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In astronomy, magnitude is a unitless measure of the brightness of an object in a defined passband, often in the visible or infrared spectrum, but sometimes across all wavelengths. An imprecise but systematic determination of the magnitude of objects was introduced in ancient times by Hipparchus.

The scale is logarithmic and defined such that each step of one magnitude changes the brightness by a factor of the fifth root of 100, or approximately 2.512. For example, a magnitude 1 star is exactly 100 times brighter than a magnitude 6 star. The brighter an object appears, the lower the value of its magnitude, with the brightest objects reaching negative values.

Astronomers use two different definitions of magnitude: apparent magnitude and absolute magnitude. The apparent magnitude (m) is the brightness of an object as it appears in the night sky from Earth. Apparent magnitude depends on an object's intrinsic luminosity, its distance, and the extinction reducing its brightness. The absolute magnitude (M) describes the intrinsic luminosity emitted by an object and is defined to be equal to the apparent magnitude that the object would have if it were placed at a certain distance from Earth, 10 parsecs for stars. A more complex definition of absolute magnitude is used for planets and small Solar System bodies, based on its brightness at one astronomical unit from the observer and the Sun.

The Sun has an apparent magnitude of −27 and Sirius, the brightest visible star in the night sky, −1.46. Apparent magnitudes can also be assigned to artificial objects in Earth orbit with the International Space Station (ISS) sometimes reaching a magnitude of −6.

History

The magnitude system dates back roughly 2000 years to the Roman poet Manilius (not, as previously believed, 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, size"[1]). To the unaided eye, a more prominent star such as Sirius or Arcturus appears larger than a less prominent star such as Mizar, which in turn appears larger than a truly faint star such as Alcor. In 1736, the mathematician John Keill described the ancient naked-eye magnitude system in this way:

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 1] 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.[2]

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". The system was a simple delineation of stellar brightness into six distinct groups but made no allowance for the variations in brightness within a group.

The scale is logarithmic and defined such that each step of one magnitude changes the brightness by a factor of the fifth root of 100, or approximately 2.512. For example, a magnitude 1 star is exactly 100 times brighter than a magnitude 6 star. The brighter an object appears, the lower the value of its magnitude, with the brightest objects reaching negative values.

Astronomers use two different definitions of magnitude: apparent magnitude and absolute magnitude. The apparent magnitude (m) is the brightness of an object as it appears in the night sky from Earth. Apparent magnitude depends on an object's intrinsic luminosity, its distance, and the extinction reducing its brightness. The absolute magnitude (M) describes the intrinsic luminosity emitted by an object and is defined to be equal to the apparent magnitude that the object would have if it were placed at a certain distance from Earth, 10 parsecs for stars. A more complex definition of absolute magnitude is used for planets and small Solar System bodies, based on its brightness at one astronomical unit from the observer and the Sun.

The Sun has an apparent magnitude of −27 and Sirius, the brightest visible star in the night sky, −1.46. Apparent magnitudes can also be assigned to artificial objects in Earth orbit with the International Space Station (ISS) sometimes reaching a magnitude of −6.

The magnitude system dates back roughly 2000 years to the Roman poet Manilius (not, as previously believed, 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, size"[1]). To the unaided eye, a more prominent star such as Sirius or Arcturus appears larger than a less prominent star such as Mizar, which in turn appears larger than a truly faint star such as Alcor. In 1736, the mathematician John Keill described the ancient naked-eye magnitude system in this way:

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 1] 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.[2]

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". The system was a simple delineation of stellar brightness into si

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 1] 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.[2]

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". The system was a simple delineation of stellar brightness into six distinct groups but made no allowance for the variations in brightness within a group.

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 arc minutes (2′) in apparent diameter (​130 of a degree, or ​115 the diameter of the full moon), with second through sixth magnitude stars measuring ​1 12′, ​1 112′, ​34′, ​12′, and ​13′, respectively.[3] 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 that was larger for brighter stars and smaller for fainter ones. Astronomers from Galileo to 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.[4] Johannes Hevelius produced a very precise table of star sizes measured telescopically, but now the measured diameters ranged from just over six seconds of arc for first magnitude down to just under 2 seconds for sixth magnitude.[4][5] 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.[4] Even well into the nineteenth century the magnitude system continued to be described in terms of six classes determined by apparent size, in which

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.[6]

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 sources of light. Following advances in understanding the 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/cm2) so that brighter stars appeared larger.

Early 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) demonstrated that first magnitude stars are about 100 times brighter than sixth magnitude stars.

Thus in 1856 Norman Pogson of Oxford proposed that a logarithmic scale of 5100 ≈ 2.512 be adopted b

Thus in 1856 Norman Pogson of Oxford proposed that a logarithmic scale of 5100 ≈ 2.512 be adopted between magnitudes, so five magnitude steps corresponded precisely to a factor of 100 in brightness.[7][8] Every interval of one magnitude equates to a variation in brightness of 5100 or roughly 2.512 times. Consequently, a magnitude 1 star is about 2.5 times brighter than a magnitude 2 star, 2.52 brighter than a magnitude 3 star, 2.53 brighter than a magnitude 4 star, and so on.

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 or Vega are magnitude 0, and Sirius is magnitude −1.46.[citation needed]

As mentioned above, the scale appears to work 'in reverse', with objects with a negative magnitude being brighter than those with a positive magnitude. The more negative the value, the brighter the object.

Real Number Line.PNG
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Objects appearing farther to the left on this line are brighter, while objects appearing farther to the right are dimmer. Thus zero appears in the middle, with the brightest objects on the far left, and the dimmest objects on the far right.

Apparent and absolute magnitude

Under the modern logarithmic magnitude scale, two

Under the modern logarithmic magnitude scale, two objects, one of which is used as a reference or baseline, whose intensities (brightnesses) measured from Earth in units of power per unit area (such as watts per square metre, W m−2) are I1 and Iref, will have magnitudes m1 and mref related by