Magnitude (astronomy)

# Magnitude (astronomy)

Discussion

Encyclopedia
Magnitude is the logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...

ic measure of the brightness of an object, in astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

, measured in a specific wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

or passband
Passband
A passband is the range of frequencies or wavelengths that can pass through a filter without being attenuated.A bandpass filtered signal , is known as a bandpass signal, as opposed to a baseband signal....

, usually in optical
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

or near-infrared
Infrared
Infrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...

wavelengths.

## Background

The magnitude system dates back roughly 2000 years to the Greek astronomer Hipparchus
Hipparchus
Hipparchus, the common Latinization of the Greek Hipparkhos, can mean:* Hipparchus, the ancient Greek astronomer** Hipparchic cycle, an astronomical cycle he created** Hipparchus , a lunar crater named in his honour...

(or the Alexandrian astronomer Ptolemy
Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...

—references vary) who classified stars by their apparent brightness, which they saw as size (“magnitude means bigness”). To the unaided eye, a more prominent star such as Sirius
Sirius
Sirius is the brightest star in the night sky. With a visual apparent magnitude of −1.46, it is almost twice as bright as Canopus, the next brightest star. The name "Sirius" is derived from the Ancient Greek: Seirios . The star has the Bayer designation Alpha Canis Majoris...

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. The following quote from 1736 gives an excellent description of the ancient naked-eye magnitude system:

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 fame 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.

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".

Tycho Brahe
Tycho Brahe
Tycho Brahe , born Tyge Ottesen Brahe, was a Danish nobleman known for his accurate and comprehensive astronomical and planetary observations...

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
Minute of arc
A minute of arc, arcminute, or minute of angle , is a unit of angular measurement equal to one sixtieth of one degree. In turn, a second of arc or arcsecond is one sixtieth of one minute of arc....

(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. 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
Galileo Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...

to Jaques Cassini
Jacques Cassini
Jacques Cassini was a French astronomer, son of the famous Italian astronomer Giovanni Domenico Cassini.Cassini was born at the Paris Observatory. Admitted at the age of seventeen to membership of the French Academy of Sciences, he was elected in 1696 a fellow of the Royal Society of London, and...

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. Johannes Hevelius
Johannes Hevelius
Johannes Hevelius Some sources refer to Hevelius as Polish:Some sources refer to Hevelius as German:*Encyplopedia Britannica * of the Royal Society was a councilor and mayor of Danzig , Pomeranian Voivodeship, in the Polish-Lithuanian Commonwealth...

produced a very precise table of star sizes measured telescopically, but now the measured diameters ranged from just over six seconds of arc
Minute of arc
A minute of arc, arcminute, or minute of angle , is a unit of angular measurement equal to one sixtieth of one degree. In turn, a second of arc or arcsecond is one sixtieth of one minute of arc....

for first magnitude down to just under 2 seconds for sixth magnitude. By the time of William Herschel
William Herschel
Sir Frederick William Herschel, KH, FRS, German: Friedrich Wilhelm Herschel was a German-born British astronomer, technical expert, and composer. Born in Hanover, Wilhelm first followed his father into the Military Band of Hanover, but emigrated to Britain at age 19...

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. 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.

However, by the mid-nineteenth century astronomers had measured the distances to stars via stellar parallax
Stellar parallax
Stellar parallax is the effect of parallax on distant stars in astronomy. It is parallax on an interstellar scale, and it can be used to determine the distance of Earth to another star directly with accurate astrometry...

, and so understood that stars are so far away as to essentially appear as point sources
Point source
A point source is a localised, relatively small source of something.Point source may also refer to:*Point source , a localised source of pollution**Point source water pollution, water pollution with a localized source...

of light. Following advances in understanding the diffraction of light and Astronomical seeing
Astronomical seeing
Astronomical seeing refers to the blurring and twinkling of astronomical objects such as stars caused by turbulent mixing in the Earth's atmosphere varying the optical refractive index...

, 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. 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 be adopted between magnitudes, so five magnitude steps corresponded precisely to a factor of 100 in brightness. 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.

## Apparent magnitude

Under the modern logarithmic magnitude scale, two objects whose intensities (brightnesses) measured from Earth in units of power per unit area (such as Watts per square centimeter or W/cm2) are I1 and I2 will have magnitudes m1 and m2 related by

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
Astronomer
An astronomer is a scientist who studies celestial bodies such as planets, stars and galaxies.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using...

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 List of brightest stars). To use the stars mentioned in the "Background" section of this article as examples, 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 be classified as "stars of the first magnitude".

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
The Hubble Space Telescope is a space telescope that was carried into orbit by a Space Shuttle in 1990 and remains in operation. A 2.4 meter aperture telescope in low Earth orbit, Hubble's four main instruments observe in the near ultraviolet, visible, and near infrared...

:
| |
Apparent
magnitude
Brightness
relative to
magnitude 0
ExampleApparent
magnitude
Brightness
relative to
magnitude 0
ExampleApparent
magnitude
Brightness
relative to
magnitude 0
Example
-27 6.3×1010 Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

630 SN 1006
SN 1006
SN 1006 was a supernova, widely seen on Earth beginning in the year 1006 AD; Earth was about 7,200 light-years away from the supernova. It was the brightest apparent magnitude stellar event in recorded history reaching an estimated -7.5 visual magnitude...

supernova
Supernova
A supernova is a stellar explosion that is more energetic than a nova. It is pronounced with the plural supernovae or supernovas. Supernovae are extremely luminous and cause a burst of radiation that often briefly outshines an entire galaxy, before fading from view over several weeks or months...

13 6.3×10-6 3C 273 quasar
Quasar
A quasi-stellar radio source is a very energetic and distant active galactic nucleus. Quasars are extremely luminous and were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than...

-26 2.5×1010
250 International Space Station
International Space Station
The International Space Station is a habitable, artificial satellite in low Earth orbit. The ISS follows the Salyut, Almaz, Cosmos, Skylab, and Mir space stations, as the 11th space station launched, not including the Genesis I and II prototypes...

(max)
14 2.5×10-6 Pluto
Pluto
Pluto, formal designation 134340 Pluto, is the second-most-massive known dwarf planet in the Solar System and the tenth-most-massive body observed directly orbiting the Sun...

(max)
-25 1.0×1010
100 Venus
Venus
Venus is the second planet from the Sun, orbiting it every 224.7 Earth days. The planet is named after Venus, the Roman goddess of love and beauty. After the Moon, it is the brightest natural object in the night sky, reaching an apparent magnitude of −4.6, bright enough to cast shadows...

(max)
15 1.0×10-6
-24 4.0×109
40 16 4.0×10-7 Charon
Charon (moon)
Charon is the largest satellite of the dwarf planet Pluto. It was discovered in 1978 at the United States Naval Observatory Flagstaff Station. Following the 2005 discovery of two other natural satellites of Pluto , Charon may also be referred to as Pluto I...

(max)
-23 1.6×109
16 Jupiter
Jupiter
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...

(max)
17 1.6×10-7
-22 6.3×108
6.3 Mercury
Mercury (planet)
Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 Earth days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three rotations about its axis for every two orbits...

(max)
18 6.3×10-8
-21 2.5×108
2.5 Sirius
Sirius
Sirius is the brightest star in the night sky. With a visual apparent magnitude of −1.46, it is almost twice as bright as Canopus, the next brightest star. The name "Sirius" is derived from the Ancient Greek: Seirios . The star has the Bayer designation Alpha Canis Majoris...

19 2.5×10-8
-20 1.0×108 0 1.0 Vega
Vega
Vega is the brightest star in the constellation Lyra, the fifth brightest star in the night sky and the second brightest star in the northern celestial hemisphere, after Arcturus...

20 1.0×10-8
-19 4.0×107 1 0.40 Antares
Antares
Antares is a red supergiant star in the Milky Way galaxy and the sixteenth brightest star in the nighttime sky . Along with Aldebaran, Spica, and Regulus it is one of the four brightest stars near the ecliptic...

21 4.0×10-9 Callirrhoe (small satellite of Jupiter)
-18 1.6×107 2 0.16 Polaris
Polaris
Polaris |Alpha]] Ursae Minoris, commonly North Star or Pole Star, also Lodestar) is the brightest star in the constellation Ursa Minor. It is very close to the north celestial pole, making it the current northern pole star....

22 1.6×10-9
-17 6.3×106 3 0.063 Cor Caroli
Cor Caroli
Cor Caroli is the brightest star in the northern constellation Canes Venatici...

23 6.3×10-10
-16 2.5×106 4 0.025 Acubens 24 2.5×10-10
-15 1.0×106 5 0.010 Vesta
Vesta
-Astronomy:* 4 Vesta, second largest asteroid in the solar system, also a proto-planet, named after the Roman deity* Vesta family, group of asteroids that includes 4 Vesta- Places :* Monte Vesta, Lombardy, Italy* Temple of Vesta, Rome, Italy...

asteroid
Asteroid
Asteroids are a class of small Solar System bodies in orbit around the Sun. They have also been called planetoids, especially the larger ones...

(max)
25 1.0×10-10 Fenrir (small satellite of Saturn)
-14 4.0×105 6 4.0×10-3 typical limit of naked eye 26 4.0×10-11
-13 1.6×105 Full moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...

7 1.6×10-3 Ceres (max) 27 1.6×10-11 visible light limit of 8m ground-based telescopes
-12 6.3×104 8 6.3×10-4 Neptune
Neptune
Neptune is the eighth and farthest planet from the Sun in the Solar System. Named for the Roman god of the sea, it is the fourth-largest planet by diameter and the third largest by mass. Neptune is 17 times the mass of Earth and is slightly more massive than its near-twin Uranus, which is 15 times...

(max)
28 6.3×10-12
-11 2.5×104 9 2.5×10-4 29 2.5×10-12
-10 1.0×104 10 1.0×10-4 typical limit of 7x50 binoculars 30 1.0×10-12
-9 4.0×103 Iridium flare 11 4.0×10-5 31 4.0×10-13
-8 1.6×103 12 1.6×10-5 32 1.6×10-13 visible light limit of Hubble Space Telescope
Hubble Space Telescope
The Hubble Space Telescope is a space telescope that was carried into orbit by a Space Shuttle in 1990 and remains in operation. A 2.4 meter aperture telescope in low Earth orbit, Hubble's four main instruments observe in the near ultraviolet, visible, and near infrared...

## Absolute scale based on Vega

The star Vega
Vega
Vega is the brightest star in the constellation Lyra, the fifth brightest star in the night sky and the second brightest star in the northern celestial hemisphere, after Arcturus...

has been defined as having a magnitude of zero, or at least near. Modern instruments as bolometer
Bolometer
A bolometer is a device for measuring the power of incident electromagnetic radiation via the heating of a material with a temperature-dependent electrical resistance. It was invented in 1878 by the American astronomer Samuel Pierpont Langley...

A radiometer is a device for measuring the radiant flux of electromagnetic radiation. Generally, the term radiometer denotes an infrared radiation detector, yet it also includes detectors operating on any electromagnetic wavelength....

s give Vega a brightness of about 0.03. The brightest star, Sirius
Sirius
Sirius is the brightest star in the night sky. With a visual apparent magnitude of −1.46, it is almost twice as bright as Canopus, the next brightest star. The name "Sirius" is derived from the Ancient Greek: Seirios . The star has the Bayer designation Alpha Canis Majoris...

, has a magnitude of −1.46. or -1.5. However, Vega has been found to vary in brightness, and other standards have been proposed.

## Problems

The human eye is easily fooled, and Hipparchus's scale has had problems. For example, the human eye is more sensitive to yellow
Yellow
Yellow is the color evoked by light that stimulates both the L and M cone cells of the retina about equally, with no significant stimulation of the S cone cells. Light with a wavelength of 570–590 nm is yellow, as is light with a suitable mixture of red and green...

/red
Red
Red is any of a number of similar colors evoked by light consisting predominantly of the longest wavelengths of light discernible by the human eye, in the wavelength range of roughly 630–740 nm. Longer wavelengths than this are called infrared , and cannot be seen by the naked eye...

light than to blue
Blue
Blue is a colour, the perception of which is evoked by light having a spectrum dominated by energy with a wavelength of roughly 440–490 nm. It is considered one of the additive primary colours. On the HSV Colour Wheel, the complement of blue is yellow; that is, a colour corresponding to an equal...

, and photograph
Photograph
A photograph is an image created by light falling on a light-sensitive surface, usually photographic film or an electronic imager such as a CCD or a CMOS chip. Most photographs are created using a camera, which uses a lens to focus the scene's visible wavelengths of light into a reproduction of...

ic film more to blue than to yellow/red, giving different values of visual magnitude and photographic magnitude
Photographic magnitude
Before the advent of photometers which accurately measure the brightness of astronomical objects, the apparent magnitude of an object was obtained by taking a picture of it with a camera. These images, made on photoemulsive film or plates, were more sensitive to the blue end of the visual spectrum...

. Furthermore, many people find it counter-intuitive that a high magnitude star is dimmer than a low magnitude star.

## Apparent- and absolute-magnitude

Two specific types of magnitudes distinguished by astronomers are:
• Apparent magnitude
Apparent magnitude
The apparent magnitude of a celestial body is a measure of its brightness as seen by an observer on Earth, adjusted to the value it would have in the absence of the atmosphere...

, the apparent brightness of an object. For example, Alpha Centauri
Alpha Centauri
Alpha Centauri is the brightest star in the southern constellation of Centaurus...

has higher apparent magnitude (i.e. lower value) than Betelgeuse
Betelgeuse
Betelgeuse, also known by its Bayer designation Alpha Orionis , is the eighth brightest star in the night sky and second brightest star in the constellation of Orion, outshining its neighbour Rigel only rarely...

, because it is much closer to the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

.
• Absolute magnitude
Absolute magnitude
Absolute magnitude is the measure of a celestial object's intrinsic brightness. it is also the apparent magnitude a star would have if it were 32.6 light years away from Earth...

, which measures the luminosity
Luminosity
Luminosity is a measurement of brightness.-In photometry and color imaging:In photometry, luminosity is sometimes incorrectly used to refer to luminance, which is the density of luminous intensity in a given direction. The SI unit for luminance is candela per square metre.The luminosity function...

of an object (or reflected light for non-luminous objects like asteroid
Asteroid
Asteroids are a class of small Solar System bodies in orbit around the Sun. They have also been called planetoids, especially the larger ones...

s); it is the object's apparent magnitude as seen from a certain distance. For star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

s it is 10 parsec
Parsec
The parsec is a unit of length used in astronomy. It is about 3.26 light-years, or just under 31 trillion kilometres ....

s (10 x 3.26 light years). Betelgeuse has much higher absolute magnitude than Alpha Centauri, because it is much more luminous.

Usually only apparent magnitude is mentioned, because it can be measured directly; absolute magnitude can be calculated from apparent magnitude and distance using;
This is known as the distance modulus
Distance modulus
-Definition:The distance modulus \mu=m-M is the difference between the apparent magnitude m and the absolute magnitude M of an astronomical object...

, where d is the distance to the star measured in parsecs
Parsec
The parsec is a unit of length used in astronomy. It is about 3.26 light-years, or just under 31 trillion kilometres ....

.