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O¨pik(Opik),ErnstJulius(1893–1985) ENCYCLOPEDIAOFASTRONOMYANDASTROPHYSICS O¨pik (Opik), Ernst Julius (1893–1985) Born in Estonia, O¨pik studied at Moscow University, and helped establish Turkestan University in Tashkent, becomingtheAstronomer(director)atTartuObservatory in Estonia. He fled the RedArmy by horse cart during theSecondWorldWarandwenttoArmaghObservatory (NorthernIreland)in1948. Hiswide-ranginginterestsare reflected in his discoveries and theories. These include the discovery of degenerate stars, e.g. white dwarfs, in his calculation of the density of o2 Eridani (1915). He calculatedthedistanceofM31as450000parsecsfromthe Sun(1922). Hecomputedbyhandevolutionarymodels of main-sequence stars into giants (1938) over a decade earlier than the computer computations of HOYLE and SCHWARZSCHILD.Hepredictedthedensityofcratersonthe surface of Mars, which was confirmed 15 years later by planetary probes. He put forward an unproven theory of the IceAges based on a calculation of changes in the convectionintheinternalstructureoftheSunratherthan MILANKOVITCHcycles. Copyright©NaturePublishingGroup2001 BrunelRoad,Houndmills,Basingstoke,Hampshire,RG216XS,UKRegisteredNo.785998 andInstituteofPhysicsPublishing2001 1 DiracHouse,TempleBack,Bristol,BS16BE,UK Ångstro¨m,AndersJonas(1814–74) ENCYCLOPEDIAOFASTRONOMYANDASTROPHYSICS Ångstro¨m, Anders Jonas (1814–74) Physicist,borninLo¨dgo¨,Sweden. Hewaskeeperofthe observatory and professor at Uppsala where he studied heat,magnetismandopticsandexaminedthespectraof the Sun and auroras. His name is commemorated with the angstrom unit, 10−10 m, which is used for measuring wavelengths of light and x-rays, and the separation of atomsinmoleculesandcrystals. Copyright©NaturePublishingGroup2001 BrunelRoad,Houndmills,Basingstoke,Hampshire,RG216XS,UKRegisteredNo.785998 andInstituteofPhysicsPublishing2001 1 DiracHouse,TempleBack,Bristol,BS16BE,UK 61Cygni ENCYCLOPEDIAOFASTRONOMYANDASTROPHYSICS 61 Cygni Thestar61Cygniisimportantbecauseofitslargeproper motion, first measured at the Palermo Observatory by GiuseppePiazzi(1746–1826). Thestarbecamepopularly knownas‘Piazzi’sflyingstar’.Itsmeasuredannualproper motionof5.23(cid:1)(cid:1) isstilltheseventhlargestknown, andis thelargestforanaked-eyestar(apparentmagnitude4.8). Thisstarwasalsothefirsttohaveitsannualparallax reliably determined, by Friedrich Bessel (1784–1846). Bessel’smeasurementof0.314(cid:1)(cid:1),madeatKo¨nigsbergwith Fraunhofer’s6.25inchheliometerin1838,comparesquite wellwiththemodernvalueof0.286(cid:1)(cid:1). Determinationsof stellarparallaxmadeinthesameyearbyotherobservers werefarlessaccurate. Itistheeleventhcloseststar,ata distanceof11.4light-years. 61 Cygni is also a well-known binary system, with a period of 653.3 years. Its components are currently separated by 30.3(cid:1)(cid:1) at position angle 150◦. The primary star 61 Cyg A is an orange dwarf, spectral type K5V, ofapparentmagnitude5.20andabsolutemagnitude7.5. Its companion 61 Cyg B is also an orange dwarf, of spectral type K7V, with an apparent magnitude of 6.05 and absolute magnitude 8.3. The system is reputed to be the most extensively observed double star, some thousandsofvisualobservationsbeingsupplementedby morethan34000photographicplates. Preciseastrometric measurements of these plates have indicated that the systemhasatleastoneinvisiblecomponent, believedto beaplanetofsimilarmasstoJupiter,andperhapsasmany asthree,withorbitalperiodsofbetween5and12years. Copyright©NaturePublishingGroup2001 BrunelRoad,Houndmills,Basingstoke,Hampshire,RG216XS,UKRegisteredNo.785998 andInstituteofPhysicsPublishing2001 1 DiracHouse,TempleBack,Bristol,BS16BE,UK AbastumaniAstrophysicalObservatory ENCYCLOPEDIAOFASTRONOMYANDASTROPHYSICS Abastumani Astrophysical Observatory The Abastumani Astrophysical Observatory (AbAO)— longitude,42.83;latitude,41.81degrees—wasfoundedin 1932. ItislocatedinAbastumani,inthesouth-westpart oftheRepublicofGeorgia,250kmwestofthecapitalcity Tbilisi,onthetopofMountKanobiliat1700m. AbAO’s primary mission is to enable astronomers of the former Soviet Union to carry out high-quality observations. The average number of clear nights is 130 per year with 25% of seeings smaller than one arcsec. Atpresent, about100staffmembersworkatthe Observatoryinsixdepartmentsandfourlaboratories.The Observatory’smainfacilitiesare125cmRitchey–Chre´tien and70cmmeniscustelescopes. The major research areas are accretion disks and pulsars astrophysics, solar system cosmogony, objec- tiveprismspectroscopy,low-amplitudeshort-periodvari- ables, AGNs variability, solar physics, solar–terrestrial phenomenaandatmosphericphysics. Forfurtherinformationsee http://gamma.bu.edu/webt/abastumani. Copyright©NaturePublishingGroup2001 BrunelRoad,Houndmills,Basingstoke,Hampshire,RG216XS,UKRegisteredNo.785998 andInstituteofPhysicsPublishing2001 1 DiracHouse,TempleBack,Bristol,BS16BE,UK Abbe,Ernst(1840–1905) ENCYCLOPEDIAOFASTRONOMYANDASTROPHYSICS Abbe, Ernst (1840–1905) BorninEisenach,GrandDuchyofSaxe-Weimar-Eisenach (nowGermany),Abbebecamedirectoroftheobservatory atJenaandresearchdirectoroftheCARLZEISSopticalworks in Jena. He discovered the Abbe sine condition, which describesalensthatwillformanimage,withoutdefects of coma and spherical aberration. His mathematical treatmentfoundedthepresent-dayscienceofoptics. Copyright©NaturePublishingGroup2001 BrunelRoad,Houndmills,Basingstoke,Hampshire,RG216XS,UKRegisteredNo.785998 andInstituteofPhysicsPublishing2001 1 DiracHouse,TempleBack,Bristol,BS16BE,UK Abbott,Francis(1799–1883) ENCYCLOPEDIAOFASTRONOMYANDASTROPHYSICS Abbott, Francis (1799–1883) Watchmaker,borninDerby,England,convict,transported toTasmaniain1845. Hemadeastronomicalobservations attheRossbankObservatoryaftertheendofhissentence until its closure in 1854 and in his private laboratory in Hobart. Copyright©NaturePublishingGroup2001 BrunelRoad,Houndmills,Basingstoke,Hampshire,RG216XS,UKRegisteredNo.785998 andInstituteofPhysicsPublishing2001 1 DiracHouse,TempleBack,Bristol,BS16BE,UK AbellClusters ENCYCLOPEDIAOFASTRONOMYANDASTROPHYSICS Abell Clusters distribution), the composition of the galaxy population (i.e. the fractions of galaxies of different morphological Abell clusters are the most conspicuous groupings of types),thedistributionsoftheluminositiesofthegalaxies, galaxies identified by George Abell on the plates of the the detailed dynamics of the various galaxy classes, firstphotographicsurveymadewiththeSCHMIDTTELESCOPE dynamicalsubstructureandsegregationandthefraction atMountPalomarinthe1950s. Sometimes,thetermAbell of the total mass consisting of baryonic (i.e. ‘ordinary’ clustersisusedasasynonymofnearby,opticallyselected nucleonic) matter. An important recent development is galaxyclusters. thesearchfor,andstudyof,galaxyclustersatverylarge George Abell constructed a catalogue containing distances(i.e.athighredshifts),whicharethe‘forebears’ 2712 of the richest such groupings in the northern sky, ofthelocalrichclustersintheAbellcatalogue. Forthose which was later extended to the southern sky. It is youngerclustersathighredshifts,theAbellclustersserve no exaggeration to say that the total sample of 4076 asalocal,present-day,referencepopulation. clustercandidatesoverthewholeskyhasrevolutionized the study of the large-scale structure in the universe. Abellclustersasasubsetofthetotalcluster The Abell catalogue has formed the basis for the first population quantitativestudiesofthedensestcomponentofthelarge- WhensearchingforclustercandidatesonthePalomarSky scalestructureinthelocaluniverse. Inrecentyears, the Surveyplates,Abellhadnoinformationaboutdistances definitionofsamplesofcandidateclustersfromwide-field (or redshifts) of the galaxies. Therefore he used the survey plates has been repeated with automatic plate- distributionofthegalaxiesinapparentmagnitudetoselect scanning machines. This showed objectively that the those peaks in the projected galaxy distribution that are subjectivefactorinAbell’svisualselectionisquitesmall, mostlikelytocorrespondtoaspatiallycompactstructure. atleastforthericherandmorenearbyclusters. Taking the magnitude of the 10th brightest galaxy as an The reality of the cluster candidates in Abell’s approximate‘standardcandle’,aredshiftwasestimated; catalogue has been the subject of some debate, until this yields the angle subtended by a fixed linear size spectroscopicobservationsoflargenumbersofgalaxiesin of 1.5h−1 Mpc at the distance of the cluster (where h is the directions of theAbell clusters showed convincingly thevalueofthepresentHubbleparameter, expressedin thatonlyasmallfractionoftherichclustersaretheresult units of 100 km s−1 Mpc−1). In a circular aperture with ofchancesuperpositions. Thatis,averylargefractionof radiusequaltothatangle,thenumberofgalaxieswitha therichclustercandidatesinthecataloguemadebyAbell magnitudenotmorethantwomagnitudesfainterthanthe (or,includingthesouthernclusters,byAbell,Corwinand third-brightestgalaxywascounted. Finally,thenumberof Olowin)representcompact,localizedpeaksinthespatial unrelatedgalaxiesintheaperture(anddowntothesame distributionofgalaxies,mostlywithredshiftslessthan0.2, magnitudelimit)wasestimatedfromthegalaxydensity andheldtogetherbygravity. inbackgroundfieldswithoutobviousclustercandidates. Alreadyinthe1930s,FritzZWICKYhadconcludedthat Thecorrectednumberofgalaxies(therichnesscount, theluminousmatter(i.e.thegalaxies)inclustersrepresents i.e. the estimated number of members in the aperture onlyabout10%ofthetotalclustermass,mostofwhichcan above the magnitude limit) was found to have an therefore be detected only through its gravitation. This uncertainty of about 17. Therefore, only clusters with has led to estimates of the total mass (both visible and a corrected galaxy count of at least 50 were considered dark matter) by various means. The most common of by Abell to have been sampled in an unbiased fashion those are the velocities of the galaxies in the cluster, the outtoredshiftsof0.1–0.2. InAbell’soriginal(‘northern’) amount and temperature of the hot (x-ray-emitting) gas catalogue,1682ofthe2712clustercandidateshaveacount and the distortion of the images of galaxies at distances of at least 50. The lower limit in richness count must wellbeyondthatoftheclusterbyGRAVITATIONALLENSING. be applied if one uses the Abell catalogue for statistical For a long time, several of the better-known Abell purposes.Clearly,manylessrichclustersexistbutatlarger clusters, like those in the COMA BERENICES and PERSEUS distances–redshiftstheircontrastwithrespecttothefieldis constellations, have shaped our vision of the class of toolowtoallowarobustdefinitionofastatisticallyreliable rich, populous, clusters. In this schematic view, rich sample. clustersaresmooth,roundandvirializedstructures. This In recent years, an extensive redshift survey (the idealizedpicturecoexistedwiththeknowledgethatthere ESO Nearby Abell Cluster Survey) has been made of aresignificantvariationsinthevariouspropertiesofthe close to 6000 galaxies in about 100 cluster candidates Abell clusters. This has led to many studies of those (mostlyfromthesouthernpartoftheAbell,Corwinand properties,andofcorrelationsbetweenthem,aswellasto Olowin catalogue) with a richness count of at least 50 severalattemptstodescribetheformationandevolution andestimatedredshiftslessthan0.1(seeGALAXYREDSHIFT of rich clusters. It is now realized that clusters are still SURVEYS). The contamination in these redshift surveys by formingandevolvingatthepresentepoch. galaxiesthatdonotbelongtothemainclusterisfarfrom Among the cluster properties that can be studied, negligible, i.e. about 25%. However, the majority of the andforwhichtheoreticalpredictionshavebeenmadeare redshift surveys contains a spatially compact cluster to the 3D shape (or rather, the axial ratios of the galaxy whichatleast50%ofthegalaxieswithmeasuredredshifts Copyright©NaturePublishingGroup2001 BrunelRoad,Houndmills,Basingstoke,Hampshire,RG216XS,UKRegisteredNo.785998 andInstituteofPhysicsPublishing2001 1 DiracHouse,TempleBack,Bristol,BS16BE,UK AbellClusters ENCYCLOPEDIAOFASTRONOMYANDASTROPHYSICS belong. Onlyabout10%ofthecandidateclustersappear or any combination of those. The projected distribution to be a superposition of two almost equally rich (but of the galaxies has many forms and ranges between the relatively poor) systems at different redshifts along the followingextremes. Theremaybeacentralconcentration samelineofsight. of bright galaxies, generally of early type, i.e. ellipticals, For the spatially compact systems, the velocity and frequently one of them is a cD galaxy, i.e. a dispersionshowsaglobalcorrelationwithrichnesscount giantellipticalsurroundedbyanextendedenvelope(see (clusters with higher richness counts on average have ELLIPTICALGALAXIES).Attheotherextremethereareclusters larger velocity dispersions), but the correlation is very thatdonothaveaclearcentralconcentration. broad (at least a factor of 2 in both quantities). The In some clusters, the galaxy distribution is quite uncertainty in the visually estimated richness counts smooth, and in general those clusters contain relatively mightbethoughttoberesponsibleforthis,butthewidth few spiral galaxies. When the fraction of spiral galaxies oftherelationdoesnotdecreaseifoneusesrichnesscounts islarge,thegalaxydistributionisingenerallessregular. basedonmachinescanninginsteadoftheoriginalones. Therelativefractionsofearly-andlate-typegalaxiesare Forasampleofabout150Abellclusterswithredshifts correlatedwithrichnesscount,andthisisamanifestation less than 0.15, cluster masses were calculated from the of the morphology–density relation. The latter shows relativevelocitiesandpositionsofthegalaxies,assuming a clear correlation between the relative fractions of thatthevirialtheoremholdsinthecentralregionsofthe ellipticals, lenticulars (S0s) and spiral galaxies, and the clusters. The cluster masses correlate fairly well with (local) projected galaxy density (and therefore radial the velocity dispersions, but the mass distributions in distance). TheS0smaycontributeupto50%inthecenter, the various intervals of richness counts appear to have with ellipticals not far behind and spiral galaxies about considerable overlap. Therefore, application of a limit 10%. Intheouterparts,ellipticalsarealmostabsentwhile in richness count to a sample ofAbell clusters (which is spiralgalaxiesmayrepresentupto60%. Notethatthese necessary for practical reasons) induces quite a diffuse areglobalvalues: individualclustersshowaconsiderable limitinmass. spreadaroundthese. The clusters, or rather cluster candidates, inAbell’s EventhoughinasizeablefractionoftheAbellclusters cataloguewithrichnesscountsofatleast50arethereforea the galaxy distribution is not very regular or circularly subsetofallclustersinthemassrangefromabout4×1013 symmetric, one can always derive the azimuthally to 2 × 1015M(cid:3). However, for clusters with a velocity averagedprojectednumberdensityprofile(cid:4)(R),inwhich dispersion of at least 800 km s−1, essentially all richness R is the projected distance from the cluster center, i.e. countsarelargerthan50. Inotherwords,allclusterswith theshortestdistancebetweenthelineofsightthrougha avelocitydispersionofatleast800kms−1 arecontained galaxy and the cluster center. Several expressions have inthesamplewithalimitingcountof50,andtheestimate beenproposedforthemathematicaldescriptionof(cid:4)(R), oftheirspacedensityisunbiased. Clusterswithapparent velocitydispersionsgreaterthanabout1200kms−1 turn avlalluofewofh(cid:4)ic(hRh),aiv.ee.t(cid:4)h(rRee=pa0r)a,macehtearrsa.cTtehroissteicalreentghtehcRen(ttrhael outeithertobesuperpositionsortohavelotsofdynamical c distance at which (cid:4)(R) has decreased by a given factor, substructure. say2)andameasureofthedecreaseof(cid:4)(R)intheouter With the advent of all-sky x-ray surveys like those parts(generallythelogarithmicslopeαof(cid:4)(R)). fromtheEINSTEIN(HEAO-2)andROSATmissions,ithasbecome Recently, (cid:4)(R) has been derived for galaxies of possible to construct complete samples of clusters for different morphological types in about 70 rich Abell whichthex-rayfluxfromthehotgasinthepotentialwellof clusters. In individual clusters, the number of galaxies theclusterislargerthanathresholdvalue. Thisproduces of a particular type is generally not sufficient to allow clustercataloguesthatarefundamentallydifferentfrom, an accurate estimate of the three parameters of (cid:4)(R). andthuscomplementaryto,theAbellcatalogue,although By properly combining data for many clusters one can there is quite some overlap. The mass of the x-ray gas compare the representations of (cid:4)(R) for ellipticals, S0s, is generally at least as large as the mass of the cluster spiralsandgalaxieswithemissionlines(mostlyvery‘late’ galaxies, but the combined mass of these two baryonic spirals, such as Sc and Sd, with ionized gas in their components is typically only 10–15% of the total mass. interstellar medium). In other words, by sacrificing the When the total mass of a cluster can be estimated both detailed properties of individual clusters, one obtains a from the kinematics of the galaxies and from the x-ray temperatureandbrightness,thetwoestimatesingeneral pictureofanaveragerichAbellcluster. agreereasonablywell. Thereappearstobeaclearcorrelationbetweengalaxy type and (cid:4)(R): the characteristic length R increases c PropertiesofthegalaxypopulationinAbell markedlyfromearlytolategalaxytype(fromabout0.1to clusters 0.5Mpc).Thisshowsthatellipticalsareindeedmuchmore Inthepast, severalschemeshavebeenproposedforthe centrally concentrated than spirals, while the emission- classification of Abell clusters. All of them summarize linegalaxiesformthemostextendedpopulation. These in one way or another the distribution of the cluster differences must be accompanied by differences in the galaxies in position, magnitude or morphological type, kinematics of galaxies of the various types, because all Copyright©NaturePublishingGroup2001 BrunelRoad,Houndmills,Basingstoke,Hampshire,RG216XS,UKRegisteredNo.785998 andInstituteofPhysicsPublishing2001 2 DiracHouse,TempleBack,Bristol,BS16BE,UK AbellClusters ENCYCLOPEDIAOFASTRONOMYANDASTROPHYSICS galaxyclassesmoveinthesameclusterpotential,which The shapes of Abell clusters have been derived ismostlydeterminedbythedarkmatter. from the projected distributions of galaxies. Using the Such kinematical differences are indeed observed: galaxy positions irrespective of galaxy type, one can the ellipticals and S0s show the smallest dispersion of calculatetheapparentellipticityofacluster. Ingeneral, the line-of-sight component of their velocities, and this the richer clusters are less elongated than the less rich dispersion varies little with projected distance from the ones. The apparent ellipticities for a cluster sample center. Spirals, and in particular emission-line galaxies, of about 100 northern Abell clusters suggest that the have a larger velocity dispersion (by as much as 20– elongated clusters are prolate (cigar like) rather than 30%)whichdecreasesmarkedlytowardslargerprojected oblate. Comparison of these data with the results of distances. Actually, the kinematics of the emission-line numericalN-bodycalculationscanconstrainthetheories galaxies indicates that they have not yet traversed the ofstructureformation. densecentralcores,whichisprobablythereasonwhythey Thefulldistributionofthemassesofavolume-limited havenotyetlosttheirline-emittinggasinencounterswith sampleofAbellclusters(i.e.itsshapeandnormalization) othergalaxies. can also give information for cosmological structure Combining the projected galaxy distributions with formationtheory. AsthesampleofAbellclusterswitha the kinematics one may estimate the distribution of the limiting richness count of 50 has a rather badly defined total (visible plus dark) mass via the Jeans equation of completeness at smaller masses, one must restrict the stellar dynamics. By comparing the distribution of the comparisonbetweenobservationsandpredictionstothe dark matter with that of the luminosity of the galaxies, most massive clusters for which the Abell catalog is complete. one can in principle study the variation of the so-called Itisfarfromtrivialtoderiveindependentinformation mass-to-light ratio with distance from the cluster center. fortheseveralparametersintheformationtheoriesthat Thismaygivecluesaboutdetailsoftheformationprocess, influence the properties of the most massive structures. suchastheeffectsofgalaxyencounters,theroleofthedark Yet, there seems to be general agreement that the latter matterhaloesofthegalaxies,etc. aremorenaturallyunderstoodinauniverseinwhichthe matter density is considerably smaller than the critical Abellclustersascosmologicalprobes density. Several observational properties of Abell clusters have beenusedtoconstrainthetheoriesofformationoflarge- Bibliography scalestructureintheuniverseandtheparametersinthose Book: theories (see also UNIVERSE: SIMULATIONS OF STRUCTUREAND GALAXYFORMATION). These properties include the spatial Giurin G and Mezzetti M (ed) 1999 Observational distribution of Abell clusters, their shapes and their Cosmology:TheDevelopmentofGalaxySystems(Astron. masses. Indifferentways,theseallcarryinformationon SocietyofthePacificConf.Ser.176) thewayinwhichthelargestwell-developedstructuresin Journalarticles: theuniversehaveformedthroughthegrowthoftheinitial fluctuationsinthematterdensity. AbellGO1958Thedistributionofrichclustersofgalaxies The spatial distribution of Abell clusters has been Astrophys.J.Suppl.3211–88 analyzedthroughthetwo-pointcorrelationfunctionξ(r), AbellGO,CorwinHGandOlowinRP1989Acatalogof i.e.thefractionofclusterpairswithacertainseparation, richclustersofgalaxiesAstrophys.J.Suppl.701–138 in excess of the expected number of pairs for a random distribution,whichhasbeenderivedforclustersofvarious Reviews: richness counts. In general, the correlation function is found to have a power-law form: ξ(r) = (r/r )−γ; Bahcall N A 1977 Clusters of galaxies Ann. Rev. Astron. 0 the exponent γ (about 2) does not appear to depend Astrophys.15505 on the limiting richness count, but the value of the Bahcall N A 1988 Large-scale structure in the Universe correlation length r does, and is larger for the richer indicated by galaxy clusters Ann. Rev. Astron. 0 clusters (with a characteristic value of about 20 Mpc). Astrophys.26631 SarazinCL1986X-rayemissionfromclustersofgalaxies In principle, these data allow one to derive the value of Rev.Mod.Phys.581 thecosmologicaldensityaswellastheamplitudeofthe fluctuationspectrum. Another aspect of the distribution of rich Abell PeterKatgert clusters is that they are generally located in the vertices where the sheets and filaments in the general galaxy distribution come together. Therefore, the distribution of rich clusters has sometimes been compared with the distribution of the vertices in so-called Voronoi tesselations,whicharegeometricpartitioningsofspace. Copyright©NaturePublishingGroup2001 BrunelRoad,Houndmills,Basingstoke,Hampshire,RG216XS,UKRegisteredNo.785998 andInstituteofPhysicsPublishing2001 3 DiracHouse,TempleBack,Bristol,BS16BE,UK Aberration ENCYCLOPEDIAOFASTRONOMYANDASTROPHYSICS Aberration (1) The apparent displacement of a star from its mean position on the celestial sphere due to the velocity of the Earth in its orbit around the Sun. The phenomenon was discovered in 1729 by James Bradley (1693–1762) whowas,infact,tryingtomeasurestellarparallax. The displacementiscausedbythecombinationofthevelocity oftheEarthandthevelocityoflightapproachingfromthe source.IftheEarthwerestationary,lightfromastarwould arrivefromthetruedirectionofthissource,butthemotion oftheEarthcausesthelighttoappeartobeapproaching from a point which is slightly displaced in the direction oftheEarth’smotion. Inthecourseofayear,astheEarth travelsroundtheSun,astarwilltraceoutasmallellipsein theskyaboutitsmeanposition. Themaximumradiusof thisellipse(inradians)isequaltotheratioofthespeedof theEarthtothespeedoflight(30kms−1:300000kms−1), that is about 20.5 seconds of arc. The eccentricity of the ellipse depends on the celestial latitude of the star (the figure becomes a circle at the pole of the ecliptic and a straightlineontheecliptic). Thedisplacementduetoaberrationismuchgreater thanthatduetoparallax(theannualparallaxofthenearest star is 0.76 seconds of arc) and this must be allowed for beforetheparallaxcanbedeterminedforastar.Asimilar, thoughsmaller,aberrationeffectoccursduetothespeed ofrotationoftheEarthonitsaxis.Thisisknownasdiurnal aberration. (2) In optical systems, such as lenses and curved mirrors,aberrationreferstotheinabilityofthesystemto produce a perfect image. Unlike a plane mirror, which doesnotcreateaberrations,alensorcurvedmirrorisan imperfect image producer, becoming ideal only for rays passingthrough(orreflectingfrom)itscenterparallelto theopticalaxis(alinethroughthecenter, perpendicular tothelenssurfaces). Themainaberrationsarechromatic, spherical,comaandastigmatism. Seealso: astigmatism,atmosphericrefraction,chromatic aberration,coma,scintillation,sphericalaberration. Copyright©NaturePublishingGroup2001 BrunelRoad,Houndmills,Basingstoke,Hampshire,RG216XS,UKRegisteredNo.785998 andInstituteofPhysicsPublishing2001 1 DiracHouse,TempleBack,Bristol,BS16BE,UK

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