apparent magnitude

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apparent magnitude
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{{for|a more detailed discussion of the history of the magnitude system|Magnitude (astronomy)}}{{short description|measure of brightness for celestial objects, as seen from Earth}}File:65Cyb-LB3-apmag.jpg|thumb|300px|right|Asteroid 65 Cybele65 CybeleThe apparent magnitude ({{mvar|m}}) of an astronomical object is a number that is a measure of its brightness as seen by an observer on Earth. The magnitude scale is logarithmic. A difference of 1 in magnitude corresponds to a change in brightness by a factor of {{radic|100|5}}, or about 2.512. The brighter an object appears, the lower its magnitude value (i.e. inverse relation), with the brightest astronomical objects having negative apparent magnitudes: for example Sirius at −1.46.The measurement of apparent magnitudes or brightnesses of celestial objects is known as photometry. Apparent magnitudes are used to quantify the brightness of sources at ultraviolet, visible, and infrared wavelengths. An apparent magnitude is usually measured in a specific passband corresponding to some photometric system such as the UBV system. In standard astronomical notation, an apparent magnitude in the V ("visual") filter band would be denoted either as mV or often simply as V, as in "mV = 15" or "V = 15" to describe a 15th-magnitude object.


{|class="wikitable" style="float: right; margin-left: 1em; text-align: center;"! Visible totypicalhumaneye! Apparentmagnitude! Bright-nessrelativeto Vega! Number of stars brighter thanapparent magnitudeWEB,weblinkweblink" title="">weblink 2008-02-06, Magnitude, National Solar Observatory—Sacramento Peak, 2006-08-23, in the night sky
Yes|1 (Sirius)
0}}0.0 100% 4
0}}1.0 40% 15
0}}2.0 16% 48
0}}3.0 6.3% 171
0}}4.0 2.5% 513
0}}5.0 1.0% {{val|1602}}
0}}6.0 0.4% {{val|4800}}
0}}6.5 0.25% {{val|9100}}Bright Star Catalogue
No0}}7.0 0.16% {{val|14000}}
0}}8.0 0.063% {{val|42000}}
0}}9.0 0.025% {{val|121000}}
The scale used to indicate magnitude originates in the Hellenistic practice of dividing stars visible to the naked eye into six magnitudes. The brightest stars in the night sky were said to be of first magnitude ({{mvar|m}} = 1), whereas the faintest were of sixth magnitude ({{mvar|m}} = 6), which is the limit of human visual perception (without the aid of a telescope). Each grade of magnitude was considered twice the brightness of the following grade (a logarithmic scale), although that ratio was subjective as no photodetectors existed. This rather crude scale for the brightness of stars was popularized by Ptolemy in his Almagest and is generally believed to have originated with Hipparchus.In 1856, Norman Robert Pogson formalized the system by defining a first magnitude star as a star that is 100 times as bright as a sixth-magnitude star, thereby establishing the logarithmic scale still in use today. This implies that a star of magnitude {{mvar|m}} is about 2.512 times as bright as a star of magnitude {{math|m + 1}}. This figure, the fifth root of 100, became known as Pogson's Ratio.JOURNAL,weblinkfull/seri/MNRAS/00170000012.000.html, Magnitudes of Thirty-six of the Minor Planets for the first day of each month of the year 1857, Norman Robert Pogson, N., Pogson, Monthly Notices of the Royal Astronomical Society, MNRAS, 17, 12, 1856, 1856MNRAS..17...12P, 10.1093/mnras/17.1.12, The zero point of Pogson's scale was originally defined by assigning Polaris a magnitude of exactly 2. Astronomers later discovered that Polaris is slightly variable, so they switched to Vega as the standard reference star, assigning the brightness of Vega as the definition of zero magnitude at any specified wavelength.Apart from small corrections, the brightness of Vega still serves as the definition of zero magnitude for visible and near infrared wavelengths, where its spectral energy distribution (SED) closely approximates that of a black body for a temperature of {{val|11000|u=K}}. However, with the advent of infrared astronomy it was revealed that Vega's radiation includes an Infrared excess presumably due to a circumstellar disk consisting of dust at warm temperatures (but much cooler than the star's surface). At shorter (e.g. visible) wavelengths, there is negligible emission from dust at these temperatures. However, in order to properly extend the magnitude scale further into the infrared, this peculiarity of Vega should not affect the definition of the magnitude scale. Therefore, the magnitude scale was extrapolated to all wavelengths on the basis of the black-body radiation curve for an ideal stellar surface at {{val|11000|u=K}} uncontaminated by circumstellar radiation. On this basis the spectral irradiance (usually expressed in janskys) for the zero magnitude point, as a function of wavelength, can be computed.See weblink" title="https:/-/">weblink. Small deviations are specified between systems using measurement apparatuses developed independently so that data obtained by different astronomers can be properly compared, but of greater practical importance is the definition of magnitude not at a single wavelength but applying to the response of standard spectral filters used in photometry over various wavelength bands.With the modern magnitude systems, brightness over a very wide range is specified according to the logarithmic definition detailed below, using this zero reference. In practice such apparent magnitudes do not exceed 30 (for detectable measurements). The brightness of Vega is exceeded by four stars in the night sky at visible wavelengths (and more at infrared wavelengths) as well as the bright planets Venus, Mars, and Jupiter, and these must be described by negative magnitudes. For example, Sirius, the brightest star of the celestial sphere, has an apparent magnitude of −1.4 in the visible. Negative magnitudes for other very bright astronomical objects can be found in the table below.Astronomers have developed other photometric zeropoint systems as alternatives to the Vega system. The most widely used is the AB magnitude system,JOURNAL, Oke, J. B., Gunn, J. E., Secondary standard stars for absolute spectrophotometry, The Astrophysical Journal, March 15, 1983, 266, 713–717, 10.1086/160817, 1983ApJ...266..713O, in which photometric zeropoints are based on a hypothetical reference spectrum having constant flux per unit frequency interval, rather than using a stellar spectrum or blackbody curve as the reference. The AB magnitude zeropoint is defined such that an object's AB and Vega-based magnitudes will be approximately equal in the V filter band.


File:VISTA Magellanic Cloud Survey view of the Tarantula Nebula.jpg|thumb|upright=1.2|Image of 30 Doradus taken by ESO's VISTA. This nebulanebula(File:Apparent magnitude.svg|thumb|A graph of apparent magnitude against brightness)As the amount of light actually received by a telescope is reduced by transmission through the Earth's atmosphere, any measurement of apparent magnitude is corrected for what it would have been as seen from above the atmosphere. The dimmer an object appears, the higher the numerical value given to its apparent magnitude, with a difference of 5 magnitudes corresponding to a brightness factor of exactly 100. Therefore, the apparent magnitude {{mvar|m}}, in the spectral band {{mvar|x}}, would be given by
m_{x}= -5 log_{100} left(frac {F_x}{F_{x,0}}right),
which is more commonly expressed in terms of common (base-10) logarithms as
m_{x} = -2.5 log_{10} left(frac {F_x}{F_{x,0}}right),
where {{mvar|Fx}} is the observed flux density using spectral filter {{mvar|x}}, and {{math|Fx,0}} is the reference flux (zero-point) for that photometric filter. Since an increase of 5 magnitudes corresponds to a decrease in brightness by a factor of exactly 100, each magnitude increase implies a decrease in brightness by the factor {{radic|100|5}} ≈ 2.512 (Pogson's ratio). Inverting the above formula, a magnitude difference {{math|m1 − m2 {{=}} Δm}} implies a brightness factor of
frac{F_2}{F_1} = 100^frac{Delta m}{5} = 10^{0.4 Delta m} approx 2.512^{Delta m}.

Example: Sun and Moon

What is the ratio in brightness between the Sun and the full Moon?The apparent magnitude of the Sun is −26.74 (brighter), and the mean apparent magnitude of the full moon is −12.74 (dimmer).Difference in magnitude:
x = m_1 - m_2 = (-12.74) - (-26.74) = 14.00.
Brightness factor:
v_b = 10^{0.4 x} = 10^{0.4 times 14.00} approx 398,107.17.
The Sun appears about {{val|400000}} times brighter than the full moon.

Magnitude addition

Sometimes one might wish to add brightnesses. For example, photometry on closely separated double stars may only be able to produce a measurement of their combined light output. How would we reckon the combined magnitude of that double star knowing only the magnitudes of the individual components? This can be done by adding the brightnesses (in linear units) corresponding to each magnitude.WEB, Magnitude Arithmetic,weblink Weekly Topic, Caglow, 30 January 2012,
10^{-m_f times 0.4} = 10^{-m_1 times 0.4} + 10^{-m_2 times 0.4}.
Solving for m_f yields
m_f = -2.5log_{10} left(10^{-m_1 times 0.4} + 10^{-m_2 times 0.4} right),
where {{mvar|mf}} is the resulting magnitude after adding the brightnesses referred to by {{math|m1}} and {{math|m2}}.

Absolute magnitude

Since flux decreases with distance according to the inverse-square law, a particular apparent magnitude could equally well refer to a star at one distance, or a star four times brighter at twice that distance, and so on. When one is not interested in the brightness as viewed from Earth, but the intrinsic brightness of an astronomical object, then one refers not to the apparent magnitude but the absolute magnitude. The absolute magnitude {{mvar|M}}, of a star or astronomical object is defined as the apparent magnitude it would have as seen from a distance of 10 parsecs (about 32.6 light-years). The absolute magnitude of the Sun is 4.83 in the V band (yellow) and 5.48 in the B band (blue).WEB
, Some Useful Astronomical Definitions
, Stony Brook Astronomy Program
, Aaron
, Evans
, 2009-07-12, In the case of a planet or asteroid, the absolute magnitude {{mvar|H}} rather means the apparent magnitude it would have if it were 1 astronomical unit from both the observer and the Sun, and fully illuminated (a configuration that is only theoretically achievable, with the observer situated on the surface of the Sun).

STANDARD REFERENCE VALUES {, class"wikitable floatright" style"text-align:center;", + Standard apparent magnitudes and fluxes for typical bands{{cite web

, Astronomical Magnitude Systems
, Harvard-Smithsonian Center for Astrophysics
, John
, Huchra
, 2017-07-18
, ! rowspan="2" | Band! rowspan="2" | {{mvar|λ}}(μm)! rowspan="2" | {{math|{{sfrac|Δλ|λ}}}}(FWHM)! colspan="2" | Flux at {{math|m {{=}} 0}}, {{math|Fx,0}}
! Jy! 10−20 erg/(s·cm2·Hz)
| 1.81
| 4.26
| 3.64
| 3.08
| 2.55
| 1.60
| 1.08
| 0.67
| 3.73
| 4.49
| 4.76
| 4.81
It is important to note that the scale is logarithmic: the relative brightness of two objects is determined by the difference of their magnitudes. For example, a difference of 3.2 means that one object is about 19 times as bright as the other, because Pogson's Ratio raised to the power 3.2 is approximately 19.05.A common misconception is that the logarithmic nature of the scale is because the human eye itself has a logarithmic response. In Pogson's time this was thought to be true (see Weber–Fechner law), but it is now believed that the response is a power law (see Stevens' power law).JOURNAL, Misconceptions About Astronomical Magnitudes, Eric Schulman, E., Schulman, C. V., Cox, American Journal of Physics, 65, 10, 1003, 1997, 1997AmJPh..65.1003S, 10.1119/1.18714, Magnitude is complicated by the fact that light is not monochromatic. The sensitivity of a light detector varies according to the wavelength of the light, and the way it varies depends on the type of light detector. For this reason, it is necessary to specify how the magnitude is measured for the value to be meaningful. For this purpose the UBV system is widely used, in which the magnitude is measured in three different wavelength bands: U (centred at about 350 nm, in the near ultraviolet), B (about 435 nm, in the blue region) and V (about 555 nm, in the middle of the human visual range in daylight). The V band was chosen for spectral purposes and gives magnitudes closely corresponding to those seen by the light-adapted human eye, and when an apparent magnitude is given without any further qualification, it is usually the V magnitude that is meant, more or less the same as visual magnitude.Because cooler stars, such as red giants and red dwarfs, emit little energy in the blue and UV regions of the spectrum their power is often under-represented by the UBV scale. Indeed, some L and T class stars have an estimated magnitude of well over 100, because they emit extremely little visible light, but are strongest in infrared.Measures of magnitude need cautious treatment and it is extremely important to measure like with like. On early 20th century and older orthochromatic (blue-sensitive) photographic film, the relative brightnesses of the blue supergiant Rigel and the red supergiant Betelgeuse irregular variable star (at maximum) are reversed compared to what human eyes perceive, because this archaic film is more sensitive to blue light than it is to red light. Magnitudes obtained from this method are known as photographic magnitudes, and are now considered obsolete.For objects within the Milky Way with a given absolute magnitude, 5 is added to the apparent magnitude for every tenfold increase in the distance to the object. For objects at very great distances (far beyond the Milky Way), this relationship must be adjusted for redshifts and for non-Euclidean distance measures due to general relativity.JOURNAL, 2014CQGra..31t5001U, 1402.1933, Nonlinear relativistic corrections to cosmological distances, redshift and gravitational lensing magnification: II. Derivation, Classical and Quantum Gravity, 31, 20, 205001, Umeh, Obinna, Clarkson, Chris, Maartens, Roy, 2014, 10.1088/0264-9381/31/20/205001, ARXIV, astro-ph/0210394, The K correction, Hogg, David W., Baldry, Ivan K., Blanton, Michael R., Eisenstein, Daniel J., 2002, For planets and other Solar System bodies the apparent magnitude is derived from its phase curve and the distances to the Sun and observer.{{clear}}

Table of notable celestial objects{| class"wikitable"|+Apparent visual magnitudes of known celestial objects

! Apparentmagnitude(V)! width="215px" | Object! Seen from...!Notes
gamma-ray burst GRB 080319B >Astronomical unit>AU away|
R136a1 >| seen from 1 AU away|
Zeta1 Scorpii>Zeta1 Scorpii seen from 1 AU away|
Rigel >| seen from 1 AU away|It would be seen as a large very bright bluish disk of 35° apparent diameter.
Sirius A >| seen from 1 AU away|
Sun >Mercury (planet)>Mercury at perihelion|
| seen from Venus at perihelion|
| seen from Earth|About 400,000 times brighter than mean full moon
| seen from Mars at aphelion|
Minimum brightness that causes the typical eye slight pain to look at
| seen from Jupiter at aphelion|
| seen from Saturn at aphelion|
| seen from Uranus at aphelion|
| seen from Neptune|
| seen from Pluto at aphelion|
Eris (dwarf planet)>Eris at aphelion|
full moon >| seen from Earth at perihelionOpposition surge>opposition effect)
90377 Sedna>Sedna at aphelion|
Comet Ikeya–Seki>Ikeya–Seki (1965) seen from EarthKreutz Sungrazer of modern timesHTTP://WWW.ICQ.EPS.HARVARD.EDU/BRIGHTEST.HTMLPUBLISHER=INTERNATIONAL COMET QUARTERLY, 18 December 2011,
Iridium flare>Iridium (satellite) flare seen from Earth|maximum brightness
SN 1006>supernova of 1006 seen from Earth|the brightest stellar event in recorded history (7200 light-years away)
The total integrated magnitude of the night sky >| seen from Earth|
SN 1054>Crab Supernova of 1054 seen from Earth|(6500 light-years away)
International Space Station >| seen from Earthperigee and fully lit by the SunHTTP://WWW.HEAVENS-ABOVE.COM/SATINFO.ASPX?SATID=25544PUBLISHER=HEAVENS-ABOVE, 2007-12-22,
| seen from Earth|maximum brightness when illuminated as a crescent
| seen from Earth|mean brightness
Faintest objects observable during the day with naked eye when Sun is high
Epsilon Canis Majoris >| seen from EarthList of brightest stars>brightest star of the last and next five million years
| seen from Earth|minimum brightness when it is on the far side of the Sun
| seen from Earth|maximum brightness
| seen from Earth|maximum brightness
Faintest objects visible during the day with naked eye when Sun is less than 10° above the horizon
new moon >| seen from Earth|minimum brightness
| seen from Earth|maximum brightness at superior conjunction (unlike Venus, Mercury is at its brightest when on the far side of the Sun, the reason being their different phase curves)
| seen from Earth|mean brightness
| seen from Earth|minimum brightness
| seen from Earth|Brightest star except for the Sun at visible wavelengths
Eta Carinae >| seen from Earth|apparent brightness as a supernova impostor in April 1843
Canopus (star)>Canopus seen from Earth|2nd brightest star in night sky
| seen from Earth|maximum brightness near opposition and perihelion when the rings are angled toward Earth
Halley's Comet#History>Halley's comet seen from Earth|Expected apparent magnitude at 2061 passage
Alpha Centauri AB >| seen from Earth|Combined magnitude (3rd brightest star in night sky)
Arcturus (star)>Arcturus seen from Earth|4th brightest star to the naked eye
| seen from Earth|4th brightest individual star visible telescopically in the night sky
Vega >| seen from Earth|which was originally chosen as a definition of the zero point
| seen from Earth|mean brightness
| seen from Alpha Centauri|
| seen from Earth|mean brightness
| seen from Earth|mean brightness
| seen from Earth|minimum brightness
| seen from Earth|minimum brightness
SN 1987A >| seen from Earth|in the Large Magellanic Cloud (160,000 light-years away)
Faintest stars visible in an urban neighborhood with naked eye
Andromeda Galaxy >| seen from Earth|M31
| +4|Orion Nebula|seen from Earth|M42
Ganymede (moon)>Ganymede seen from Earth|maximum brightness (moon of Jupiter and the largest moon in the Solar System)
Messier 41>M41 seen from EarthAristotleHTTP://MESSIER.SEDS.ORG/MORE/M041_ARI.HTMLDATE=2006-07-28ACCESSDATE=2009-11-29,
| +4.5|Sagittarius Dwarf Spheroidal Galaxy|seen from Earth|
4 Vesta>Vesta seen from Earth|maximum brightness
WEBSITE=NSSDC.GSFC.NASA.GOVACCESS-DATE=2018-11-08, | seen from Earth|maximum brightness
| seen from Earth|mean brightness
Triangulum Galaxy>M33 seen from Earthnaked eye seeing under dark skiesHTTP://SIMBAD.U-STRASBG.FR/SIMBAD/SIM-ID?IDENT=M33PUBLISHER=SIMBAD ASTRONOMICAL DATABASELAST=LODRIGUSSDATE=1993, 2009-11-27, (Shows bolometric magnitude not visual magnitude.)
gamma-ray burst GRB 080319B >| seen from Earth|Peak visual magnitude (the "Clarke Event") seen on Earth on March 19, 2008 from a distance of 7.5 billion light-years.
| seen from Earth|minimum brightness
2 Pallas>Pallas seen from Earth|maximum brightness
Approximate limit of stars observed by a mean naked eye observer under very good conditions. There are about 9,500 stars visible to mag 6.5.
Ceres (dwarf planet)>Ceres seen from Earth|maximum brightness
7 Iris>Iris seen from Earth|maximum brightness
Messier 81>M81 seen from EarthDATE=2007-09-02ACCESSDATE=2009-11-28,
''Extreme naked-eye limit, Class 1 on Bortle scale, the darkest skies available on EarthFEBRUARY 2001>TITLE=THE BORTLE DARK-SKY SCALE AUTHOR=JOHN E. BORTLE ACCESSDATE=2009-11-18, ''
| seen from Earth|minimum brightness
WEBSITE=NSSDC.GSFC.NASA.GOVACCESS-DATE=2018-11-08, planet Neptune seen from Earth|maximum brightness
| seen from Earth|mean brightness
| seen from Earth|minimum brightness
Titan (moon)>Titan seen from Earth|maximum brightness; largest moon of Saturn; mean opposition magnitude 8.4
| +8.29|star UY Scuti|seen from Earth|Maximum brightness; largest known star by radius
10 Hygiea >| seen from Earth|maximum brightness
Faintest objects visible using common 7×50 binoculars under typical conditions
Iapetus (moon)>Iapetus seen from Earth|maximum brightness, brightest when west of Saturn and takes 40 days to switch sides
| +10.7|Luhman 16|seen from Earth|Closest brown dwarfs
| +11.05|star Proxima Centauri|seen from Earth|2nd closest star
| +11.8
Phobos (moon)>Phobos|seen from Earth|Maximum brightness; brightest moon of Mars
| +12.23|star R136a1|seen from Earth
WORK=SPACE.COM, 2018-11-05,
| +12.89
Deimos (moon)>Deimos|seen from Earth|Maximum brightness
quasar 3C 273 >| seen from Earth|brightest (luminosity distance of 2.4 billion light-years)
Triton (moon)>Triton seen from Earth|Maximum brightness
Pluto#Observation>Pluto seen from Earth|maximum brightness, 725 times fainter than magnitude 6.5 naked eye skies
| +13.9
Titania (moon)>Titania|seen from Earth|Maximum brightness; brightest moon of Uranus
| +14.1|star WR 102|seen from Earth|Hottest known star
Centaur (minor planet)>centaur 2060 Chiron >| seen from Earth|maximum brightness
Charon (moon)>Charon seen from Earth|maximum brightness (the largest moon of Pluto)
Makemake >| seen from EarthOpposition (astronomy and astrology)>opposition brightness
Haumea >| seen from Earth|Current opposition brightness
Eris (dwarf planet)>Eris seen from Earth|Current opposition brightness
Callirrhoe (moon)>Callirrhoe seen from Earth|(small ≈8 km satellite of Jupiter)
''Faintest objects observable in visible light with a 600 mm (24″) Ritchey-Chrétien telescope with 30 minutes of stacked images (6 subframes at 5 minutes each) using a Charge-coupled device2009-10-05PUBLISHER=LIGHTBUCKETSURL=HTTP://WWW.LIGHTBUCKETS.COM/NEWS/37/17-NEW-ASTEROIDS-FOUND-BY-LIGHTBUCKETS/DEAD-URL=YESACCESSDATE=2009-11-15, ''
Hydra (moon)>Hydra seen from Earth|maximum brightness of Pluto's moon
Nix (moon)>Nix seen from Earth|maximum brightness of Pluto's moon
Fenrir (moon)>Fenrir seen from Earth|(small ≈4 km satellite of Saturn)
| seen from Earth5000e9kmlk=on}} from the SunMagnitude difference is 2.512 log10[(5000/5)2 × (4999/4)2] ˜ 30.6, so Jupiter is 30.6 magnitudes fainter at 5000 AU
Faintest objects observable with an 8-meter class ground-based telescope such as the Subaru Telescope in a 10-hour imageWhat is the faintest object imaged by ground-based telescopes?, by: The Editors of Sky Telescope, July 24, 2006
Halley's Comet >| seen from EarthDATE=2003-09-01ESO>ARCHIVEURL=HTTPS://WEB.ARCHIVE.ORG/WEB/20090301212846/HTTP://WWW.ESO.ORG/PUBLIC/OUTREACH/PRESS-REL/PR-2003/PHOT-27-03.HTMLDEADURL=NO, 2009-02-22,
2003 BH| seen from Earth|observed magnitude of ≈15-kilometer Kuiper belt object Seen by the Hubble Space Telescope (HST) in 2003, dimmest known directly-observed asteroid.
''Faintest objects observable in visible light with Hubble Space TelescopeILLINGWORTH >FIRST1=G. D. FIRST2=D. FIRST3=P. A. FIRST4=R. J. FIRST5=I. FIRST6=M. FIRST7=P. G. FIRST8=M. FIRST9=M. FIRST10=C. M. FIRST11=V. JOURNAL=THE ASTROPHYSICAL JOURNAL SUPPLEMENT SERIES VOLUME=209 PAGES=6 BIBCODE=2013APJS..209....6I, 10.1088/0067-0049/209/1/6, ''
''Faintest objects observable in visible light with James Webb Space Telescope]weblink (retrieved Sep 14 2017)
LBV 1806-20 >| seen from Earth|a luminous blue variable star, expected magnitude at visible wavelengths due to interstellar extinction
{{See also|List of brightest stars}}
Some of the above magnitudes are only approximate. Telescope sensitivity also depends on observing time, optical bandpass, and interfering light from scattering and airglow.

See also

{{Colbegin|colwidth=20em}} {{colend}}


WEB, AstDys (10) Hygiea Ephemerides, Department of Mathematics, University of Pisa, Italy,weblink 2010-06-26, WEB, AstDys (2060) Chiron Ephemerides, Department of Mathematics, University of Pisa, Italy,weblink 2010-06-26, WEB, AstDys (136472) Makemake Ephemerides, Department of Mathematics, University of Pisa, Italy,weblink 2010-06-26, WEB, AstDys (136108) Haumea Ephemerides, Department of Mathematics, University of Pisa, Italy,weblink 2010-06-26, WEB, Sirius, SIMBAD Astronomical Database,weblink 2010-06-26, WEB, Canopus, SIMBAD Astronomical Database,weblink 2010-06-26, WEB, Vega, SIMBAD Astronomical Database,weblink 2010-04-14, WEB, Arcturus, SIMBAD Astronomical Database,weblink 2010-06-26, {{cite web |title=Vmag

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