an input signal in which case that is used instead i.e. you always see the beam regardless of the input signal.

Note: If it is set to NORM then the oscilloscope won't trigger (unless there is an input signal) so again you won't see anything!

How to use an oscilloscope: Channel LevelThe level adjust control moves the channel beam up and down on the display so you need to adjust it as the beam may be positioned outside the display. Each channel has a level control located beside the channel amplifier (here it's on the far right). How to use an oscilloscope : Setting up.Most oscilloscopes have a test point that generates a low frequency square wave (~1kHz) and you can use it to setup the oscilloscope and the oscilloscope probes.

First of all adjust the focus and intensity (after finding the beam) to get the best looking display - a nice sharp line.

Then set the input to ac and plug in the probe to the channel you are looking at and then attach the probe tip to the test point. You should then see the square wave - adjust the channel amplifier until its a good size in the display screen.

How to use an oscilloscope : Adjust a x10 probe.Each probe has an adjustment screw terminal for probe compensation of the x10 mode.

Note: Times 10 means that the probe divides down the input signal by a factor of 10. Inside the probe in addition to the resistive divider is a capacitive divider - the screw terminal is adjusting one of the capacitors.

Adjust the trigger level so that the signal is stable and you can see a stable square wave.

Adjust the probe while looking at the signal so that the square wave has sharp edges at all corners i.e. shows high frequencies accurately.

There may be undershoot (rounded corners) or overshoot (spikes at the corners) just adjust the screw terminal until these disappear and you have no overshoot and no undershoot.

You have now adjusted the probe correctly.

How to use an oscilloscope: Making measurementsThere are two fundamental things you can measure with an oscilloscope

• Voltage
• Time

How to use an oscilloscope : Measuring Voltage and frequencyUsing the channel amplifier setting you can measure voltage here the amplifier is set to 0.2V per (vertical) division.

Just adjust the channel amplifier setting until the signal you are looking at 'just' fills the screen - this gives the maximum (most accurate) view of the signal.

You can measure DC or AC signals by selecting the appropriate switch setting.

GND sets the input of the channel amplifier to ground ignoring the input signal and it useful to find out where the zero volt reference is on the screen.

How to use an oscilloscope: Measuring DC signalsBefore you measure a steady DC signal set the switch to GND and move the trace to the lowest horizontal graticule (black lines on screen). This sets the zero voltage position - now set the switch to DC and put the probe on the DC signal - adjust the channel amplifier to keep the signal on screen.

Count the number of divisions and multiply by the channel amplifier setting to read the voltage. Of course its easy to select an easy voltage and amplifier setting to start with e.g. 5V with a 1V/division setting will make the trace move up 5 graticule divisions.

How to use an oscilloscope: Measuring AC signalsAn AC signal is simply Alternating Current and is more commonly used to describe an alternating voltage as well and the text book AC waveform is the sinewave.

To make the measurement the amplifier settings are used in the same way as a DC measurement but now you need to start with the ground reference in the middle of the screen. So set the input switch to GND and move the trace up to the center then set the input switch to AC.

You need to do this as an AC signal moves above and below ground so to see the whole signal you need the ground reference in the middle.

Now set the trigger level and adjust the channel amplifier so that the signal fills the screen and is stable. Here's an example of a AC sinewave centered about the mid graticule.

Here settings were:

Timebase : 0.5ms/div

Amplifier: 1.0V/div

So for a quick look the signal period is (looking at the rising edge where it crosses the zero axis - ~4.7 divisions or

5.2* 0.5ms = 2.6ms

So the frequency is 1/2.6ms = 384Hz

The peak voltage is

1V/div * 2 div = 2V

and so the Vrms = Vp/sqrt(2) = 1.41Vrms.

Note: The zero axis is shown by the other channel that is switched to ground - it just helps you to see the signal more easily and is not essential.

But this is not the most accurate way you can measure the signal - to do that you have to maximize the displayed signal.

In the image to the right only half the signal is displayed because you know that a sine wave is repetitive and symmetrical. So you only need to see half the signal to fully characterize it.

Here settings were:

Timebase : 0.2ms/div

Amplifier: 0.5V/div

Half the period of the signal is 6.6 divisions

so

Half period : 6.6 * 0.2ms = 1.32ms,

Whole period : 2 * 1.32ms = 2.64ms

So there is an extra digit of accuracy obtained and the frequency is

1/2.64ms = 378.8Hz

Peak voltage is 4.2 divisions so

0.5V/div * 4.2 div = 0.5 * 4.2V = 2.1Vpeak

So Vrms = Vp/sqrt(2) = 1.49Vrms

Note: This measures the period in the most accurate way I'll leave you to figure out how you could measure both period and amplitude more accurately.

Tip: Buy a digital oscilloscope : All these calculations are done for you in real time - if you buy the right one - some also give you standard deviation, jitter and all manner of other measurements done using dsp.

Visual perceptionMain articles: stereopsis, depth perception, binocular vision, and Binocular disparity

This image demonstrates parallax. TheSun is visible above the streetlight. The reflection in the water is a virtual image of the Sun and the streetlight. The location of the virtual image is below the surface of the water, offering a different vantage point of the streetlight, which appears to be shifted relative to the more distant Sun.

As the eyes of humans and other animals are in different positions on the head, they present different views simultaneously. This is the basis of stereopsis, the process by which the brain exploits the parallax due to the different views from the eye to gain depth perception and estimate distances to objects.[3] Animals also use motion parallax, in which the animals (or just the head) move to gain different viewpoints. For example, pigeons (whose eyes do not have overlapping fields of view and thus cannot use stereopsis) bob their heads up and down to see depth.[4]

Parallax in astronomy

Parallax is an angle subtended by a line on a point. In the upper diagram the earth in its orbit sweeps the parallax angle subtended on the sun. The lower diagram shows an equal angle swept by the sun in a geostatic model. A similar diagram can be drawn for a star except that the angle of parallax would be tiny.

Parallax arises due to change in viewpoint but that can occur due to motion of the observer, or of that which is being observed, or of both. What is essential is relative motion. By observing parallax, measuring angles and using geometry, one can determine the distance to various objects.

Stellar parallaxMain article: Stellar parallax

Stellar parallax created by the relative motion between the Earth and a star, can be seen, in the Copernican model, as arising from the orbit of the Earth around the Sun: the star onlyappears to move relative to more distant objects in the sky. In a geostatic model, the movement of the star would have to be taken as real with the star oscillating across the sky with respect to the background stars.

Stellar parallax is most often measured using annual parallax, 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. The parsec (3.26 light-years) is defined as the distance for which the annual parallax is 1 arcsecond. Annual parallax is normally measured by observing the position of a star at different times of the year as the Earth moves through its orbit. Measurement of annual parallax was the first reliable way to determine the distances to the closest stars. The first successful measurements of stellar parallax were made by Friedrich Bessel in 1838 for the star 61 Cygni using a heliometer.[5]Stellar parallax remains the standard for calibrating other measurement methods. Accurate calculations of distance based on stellar parallax require a measurement of the distance from the Earth to the Sun, now based on radar reflection off the surfaces of planets.[6]

The angles involved in these calculations are very small and thus difficult to measure. The nearest star to the Sun (and thus the star with the largest parallax), Proxima Centauri, has a parallax of 0.7687 ± 0.0003 arcsec.[7] This angle is approximately that subtended by an object 2 centimeters in diameter located 5.3 kilometers away.

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 gigantic distances involved seemed entirely implausible: it was one of Tycho's principal objections to Copernican heliocentrism that in order for it to be compatible with the lack of observable stellar parallax, there would have to be an enormous and unlikely void between the orbit of Saturn and the eighth sphere (the fixed stars).[8]

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 the Milky Way Galaxy. The European Space Agency's Gaia mission, due to launch in August 2013, will be able to measure parallax angles to an accuracy of 10 microarcseconds, thus mapping nearby stars (and potentially planets) up to a distance of tens of thousands of light-years from earth.[9]

Computation

Stellar parallax motion

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 (always less than 1 arcsecond,[5] leaving the other two close to 90 degrees), the length of the long sides (in practice considered to be equal) can be determined.

Assuming the angle is small (see derivation below), the distance to an object (measured in parsecs) is the reciprocal of the parallax (measured in arcseconds): For example, the distance to Proxima Centauri is 1/0.7687=1.3009 parsecs (4.243 ly).[7]

Diurnal parallaxDiurnal parallax is a parallax that varies with rotation of the Earth or with difference of location on the Earth. The Moon and to a smaller extent the terrestrial planets or asteroids seen from different viewing positions on the Earth (at one given moment) can appear differently placed against the background of fixed stars.[10][11] Lunar parallaxLunar parallax (often short for lunar horizontal parallax or lunar equatorial horizontal parallax), is a special case of (diurnal) parallax: the Moon, being the nearest celestial body, has by far the largest maximum parallax of any celestial body, it can exceed 1 degree.[12]

The diagram (above) for stellar parallax can illustrate lunar parallax as well, if the diagram is taken to be scaled right down and slightly modified. Instead of 'near star', read 'Moon', and instead of taking the circle at the bottom of the diagram to represent the size of the Earth's orbit around the Sun, take it to be the size of the Earth's globe, and of a circle around the Earth's surface. Then, the lunar (horizontal) parallax amounts to the difference in angular position, relative to the background of distant stars, of the Moon as seen from two different viewing positions on the Earth:- one of the viewing positions is the place from which the Moon can be seen directly overhead at a given moment (that is, viewed along the vertical line in the diagram); and the other viewing position is a place from which the Moon can be seen on the horizon at the same moment (that is, viewed along one of the diagonal lines, from an Earth-surface position corresponding roughly to one of the blue dots on the modified diagram).

The lunar (horizontal) parallax can alternatively be defined as the angle subtended at the distance of the Moon by the radius of the Earth[13] -- equal to angle p in the diagram when scaled-down and modified as mentioned above.

The lunar horizontal parallax at any time depends on the linear distance of the Moon from the Earth. The Earth-Moon linear distance varies continuously as the Moon follows its perturbed and approximately elliptical orbit around the Earth. The range of the variation in linear distance is from about 56 to 63.7 earth-radii, corresponding to horizontal parallax of about a degree of arc, but ranging from about 61.4' to about 54'.[12] The Astronomical Almanac and similar publications tabulate the lunar horizontal parallax and/or the linear distance of the Moon from the Earth on a periodical e.g. daily basis for the convenience of astronomers (and formerly, of navigators), and the study of the way in which this coordinate varies with time forms part of lunar theory.

Diagram of daily lunar parallax

Parallax can also be used to determine the distance to the Moon.

One way to determine the lunar parallax from one location is by using a lunar eclipse. A 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 60.27 Earth radii or 384,399 kilometres (238,854 mi) This procedure was first used by Aristarchus of Samos[14] and Hipparchus, and later found its way into the work of Ptolemy.[citation needed] The diagram at right shows how daily lunar parallax arises on the geocentric and geostatic planetary model in which the Earth is at the centre of the planetary system and does not rotate. It also illustrates the important point that parallax need not be caused by any motion of the observer, contrary to some definitions of parallax that say it is, but may arise purely from motion of the observed.

Another method is to take two pictures of the Moon at exactly the same time from two locations on Earth and compare the positions of the Moon relative to the stars. Using the orientation of the Earth, those two position measurements, and the distance between the two locations on the Earth, the distance to the Moon can be triangulated:

Example of lunar parallax: Occultation of Pleiades by the Moon

This is the method referred to by Jules Verne in From the Earth to the Moon:

Until 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).

Solar parallaxAfter Copernicus proposed his heliocentric system, with the Earth in revolution around the Sun, it was possible to build a model of the whole solar system without 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 (now called an astronomical unit, or AU). When found 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 expansion age[15] of the visible Universe.

A primitive way to determine 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 noted that the Sun, Moon, and Earth form a right triangle (right angle at the Moon) 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.[14] 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; this conclusion, although incorrect, follows logically from his incorrect data. It does suggest that the Sun is clearly larger than the Earth, which could be taken to support the heliocentric model[citation needed].

Measuring Venus transit times to determine solar parallax

Although Aristarchus' 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.[14] 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% above the currently accepted value, 149.6 million kilometers.

Much later, the Solar System was 'scaled' using the parallax of asteroids, some of which, such as Eros, pass much closer to Earth than Venus. In a favourable opposition, Eros can approach the Earth to within 22 million kilometres.[16] 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.[17]

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. The currently accepted value of solar parallax is 8".794 143.[18]

Dynamic or moving-cluster parallaxMain article: Moving cluster method

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.[19]

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.[20]

DerivationFor a right triangle,

where is the parallax, 1 AU (149,600,000 km) is approximately the average distance from the Sun to Earth, and is the distance to the star. Using small-angle approximations (valid when the angle is small compared to 1radian),

so the parallax, measured in arcseconds, is

If the parallax is 1", then the distance is

This defines the parsec, a convenient unit for measuring distance using parallax. Therefore, the distance, measured in parsecs, is simply , when the parallax is given in arcseconds.[21]

Parallax error in astronomyPrecise parallax measurements of distance have an associated error. However this error in the measured parallax angle does not translate directly into an error for the distance, except for relatively small angles. 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

where d is the distance and p is the parallax. The approximation is far more accurate for parallax errors that are small relative to the parallax than for relatively large errors. For meaningful results in stellar astronomy, Dutch astronomer Floor van Leeuwen recommends that the parallax error be no more than 10% of the total parallax when computing this error estimate.[22]

Parallax error in measurement instruments

The correct line of sight needs to be used to avoid parallax error.

Measurements made by viewing the position of some marker relative to something to be measured are subject to parallax error if the marker is some distance away from the object of measurement and not viewed from the correct position. For example, if measuring the distance between two ticks on a line with a ruler marked on its top surface, the thickness of the ruler will separate its markings from the ticks. If viewed from a position not exactly perpendicular to the ruler, the apparent position will shift and the reading will be less accurate than the ruler is capable of.

A similar error occurs when reading the position of a pointer against a scale in an instrument such as an analog multimeter. To help the user avoid this problem, the scale is sometimes printed above a narrow strip of mirror, and the user's eye is positioned so that the pointer obscures its own reflection, guaranteeing that the user's line of sight is perpendicular to the mirror and therefore to the scale. The same effect alters the speed read on a car's speedometer by a driver in front of it and a passenger off to the side, values read from a graticule not in actual contact with the display on an oscilloscope, etc.

Photogrammetric parallaxAerial picture 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. Parallax error in photography

Contax III rangefinder camera with macro photography setting. Because the viewfinder is on top of the lens and of the close proximity of the subject, goggles are fitted in front of the rangefinder and a dedicated viewfinder installed to compensate for parallax.

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 such 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 often found above the lens of the camera, photos with parallax error are often slightly lower than intended, the classic example being the image of person with his or her head cropped off. This problem is addressed in single-lens reflex cameras, in which the viewfinder sees through the same lens through which the photo is taken (with the aid of a movable mirror), thus avoiding parallax error.

Parallax is also an issue in image stitching, such as for panoramas.

In computer graphicsMain articles: Parallax scrolling and Parallax mapping

In many early graphical applications, such as video games, the scene was constructed of independent layers that were scrolled at different speeds in a simulated parallax motion effect when the player/cursor moved, a method called parallax scrolling. 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 (such as Nintendo DS) still often use parallax.[citation needed]Parallax-based graphics continue to be used for many online applications where the bandwidth required by three-dimensional graphics is excessive.[citation needed]

Parallax scrolling has also been adapted to website design generally implemented using javascript and modern web standards.[23] The technique has since appeared in many different forms and variations on virtually thousands of websites.

Parallax in sightsParallax affects sights in many ways. On sights fitted to small arms, bows in archery, etc. the distance between the sighting mechanism and the weapon's bore or axis can introduce significant errors when firing at close range, particularly when firing at small targets. This difference is generally referred to as "sight height"[24] and is compensated for (when needed) via calculations that also take in other variables such as bullet drop, windage, and the distance at which the target is expected to be.[25] Sight height can be used to advantage when "sighting-in" rifles for field use. A typical hunting rifle (.222 with telescopic sights) sighted-in at 75m will be useful from 50m to 200m without further adjustment.[citation needed] Parallax in optical sightsFurther information: Telescopic sight#Parallax compensation

In optical sights parallax refers to the apparent movement of the reticle in relationship to the target when the user moves his/her head laterally behind the sight (up/down or left/right),[26] i.e. it is an error where the reticle does not stay aligned with the sight's own optical axis.

In optical instruments such as telescopes, microscopes, or in telescopic sights used on small arms and theodolites, the error occurs when the optics are not precisely focused: the reticle will appear to move with respect to the object focused on if one moves one's head sideways in front of the eyepiece. Some firearm telescopic sights are equipped with a parallax compensation mechanism which basically consists of a movable optical element that enables the optical system to project the picture of objects at varying distances and the reticle crosshairs pictures together in exactly the same optical plane. Telescopic sights may have no parallax compensation because they can perform very acceptably without refinement for parallax with the sight being permanently adjusted for the distance that best suits their intended usage. Typical standard factory parallax adjustment distances for hunting telescopic sights are 100 yd or 100 m to make them suited for hunting shots that rarely exceed 300 yd/m. Some target and military style telescopic sights without parallax compensation may be adjusted to be parallax free at ranges up to 300 yd/m to make them better suited for aiming at longer ranges.[citation needed] Scopes for rimfires, shotguns, and muzzleloaders will have shorter parallax settings, commonly 50 yd/m[citation needed] for rimfire scopes and 100 yd/m[citation needed] for shotguns and muzzleloaders. Scopes for airguns are very often found with adjustable parallax, usually in the form of an adjustable objective, or AO. These may adjust down as far as 3 yards (2.74 m).[citation needed]

Non-magnifying reflector or "reflex" sights have the ability to be theoretically "parallax free". But since these sights use parallel collimated light this is only true when the target is at infinity. At finite distances eye movement perpendicular to the device will cause parallax movement in the reticle image in exact relationship to eye position in the cylindrical column of light created by the collimating optics.[27][28] Firearm sights, such as some red dot sights, try to correct for this via not focusing the reticle at infinity, but instead at some finite distance, a designed target range where the reticle will show very little movement due to parallax.[27] Some manufactures market reflector sight models they call "parallax free",[29] but this refers to an optical system that compensates for off axis spherical aberration, an optical error induced by the spherical mirror used in the sight that can cause the reticle position to diverge off the sight's optical axis with change in eye position.[30][31]

Artillery gunfireBecause of the positioning of field or naval artillery guns, each one has a slightly different perspective of the target relative to the location of the fire-control system itself. Therefore, when aiming its guns at the target, the fire control system must compensate for parallax in order to assure that fire from each gun converges on the target. Parallax rangefinders

Parallax theory for finding naval distances

A coincidence rangefinder or parallax rangefinder can be used to find distance to a target.

As a metaphorIn 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 artist Sarah Morris named her studio Parallax, in reference to her parallel production of paintings and films.

The metaphor is invoked by Slovenian philosopher Slavoj Žižek in his work The Parallax View. Žižek borrowed the concept of "parallax view" from the Japanese philosopher and literary critic Kojin Karatani. "The philosophical twist to be added (to parallax), of course, is that the observed distance is not simply subjective, since the same object that 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