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| {{Other uses|Magnitude (disambiguation)}}
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| '''Magnitude''' is the [[logarithm]]ic measure of the brightness of an object, in [[astronomy]], measured in a specific [[wavelength]] or [[passband]], usually in [[light|optical]] or [[infrared|near-infrared]] wavelengths.
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| The sun has an apparent magnitude of -27, a full moon -13 and the brightest planet Venus measures -5. The brightest man-made objects, Iridium flares are ranked at -9 and the International Space Station -6.
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| ==Background==
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| The magnitude system dates back roughly 2000 years to the Greek astronomer [[Hipparchus]] (or the Alexandrian astronomer [[Ptolemy]]—references vary) who classified stars by their apparent brightness, which they saw as size (“magnitude means bigness”<ref>
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| {{Citation
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| | last = Heifetz
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| | first = M.
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| | last2 = Tirion
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| | first2 = W.
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| | title = A walk through the heavens: a guide to stars and constellations and their legends
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| | year = 2004
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| | publisher = Cambridge University Press
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| | publication-place = Cambridge
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| | page = 6
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| }}</ref>). To the unaided eye, a more prominent star such as [[Sirius]] or [[Arcturus]] appears larger than a less prominent star such as [[Mizar and Alcor|Mizar]], which in turn appears larger than a truly faint star such as [[Mizar and Alcor|Alcor]]. The following quote from 1736 gives an excellent description of the ancient naked-eye magnitude system:
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| <blockquote>
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| The ''fixed Stars'' appear to be of different Bignesses, not because they really are so, but because they are not all equally distant from us [Note—today astronomers know that the brightness of stars is a function of both their distance and their own luminosity]. Those that are nearest will excel in Lustre and Bigness; the more remote ''Stars'' will give a fainter Light, and appear smaller to the Eye. Hence arise the Distribution of ''Stars'', according to their Order and Dignity, into ''Classes''; the first Class containing those which are nearest to us, are called ''Stars'' of the first Magnitude; those that are next to them, are ''Stars'' of the second Magnitude ... and so forth, 'till we come to the ''Stars'' of the sixth Magnitude, which comprehend the smallest ''Stars'' that can be discerned with the bare Eye. For all the other ''Stars'', which are only seen by the Help of a Telescope, and which are called Telescopical, are not reckoned among these six Orders. Altho' the Distinction of ''Stars'' into six Degrees of Magnitude is commonly received by ''Astronomers''; yet we are not to judge, that every particular ''Star'' is exactly to be ranked according to a certain Bigness, which is one of the Six; but rather in reality there are almost as many Orders of ''Stars'', as there are ''Stars'', few of them being exactly of the same Bigness and Lustre. And even among those ''Stars'' which are reckoned of the brightest Class, there appears a Variety of Magnitude; for ''Sirius'' or ''Arcturus'' are each of them brighter than ''Aldebaran'' or the ''Bull's'' Eye, or even than the ''Star'' in ''Spica''; and yet all these ''Stars'' are reckoned among the ''Stars'' of the first Order: And there are some ''Stars'' of such an intermedial Order, that the ''Astronomers'' have differed in classing of them; some putting the same ''Stars'' in one Class, others in another. For Example: The little ''Dog'' was by ''Tycho'' placed among the ''Stars'' of the second Magnitude, which ''Ptolemy'' reckoned among the ''Stars'' of the first Class: And therefore it is not truly either of the first or second Order, but ought to be ranked in a Place between both.<ref>
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| {{Citation
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| | last = Keill
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| | first = J.
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| | title = An introduction to the true astronomy (3rd Ed.)
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| | year = 1739
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| | pages = 47–48
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| | publication-place = London
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| }}</ref>
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| </blockquote>
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| Note that the brighter the star, the smaller the magnitude: Bright "first magnitude" stars are "1st-class" stars, while stars barely visible to the naked eye are "sixth magnitude" or "6th-class".
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| [[Tycho Brahe]] attempted to directly measure the “bigness” of the stars in terms of angular size, which in theory meant that a star's magnitude could be determined by more than just the subjective judgment described in the above quote. He concluded that first magnitude stars measured 2 [[Minute of arc|arc minutes]] (2’) in apparent diameter (1/30 of a degree, or 1/15 the diameter of the full moon), with second through sixth magnitude stars measuring 3/2’, 13/12’, 3/4’, 1/2’, and 1/3’, respectively.<ref>
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| {{Citation
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| | last = Thoren
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| | first = V. E.
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| | title = The Lord of Uraniborg
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| | year = 1990
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| | publisher = Cambridge University Press
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| | publication-place = Cambridge
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| | page = 306
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| }}</ref> The development of the telescope showed that these large sizes were illusory—stars appeared much smaller through the telescope. However, early telescopes produced a spurious disk-like image of a star (known today as an [[Airy disk]]) that was larger for brighter stars and smaller for fainter one. Astronomers from [[Galileo Galilei|Galileo]] to [[Jacques Cassini|Jaques Cassini]] mistook these spurious disks for the physical bodies of stars, and thus into the eighteenth century continued to think of magnitude in terms of the physical size of a star.<ref name="Graney/Grayson"/> [[Johannes Hevelius]] produced a very precise table of star sizes measured telescopically, but now the measured diameters ranged from just over six [[Minute of arc|''seconds'' of arc]] for first magnitude down to just under 2 seconds for sixth magnitude.<ref name="Graney/Grayson">
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| {{Citation
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| | last = Graney
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| | first = C. M.
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| | last2 = Grayson
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| | first2 = T. P.
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| | title = On the Telescopic Disks of Stars: A Review and Analysis of Stellar Observations from the Early 17th through the Middle 19th Centuries
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| | journal = Annals of Science
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| | volume = 68
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| | issue = 3
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| | pages = 351–373
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| | year = 2011
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| | doi = 10.1080/00033790.2010.507472
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| }}</ref><ref>
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| {{Citation
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| | last = Graney
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| | first = C. M.
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| | title = 17th Century Photometric Data in the Form of Telescopic Measurements of the Apparent Diameters of Stars by Johannes Hevelius
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| | journal = Baltic Astronomy
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| | volume = 18
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| | issue = 3–4
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| | pages = 253–263
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| | year = 2009
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| |bibcode = 2009BaltA..18..253G |arxiv = 1001.1168 }}</ref> By the time of [[William Herschel]] astronomers recognized that the telescopic disks of stars were spurious and a function of the telescope as well as the brightness of the stars, but still spoke in terms of a star's size more than its brightness.<ref name="Graney/Grayson"/> Even well into the nineteenth century the magnitude system continued to be described in terms of six classes determined by apparent size, in which
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| <blockquote>
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| There is no other rule for classing the stars but the estimation of the observer; and hence it is that some astronomers reckon those stars of the first magnitude which others esteem to be of the second.<ref>
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| {{Citation
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| | last = Ewing
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| | first = A.
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| | last2 = Gemmere
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| | first2 = J.
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| | title = Practical Astronomy
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| | year = 1812
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| | publisher = Allison & Co.
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| | publication-place = Burlington, N. J.
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| | page = 41
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| }}</ref>
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| </blockquote>
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| However, by the mid-nineteenth century astronomers had measured the distances to stars via [[stellar parallax]], and so understood that stars are so far away as to essentially appear as [[point source]]s of light. Following advances in understanding the [[Airy disk|diffraction of light]] and [[Astronomical seeing]], astronomers fully understood both that the apparent sizes of stars were spurious and how those sizes depended on the intensity of light coming from a star (this is the star's apparent brightness, which can be measured in units such as Watts/cm<sup>2</sup>) so that brighter stars appeared larger. Photometric measurements (made, for example, by using a light to project an artificial “star” into a telescope’s field of view and adjusting it to match real stars in brightness) had shown that that first magnitude stars are about 100 times brighter than sixth-magnitude stars. Thus in 1856 Norman R. Pogson of Oxford proposed that a standard ratio of 2.512 (<math>\approx \sqrt[5]{100}</math>) be adopted between magnitudes, so five magnitude steps corresponded precisely to a factor of 100 in brightness.<ref>
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| {{Citation
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| | last = Hoskin
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| | first = M.
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| | title = The Cambridge Concise History of Astronomy
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| | year = 1999
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| | publisher = Cambridge University Press
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| | publication-place = Cambridge
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| | page = 258
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| }}</ref><ref>
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| {{Citation
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| | last = Tassoul
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| | first = J. L.
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| | last2 = Tassoul
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| | first2 = M.
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| | title = A Concise History of Solar and Stellar Physics
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| | year = 2004
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| | publisher = Princeton University Press
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| | publication-place = Princeton
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| | page = 47
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| }}</ref> This is the modern magnitude system, which measures the brightness, not the apparent size, of stars. Using this logarithmic scale, it is possible for a star to be brighter than “first class”, so Arcturus is magnitude 0, and Sirius is magnitude −1.46.
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| ==Apparent magnitude==
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| {{Main|Apparent magnitude}}
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| Under the modern logarithmic magnitude scale, two objects, one of which is a used as a reference or baseline, whose [[Intensity (physics)|intensities]] (brightnesses) measured from [[Earth]] in units of power per unit area (such as Watts per square metre or Wm<sup>−2</sup>) are I<sub>1</sub> and I<sub>ref</sub> and will have magnitudes m<sub>1</sub> and m<sub>ref</sub> related by;
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| <math>m_1-m_{ref}=-2.5\log_{10} \left ( \frac{I_1}{I_{ref}} \right )</math>
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| Using this formula, the magnitude scale can be extended beyond the ancient magnitude 1–6 range, and it becomes a precise measure of brightness rather than simply a classification system. [[Astronomer]]s can now measure differences as small as one-hundredth of a magnitude. Stars between magnitudes 1.5 and 2.5 are called second-magnitude; there are some 20 stars brighter than 1.5, which are first-magnitude stars (see the [[list of brightest stars]]). For example, [[Sirius]] is magnitude −1.46, [[Arcturus]] is −0.04, [[Aldebaran]] is 0.85, [[Spica]] is 1.04, and [[Procyon]] (the little Dog) is 0.34. Under the ancient magnitude system, all of these stars might have been classified as "stars of the first magnitude".
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| Magnitudes can also be calculated for objects far brighter than stars (such as the [[Sun]] and [[Moon]]), and for objects too faint for the human eye to see (such as [[Pluto]]). What follows is a table giving magnitudes for objects ranging from the Sun to the faintest object visible with the [[Hubble Space Telescope|Hubble Space Telescope (HST)]]:
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| {|class="wikitable" style="text-align:center; border:none; background:transparent;"
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| !Apparent<br />magnitude !! Brightness<br />relative to<br />magnitude 0 !! Example
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| !rowspan="21" style="border:none; background:transparent;"|
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| !Apparent<br />magnitude !! Brightness<br />relative to<br />magnitude 0 !! Example
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| !rowspan="21" style="border:none; background:transparent;"|
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| !Apparent<br />magnitude !! Brightness<br />relative to<br />magnitude 0 !! Example
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| |-
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| | −27||6.31{{e|10}}||Sun||−7||631||[[SN 1006|SN 1006 supernova]]||13||6.31{{e|−6}}||[[3C 273|3C 273 quasar]]
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| |-
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| | −26||2.51{{e|10}}||||−6||251||[[International Space Station|ISS]] (max)||14||2.51{{e|−6}}||Pluto (max)
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| |-
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| | −25||1{{e|10}}||||−5||100||[[Venus]] (max)||15||1{{e|−6}}||
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| |-
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| | −24||3.98{{e|9}}||||−4||39.8||||16||3.98{{e|−7}}||[[Charon (moon)|Charon]] (max)
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| |-
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| | −23||1.58{{e|9}}||||−3||15.8||[[Jupiter]] (max), [[Mars]] (max)||17||1.58{{e|−7}}||
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| |-
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| | −22||6.31{{e|8}}||||−2||6.31||[[Mercury (planet)|Mercury]] (max)||18||6.31{{e|−8}}||
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| |-
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| | −21||2.51{{e|8}}||||−1||2.51||Sirius||19||2.51{{e|−8}}||
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| |-
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| | −20||1{{e|8}}||||0||1||[[Vega]], [[Saturn]] (max)||20||1{{e|−8}}||
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| |-
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| | −19||3.98{{e|7}}||||1||0.398||[[Antares]]||21||3.98{{e|−9}}||[[Callirrhoe (moon)|Callirrhoe]] (satellite of Jupiter)
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| |-
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| | −18||1.58{{e|7}}||||2||0.158||[[Polaris]]||22||1.58{{e|−9}}||
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| |-
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| | −17||6.31{{e|6}}||||3||0.0631||[[Cor Caroli]]||23||6.31{{e|−10}}||
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| |-
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| | −16||2.51{{e|6}}||||4||0.0251||[[Acubens]]||24||2.51{{e|−10}}||
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| |-
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| | −15||1{{e|6}}||||5||0.01||[[4 Vesta|Vesta]] (max), [[Uranus]] (max)||25||1{{e|−10}}||[[Fenrir (moon)|Fenrir]] (satellite of Saturn)
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| |-
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| | −14||3.98{{e|5}}||||6||3.98{{e|−3}}||typical limit of naked eye{{refn|group=note|Under very dark skies, such as are found in remote rural areas}}||26||3.98{{e|−11}}||
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| |-
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| | −13||1.58{{e|5}}||Full moon||7||1.58{{e|−3}}||[[Ceres (dwarf planet)|Ceres]] (max)||27||1.58{{e|−11}}||visible light limit of [[Optical telescope#Astronomical research telescopes|8m telescopes]]
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| |-
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| | −12||6.31{{e|4}}||||8||6.31{{e|−4}}||[[Neptune]] (max)||28||6.31{{e|−12}}||
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| |-
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| | −11||2.51{{e|4}}||||9||2.51{{e|−4}}||||29||2.51{{e|−12}}||
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| |-
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| | −10||1{{e|4}}||||10||1{{e|−4}}||typical limit of 7x50 binoculars||30||1{{e|−12}}||
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| |-
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| | −9||3.98{{e|3}}||[[Iridium flare]]||11||3.98{{e|−5}}||||31||3.98{{e|−13}}||
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| |-
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| | −8||1.58{{e|3}}||||12||1.58{{e|−5}}||||32||1.58{{e|−13}}||visible light limit of HST
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| |}
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| ==Absolute scale based on Vega==
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| {{Main|Absolute magnitude}}
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| Under the Vega system for measuring the brightness of astronomical brightness, the star [[Vega]] is defined to have an apparent magnitude of [[zero]] as measured through all filters, although this is only an approximation e.g. its actual brightness has been measured to be 0.03 in the V (visual) band. The brightest star, [[Sirius]], has a Vega magnitude of −1.46. or −1.5. However, Vega has been found to vary in brightness, and other standards are in common use.<ref>
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| {{Citation
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| | last = Milone
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| | first = E. F.
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| | title = Astronomical Photometry: Past, Present and Future
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| | year = 2011
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| | publisher = Springer
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| | publication-place = New York
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| | pages = 182–184
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| | isbn = 978-1-4419-8049-6
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| }}</ref> One such system is the [[AB magnitude]] system, in which the reference is a source with a constant flux density per unit frequency. Another is the STMAG system, in which the reference source is instead defined to have constant flux density per unit wavelength.
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| ==Problems==
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| The human eye is easily fooled, and Hipparchus's scale has had problems. For example, the human eye is more sensitive to [[yellow]]/[[red]] light than to [[blue]], and [[photograph]]ic film more to blue than to yellow/red, giving different values of [[visual magnitude]] and [[photographic magnitude]]. Furthermore, many people find it counter-intuitive that a high magnitude star is dimmer than a low magnitude star.
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| ==Apparent and absolute magnitude==
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| Two specific types of magnitudes distinguished by astronomers are:
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| * [[Apparent magnitude]], the apparent brightness of an object. For example, [[Alpha Centauri]] has higher apparent magnitude (i.e. lower value) than [[Betelgeuse]], because it is much closer to the [[Earth]].
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| * [[Absolute magnitude]], which measures the [[luminosity]] of an object (or reflected light for non-luminous objects like [[asteroid]]s); it is the object's apparent magnitude as seen from a certain distance. For [[star]]s it is 10 [[parsec]]s (32.6 [[light year]]s). Betelgeuse has much higher absolute magnitude than Alpha Centauri, because it is much more luminous.
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| Usually only apparent magnitude is mentioned, because it can be measured directly; absolute magnitude can be calculated from apparent magnitude and distance using;
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| :<math>m - M = 5 \left( log_{10}(d) - 1 \right) </math>
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| This is known as the [[distance modulus]], where ''d'' is the distance to the star measured in [[parsec]]s.
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| ==See also==
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| {{Portal|Astronomy}}
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| * [[Absolute magnitude]]
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| * [[Apparent magnitude]]
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| * [[Photographic magnitude]]
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| ==Notes==
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| {{reflist|group=note}}
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| ==References==
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| {{reflist|2}}
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| ==External links==
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| * {{cite web
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| | url=http://curious.astro.cornell.edu/question.php?number=569
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| | title=What is apparent magnitude?
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| | first=Dave
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| | last=Rothstein
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| | publisher=Cornell University
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| | date=18 September 2003
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| | accessdate=23 December 2011
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| }}
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| * {{cite web
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| | url=http://encarta.msn.com/encyclopedia_761558851/Magnitude_(astronomy).html
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| | title=Magnitude (astronomy)
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| | archiveurl=http://www.webcitation.org/5kx6HGtvU
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| | work=MSN Encarta
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| | archivedate=1 January 2009
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| | deadurl=yes
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| | accessdate=23 December 2011
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| }}
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| {{Star|state=collapsed}}
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| [[Category:Observational astronomy]]
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| [[Category:Units of measurement in astronomy]]
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