Apparent magnitude

Apparent magnitude

Overview
The apparent magnitude (m) of a celestial body is a measure
Measurement
Measurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...

 of its brightness
Brightness
Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light. In other words, brightness is the perception elicited by the luminance of a visual target...

 as seen by an observer on 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...

, adjusted to the value it would have in the absence of the atmosphere
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

. The brighter the object appears, the lower the value of its magnitude.


The scale now used to indicate magnitude originates in the Hellenistic
Hellenistic Greece
In the context of Ancient Greek art, architecture, and culture, Hellenistic Greece corresponds to the period between the death of Alexander the Great in 323 BC and the annexation of the classical Greek heartlands by Rome in 146 BC...

 practice of dividing stars visible to the naked eye into six magnitudes.
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Unanswered Questions
Encyclopedia
The apparent magnitude (m) of a celestial body is a measure
Measurement
Measurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...

 of its brightness
Brightness
Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light. In other words, brightness is the perception elicited by the luminance of a visual target...

 as seen by an observer on 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...

, adjusted to the value it would have in the absence of the atmosphere
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

. The brighter the object appears, the lower the value of its magnitude.

History

Visible to
typical
human eye
Apparent
magnitude
Brightness
relative
to 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...

Number of stars
brighter than
apparent magnitude
Yes −1 250% 1
0 100% 4
1 40% 15
2 16% 48
3 6.3% 171
4 2.5% 513
5 1.0% 1 602
6 0.40% 4 800
No 7 0.16% 14 000
8 0.063% 42 000
9 0.025% 121 000
10 0.010% 340 000


The scale now used to indicate magnitude originates in the Hellenistic
Hellenistic Greece
In the context of Ancient Greek art, architecture, and culture, Hellenistic Greece corresponds to the period between the death of Alexander the Great in 323 BC and the annexation of the classical Greek heartlands by Rome in 146 BC...

 practice of dividing stars visible to the naked eye into six magnitudes. The brightest stars were said to be of first magnitude (m = 1), while the faintest were of sixth magnitude (m = 6), the limit of human
Human
Humans are the only living species in the Homo genus...

 visual perception
Visual perception
Visual perception is the ability to interpret information and surroundings from the effects of visible light reaching the eye. The resulting perception is also known as eyesight, sight, or vision...

 (without the aid of a telescope
Telescope
A telescope is an instrument that aids in the observation of remote objects by collecting electromagnetic radiation . The first known practical telescopes were invented in the Netherlands at the beginning of the 1600s , using glass lenses...

). Each grade of magnitude was considered twice the brightness of the following grade (a logarithmic scale
Logarithmic scale
A logarithmic scale is a scale of measurement using the logarithm of a physical quantity instead of the quantity itself.A simple example is a chart whose vertical axis increments are labeled 1, 10, 100, 1000, instead of 1, 2, 3, 4...

). This somewhat crude method of indicating the brightness of stars was popularized by 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...

 in his Almagest
Almagest
The Almagest is a 2nd-century mathematical and astronomical treatise on the apparent motions of the stars and planetary paths. Written in Greek by Claudius Ptolemy, a Roman era scholar of Egypt,...

, and is generally believed to originate with 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...

. This original system did not measure the magnitude of the 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...

. (For a more detailed discussion of the history of the magnitude system, see Magnitude
Magnitude (astronomy)
Magnitude is the logarithmic measure of the brightness of an object, in astronomy, measured in a specific wavelength or passband, usually in optical or near-infrared wavelengths.-Background:...

.)

In 1856, Norman Robert Pogson formalized the system by defining a typical first magnitude star as a star that is 100 times as bright as a typical sixth magnitude star; thus, a first magnitude star is about 2.512 times as bright as a second magnitude star. The fifth root of 100 is known as Pogson's Ratio. Pogson's scale was originally fixed by assigning 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....

 a magnitude of 2. Astronomers later discovered that Polaris is slightly variable, so they first switched to 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...

 as the standard reference star, and then switched to using tabulated zero points for the measured fluxes. The magnitude depends on the wavelength band (see below).

The modern system is no longer limited to 6 magnitudes or only to visible light. Very bright objects have negative magnitudes. For example, 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...

, the brightest star of the celestial sphere
Celestial sphere
In astronomy and navigation, the celestial sphere is an imaginary sphere of arbitrarily large radius, concentric with the Earth and rotating upon the same axis. All objects in the sky can be thought of as projected upon the celestial sphere. Projected upward from Earth's equator and poles are the...

, has an apparent magnitude of –1.4. The modern scale includes the 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...

 and the 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...

. The full Moon has a mean apparent magnitude of –12.74 and the Sun has an apparent magnitude of –26.74. 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...

 has located stars with magnitudes of 30 at visible wavelengths and the Keck telescopes
Keck telescopes
The W. M. Keck Observatory is a two-telescope astronomical observatory at an elevation of near the summit of Mauna Kea in Hawai'i. The primary mirrors of each of the two telescopes are in diameter, making them the second largest optical telescopes in the world, slightly behind the Gran Telescopio...

 have located similarly faint stars in the infrared.

Table of notable celestial objects

Apparent visual magnitudes of known celestial objects
App. Mag. (V) Celestial object
–38.00 Rigel
Rigel
Rigel is the brightest star in the constellation Orion and the sixth brightest star in the sky, with visual magnitude 0.18...

 as seen from 1 astronomical unit
Astronomical unit
An astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....

. It is seen as a large very bright bluish scorching ball of 35° apparent diameter.
–30.30 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...

 as seen from 1 astronomical unit
–29.30 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...

 as seen from 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...

 at perihelion
–27.40 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...

 as seen from Venus at perihelion
–26.74 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...

 (398,359 times brighter than mean full moon)
–25.60 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...

 as seen from Mars at aphelion
–23.00 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...

 as seen from Jupiter at aphelion
–21.70 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...

 as seen from Saturn at aphelion
–20.20 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...

 as seen from Uranus at aphelion
–19.30 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...

 as seen from 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...

–18.20 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...

 as seen from Pluto at aphelion
–16.70 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...

 as seen from Eris
Eris (dwarf planet)
Eris, formal designation 136199 Eris, is the most massive known dwarf planet in the Solar System and the ninth most massive body known to orbit the Sun directly...

 at aphelion
–12.92 Maximum brightness of 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...

 (mean is –12.74)
–11.20 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...

 as seen from Sedna
90377 Sedna
90377 Sedna is a trans-Neptunian object discovered in 2003, which was about three times as far from the Sun as Neptune. For most of its orbit it is even further from the Sun, with its aphelion estimated at 960 astronomical units , making it one of the most distant known objects in the Solar System...

 at aphelion
–9.50 Maximum brightness of an Iridium (satellite) flare
–7.50 The 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 of AD 1006, the brightest stellar event in recorded history
–6.50 The total integrated magnitude of the night sky
Night sky
The term night sky refers to the sky as seen at night. The term is usually associated with astronomy, with reference to views of celestial bodies such as stars, the Moon, and planets that become visible on a clear night after the Sun has set. Natural light sources in a night sky include moonlight,...

 as seen from 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...

–6.00 The Crab Supernova (SN 1054
SN 1054
SN 1054 is a supernova that was first observed as a new "star" in the sky on July 4, 1054 AD, hence its name, and that lasted for a period of around two years. The event was recorded in multiple Chinese and Japanese documents and in one document from the Arab world...

) of AD 1054 (6500 light years away)
–5.9 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...

 (when the ISS is at its perigee
Perigee
Perigee is the point at which an object makes its closest approach to the Earth.. Often the term is used in a broader sense to define the point in an orbit where the orbiting body is closest to the body it orbits. The opposite is the apogee, the farthest or highest point.The Greek prefix "peri"...

 and fully lit by the Sun)
–4.89 Maximum brightness of 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...

 when illuminated as a crescent
–4.00 Faintest objects observable during the day with naked eye when Sun is high
–3.99 Maximum brightness of Epsilon Canis Majoris
Epsilon Canis Majoris
Epsilon Canis Majoris is the second brightest star in the constellation Canis Major, and one of the brightest stars in the night sky. It has the Bayer designation "epsilon" despite being the second brightest and not the fifth brightest star in its constellation. It has the traditional name Adhara...

, the brightest star of the last and next five million years
Historical brightest stars
The Solar System and all of the visible stars are in different orbits about the core of the Milky Way galaxy. Thus, their relative positions change over time, and for the nearer stars this movement can be measured. As a star moves toward or away from us, its apparent brightness changes. Sirius...

–3.82 Minimum brightness of 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...

 when it is on the far side of the Sun
–2.94 Maximum brightness of 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,...

–2.91 Maximum brightness of Mars
Mars
Mars is the fourth planet from the Sun in the Solar System. The planet is named after the Roman god of war, Mars. It is often described as the "Red Planet", as the iron oxide prevalent on its surface gives it a reddish appearance...

–2.50 Faintest objects visible during the day with naked eye when Sun is less than 10° above the horizon
–2.50 Minimum brightness of new 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...

–2.45 Maximum brightness of 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...

 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)
–1.61 Minimum brightness of 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,...

–1.47 Brightest star (except for the Sun) at visible wavelengths: 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...

–0.83 Eta Carinae apparent brightness as a supernova impostor in April 1843
–0.72 Second-brightest star: Canopus
–0.49 Maximum brightness of Saturn
Saturn
Saturn is the sixth planet from the Sun and the second largest planet in the Solar System, after Jupiter. Saturn is named after the Roman god Saturn, equated to the Greek Cronus , the Babylonian Ninurta and the Hindu Shani. Saturn's astronomical symbol represents the Roman god's sickle.Saturn,...

 at opposition and when the rings are full open (2003, 2018)
–0.27 The total magnitude for the Alpha Centauri AB
Alpha Centauri
Alpha Centauri is the brightest star in the southern constellation of Centaurus...

 star system. (Third-brightest star to the naked eye)
–0.04 Fourth-brightest star to the naked eye Arcturus
−0.01 Fourth-brightest individual star visible telescopically in the sky Alpha Centauri A
Alpha Centauri
Alpha Centauri is the brightest star in the southern constellation of Centaurus...

+0.03 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...

, which was originally chosen as a definition of the zero point
+0.50 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...

 as seen from Alpha Centauri
Alpha Centauri
Alpha Centauri is the brightest star in the southern constellation of Centaurus...

1.47 Minimum brightness of Saturn
Saturn
Saturn is the sixth planet from the Sun and the second largest planet in the Solar System, after Jupiter. Saturn is named after the Roman god Saturn, equated to the Greek Cronus , the Babylonian Ninurta and the Hindu Shani. Saturn's astronomical symbol represents the Roman god's sickle.Saturn,...

1.84 Minimum brightness of Mars
Mars
Mars is the fourth planet from the Sun in the Solar System. The planet is named after the Roman god of war, Mars. It is often described as the "Red Planet", as the iron oxide prevalent on its surface gives it a reddish appearance...

3.03 The SN 1987A
SN 1987A
SN 1987A was a supernova in the outskirts of the Tarantula Nebula in the Large Magellanic Cloud, a nearby dwarf galaxy. It occurred approximately 51.4 kiloparsecs from Earth, approximately 168,000 light-years, close enough that it was visible to the naked eye. It could be seen from the Southern...

 supernova in the Large Magellanic Cloud
Large Magellanic Cloud
The Large Magellanic Cloud is a nearby irregular galaxy, and is a satellite of the Milky Way. At a distance of slightly less than 50 kiloparsecs , the LMC is the third closest galaxy to the Milky Way, with the Sagittarius Dwarf Spheroidal and Canis Major Dwarf Galaxy lying closer to the center...

 160,000 light-years away.
3 to 4 Faintest stars visible in an urban neighborhood with naked eye
3.44 The well known Andromeda Galaxy
Andromeda Galaxy
The Andromeda Galaxy is a spiral galaxy approximately 2.5 million light-years from Earth in the constellation Andromeda. It is also known as Messier 31, M31, or NGC 224, and is often referred to as the Great Andromeda Nebula in older texts. Andromeda is the nearest spiral galaxy to the...

 (M31)
4.38 Maximum brightness of Ganymede
Ganymede (moon)
Ganymede is a satellite of Jupiter and the largest moon in the Solar System. It is the seventh moon and third Galilean satellite outward from Jupiter. Completing an orbit in roughly seven days, Ganymede participates in a 1:2:4 orbital resonance with the moons Europa and Io, respectively...

 (moon of Jupiter and the largest moon in the Solar System)
4.50 M41
Messier 41
Messier 41 is an open cluster in the Canis Major constellation. It was discovered by Giovanni Batista Hodierna before 1654 and was perhaps known to Aristotle about 325 BC. M41 lies about four degrees almost exactly south of Sirius...

, an open cluster that may have been seen by Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

5.14 Maximum brightness of brightest 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...

 Vesta
4 Vesta
Vesta, formally designated 4 Vesta, is one of the largest asteroids, with a mean diameter of about . It was discovered by Heinrich Wilhelm Olbers on March 29, 1807, and is named after the Roman virgin goddess of home and hearth, Vesta....

5.32 Maximum brightness of Uranus
Uranus
Uranus is the seventh planet from the Sun. It has the third-largest planetary radius and fourth-largest planetary mass in the Solar System. It is named after the ancient Greek deity of the sky Uranus , the father of Cronus and grandfather of Zeus...

5.72 The spiral galaxy M33
Triangulum Galaxy
The Triangulum Galaxy is a spiral galaxy approximately 3 million light years from Earth in the constellation Triangulum. It is catalogued as Messier 33 or NGC 598, and is sometimes informally referred to as the Pinwheel Galaxy, a nickname it shares with Messier 101...

, which is used as a test for naked eye
Naked eye
The naked eye is a figure of speech referring to human visual perception unaided by a magnifying or light-collecting optical device, such as a telescope or microscope. Vision corrected to normal acuity using corrective lenses is considered "naked"...

 seeing under dark skies
5.73 Minimum brightness of 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...

5.8 Peak visual magnitude of gamma ray burst
Gamma ray burst
Gamma-ray bursts are flashes of gamma rays associated with extremely energetic explosions that have been observed in distant galaxies. They are the most luminous electromagnetic events known to occur in the universe. Bursts can last from ten milliseconds to several minutes, although a typical...

 GRB 080319B
GRB 080319B
GRB 080319B was a remarkable gamma-ray burst detected by the Swift satellite at 06:12 UTC on March 19, 2008. The burst set a new record for the farthest object that could be seen with the naked eye; it had a peak apparent magnitude of 5.8 and remained visible to human eyes for approximately 30...

 (the "Clarke Event") seen on Earth on March 19, 2008 from a distance of 7.5 gigalight-years.
5.95 Minimum brightness of Uranus
Uranus
Uranus is the seventh planet from the Sun. It has the third-largest planetary radius and fourth-largest planetary mass in the Solar System. It is named after the ancient Greek deity of the sky Uranus , the father of Cronus and grandfather of Zeus...

6.40 Maximum brightness of asteroid Pallas
2 Pallas
Pallas, formally designated 2 Pallas, is the second asteroid to have been discovered , and one of the largest. It is estimated to constitute 7% of the mass of the asteroid belt, and its diameter of 530–565 km is comparable to, or slightly larger than, that of 4 Vesta. It is however 20%...

6.50 Approximate limit of 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 observed by a mean naked eye
Naked eye
The naked eye is a figure of speech referring to human visual perception unaided by a magnifying or light-collecting optical device, such as a telescope or microscope. Vision corrected to normal acuity using corrective lenses is considered "naked"...

 observer under very good conditions. There are about 9,500 stars visible to mag 6.5.
6.73 Maximum brightness of dwarf planet Ceres in the asteroid belt
6.75 Maximum brightness of asteroid Iris
7 Iris
7 Iris is a large main-belt asteroid. Among the S-type asteroids, it ranks fifth in geometric mean diameter after Eunomia, Juno, Amphitrite and Herculina....

6.90 The spiral galaxy M81
Messier 81
Messier 81 is a spiral galaxy about 12 million light-years away in the constellation Ursa Major. Due to its proximity to Earth, large size and active galactic nucleus Messier 81 (also known as NGC 3031 or Bode's Galaxy) is a spiral galaxy about 12 million light-years away in the constellation Ursa...

 is an extreme naked eye
Naked eye
The naked eye is a figure of speech referring to human visual perception unaided by a magnifying or light-collecting optical device, such as a telescope or microscope. Vision corrected to normal acuity using corrective lenses is considered "naked"...

 target that pushes human eyesight and the Bortle Dark-Sky Scale
Bortle Dark-Sky Scale
The Bortle Dark-Sky Scale is a nine-level numeric scale that measures the night sky's and stars' brightness of a particular location. It quantifies the astronomical observability of celestial objects and the interference caused by light pollution and skyglow. John E...

 to the limit
7 to 8 Extreme naked eye
Naked eye
The naked eye is a figure of speech referring to human visual perception unaided by a magnifying or light-collecting optical device, such as a telescope or microscope. Vision corrected to normal acuity using corrective lenses is considered "naked"...

 limit with class 1 Bortle Dark-Sky Scale
Bortle Dark-Sky Scale
The Bortle Dark-Sky Scale is a nine-level numeric scale that measures the night sky's and stars' brightness of a particular location. It quantifies the astronomical observability of celestial objects and the interference caused by light pollution and skyglow. John E...

, the darkest skies available on Earth
7.78 Maximum brightness of 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...

8.02 Minimum brightness of 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...

8.10 Maximum brightness of Titan
Titan (moon)
Titan , or Saturn VI, is the largest moon of Saturn, the only natural satellite known to have a dense atmosphere, and the only object other than Earth for which clear evidence of stable bodies of surface liquid has been found....

 (largest moon of Saturn), mean opposition magnitude 8.4
9.01 Maximum brightness of asteroid 10 Hygiea
10 Hygiea
10 Hygiea is an asteroid located in the asteroid belt. With somewhat oblong diameters of 350–500 km, and a mass estimated to be 2.9% of the total mass of the belt, it is the fourth largest asteroid by volume and mass...

9.50 Faintest objects visible using common 7x50 binoculars
Binoculars
Binoculars, field glasses or binocular telescopes are a pair of identical or mirror-symmetrical telescopes mounted side-by-side and aligned to point accurately in the same direction, allowing the viewer to use both eyes when viewing distant objects...

 under typical conditions
10.20 Maximum brightness of Iapetus
Iapetus (moon)
Iapetus ), occasionally Japetus , is the third-largest moon of Saturn, and eleventh in the Solar System. It was discovered by Giovanni Domenico Cassini in 1671...

 (brightest when west of Saturn and takes 40 days to switch sides)
12.91 Brightest 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...

 3C 273 (luminosity distance of 2.4 giga-light years)
13.42 Maximum brightness of Triton
Triton (moon)
Triton is the largest moon of the planet Neptune, discovered on October 10, 1846, by English astronomer William Lassell. It is the only large moon in the Solar System with a retrograde orbit, which is an orbit in the opposite direction to its planet's rotation. At 2,700 km in diameter, it is...

13.65 Maximum brightness of Pluto (725 times fainter than magnitude 6.5 naked eye skies)
15.40 Maximum brightness of centaur Chiron
2060 Chiron
2060 Chiron is a minor planet in the outer Solar System. Discovered in 1977 by Charles T. Kowal , it was the first-known member of a new class of objects now known as centaurs, with an orbit between Saturn and Uranus.Although it was initially classified as an asteroid, it was later found to...

15.55 Maximum brightness of 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...

 (the large moon of Pluto)
16.80 Current opposition brightness of Makemake
17.27 Current opposition brightness of Haumea
18.70 Current opposition brightness of Eris
Eris (dwarf planet)
Eris, formal designation 136199 Eris, is the most massive known dwarf planet in the Solar System and the ninth most massive body known to orbit the Sun directly...

20.70 Callirrhoe
Callirrhoe (moon)
Callirrhoe , also known as ' , is one of Jupiter's outermost named natural satellites. It is an irregular moon that orbits in a retrograde direction. Callirrhoe was imaged by Spacewatch at Kitt Peak National Observatory from October 6 through November 4, 1999, and originally designated as asteroid...

 (small ~8 km satellite of Jupiter)
22.00 Approximate limiting magnitude of a 24" Ritchey-Chrétien telescope
Ritchey-Chrétien telescope
A Ritchey–Chrétien telescope is a specialized Cassegrain telescope designed to eliminate coma, thus providing a large field of view compared to a more conventional configuration. An RCT has a hyperbolic primary and a hyperbolic secondary mirror. It was invented in the early 1910s by American...

 with 30 minutes of stacked images (6 subframes at 300s each) using a CCD detector
Charge-coupled device
A charge-coupled device is a device for the movement of electrical charge, usually from within the device to an area where the charge can be manipulated, for example conversion into a digital value. This is achieved by "shifting" the signals between stages within the device one at a time...

22.91 Maximum brightness of Pluto's moon Hydra
Hydra (moon)
Hydra is the second outermost known natural satellite of Pluto. It was discovered along with Nix in June 2005, and is to be visited along with Pluto by the New Horizons mission in July 2015.- Discovery :...

23.38 Maximum brightness of Pluto's moon Nix
Nix (moon)
Nix is a natural satellite of Pluto. It was discovered along with Hydra in June 2005, and is to be visited along with Pluto by the New Horizons mission in July 2015.- Discovery :...

24.80 Amateur picture with greatest magnitude: quasar CFHQS J1641 +3755
25.00 Fenrir (small ~4 km satellite of Saturn)
27.00 Faintest objects observable in visible light with 8m ground-based telescopes
28.00 Jupiter if it were located 5000AU from the Sun
28.20 Halley's Comet in 2003 when it was 28AU from the Sun
31.50 Faintest objects observable in visible light with 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...

35.00 Sedna
90377 Sedna
90377 Sedna is a trans-Neptunian object discovered in 2003, which was about three times as far from the Sun as Neptune. For most of its orbit it is even further from the Sun, with its aphelion estimated at 960 astronomical units , making it one of the most distant known objects in the Solar System...

 at aphelion
Apsis
An apsis , plural apsides , is the point of greatest or least distance of a body from one of the foci of its elliptical orbit. In modern celestial mechanics this focus is also the center of attraction, which is usually the center of mass of the system...

 (900 AU)
35.00 LBV 1806-20 is a luminous blue variable star at visible wavelengths
36.00 Faintest objects observable in visible light with E-ELT
(see also List of brightest stars)

The above are only approximate values at visible wavelengths (in reality the values depend on the precise bandpass used) — see airglow for more details of telescope sensitivity.

Calculations


As the amount of light received actually depends on the thickness of the Earth's atmosphere in the line of sight to the object, the apparent magnitudes are adjusted to the value they would have in the absence of the atmosphere. The dimmer an object appears, the higher its apparent magnitude. Note that brightness varies with distance; an extremely bright object may appear quite dim, if it is far away. Brightness varies inversely with the square
Inverse-square law
In physics, an inverse-square law is any physical law stating that a specified physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity....

 of the distance. The 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...

, M, of a celestial body (outside the Solar System) is the apparent magnitude it would have if it were 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 (~32.6 light years
Light Years
Light Years is the seventh studio album by Australian recording artist Kylie Minogue. It was released on 25 September 2000 by Parlophone and Mushroom Records. The album's style was indicative of her return to "mainstream pop dance tunes"....

) away; that of a planet (or other Solar System body) is the apparent magnitude it would have if it were 1 astronomical unit
Astronomical unit
An astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....

 away from both the 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...

 and 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...

. The absolute magnitude of the Sun is 4.83 in the V band (yellow) and 5.48 in the B band (blue).

The apparent magnitude, m, in the band, x, can be defined as mx below (noting that )


where is the observed flux
Flux
In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.* In the study of transport phenomena , flux is defined as flow per unit area, where flow is the movement of some quantity per time...

 in the band x,
and is a reference flux in the same band x, such as the Vega star's for example. See Aller et al. 1982 for the most commonly used system.

Since an increase of 1 in the magnitude scale corresponds to a decrease in brightness by a certain factor, the factor would be , which is 2.512...

The variation in brightness between two luminous objects can be calculated another way by subtracting the magnitude number of the brighter object from the magnitude number of the fainter object, then using the difference as an exponent for the base number 2.512; that is to say (; and variation in brightness).

Example 1 - Sun & Moon


What is the ratio in brightness between the Sun and the full moon?



variation in brightness

The apparent magnitude of the Sun is -26.74, and the mean apparent magnitude of the full moon is -12.74. The full moon is the fainter of the two objects, while the Sun is the brighter.

Difference in magnitude







Variation in Brightness







variation in brightness = 398,359

In terms of apparent magnitude, the Sun is about 398,359 times brighter than the full moon.

Example 2 - Sirius & Polaris


What is the ratio in brightness between 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...

 and 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....

?




variation in brightness

The apparent magnitude of Sirius is -1.44, and the apparent magnitude of Polaris is 1.97. Polaris is the fainter of the two stars, while Sirius is the brighter.

Difference in magnitude







Variation in brightness







In terms of apparent magnitude, Sirius is 23.124 times brighter than Polaris the North Star.

The second thing to notice is that the scale is 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: 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 19.054607...
A common misconception is that the logarithmic nature of the scale is because the human eye
Human eye
The human eye is an organ which reacts to light for several purposes. As a conscious sense organ, the eye allows vision. Rod and cone cells in the retina allow conscious light perception and vision including color differentiation and the perception of depth...

 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
Power law
A power law is a special kind of mathematical relationship between two quantities. When the frequency of an event varies as a power of some attribute of that event , the frequency is said to follow a power law. For instance, the number of cities having a certain population size is found to vary...

 (see Stevens' power law
Stevens' power law
Stevens' power law is a proposed relationship between the magnitude of a physical stimulus and its perceived intensity or strength. It is often considered to supersede the Weber–Fechner law on the basis that it describes a wider range of sensations, although critics argue that the validity of the...

).

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
Ultraviolet
Ultraviolet light is electromagnetic radiation with a wavelength shorter than that of visible light, but longer than X-rays, in the range 10 nm to 400 nm, and energies from 3 eV to 124 eV...

), 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.

Since cooler stars, such as red giant
Red giant
A red giant is a luminous giant star of low or intermediate mass in a late phase of stellar evolution. The outer atmosphere is inflated and tenuous, making the radius immense and the surface temperature low, somewhere from 5,000 K and lower...

s and red dwarf
Red dwarf
According to the Hertzsprung-Russell diagram, a red dwarf star is a small and relatively cool star, of the main sequence, either late K or M spectral type....

s, 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
Stellar classification
In astronomy, stellar classification is a classification of stars based on their spectral characteristics. The spectral class of a star is a designated class of a star describing the ionization of its chromosphere, what atomic excitations are most prominent in the light, giving an objective measure...

 stars have an estimated magnitude of well over 100, since they emit extremely little visible light, but are strongest in 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...

.

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
Photographic film
Photographic film is a sheet of plastic coated with an emulsion containing light-sensitive silver halide salts with variable crystal sizes that determine the sensitivity, contrast and resolution of the film...

, the relative brightnesses of the blue supergiant
Supergiant
Supergiants are among the most massive stars. They occupy the top region of the Hertzsprung-Russell diagram. In the Yerkes spectral classification, supergiants are class Ia or Ib . They typically have bolometric absolute magnitudes between -5 and -12...

 Rigel
Rigel
Rigel is the brightest star in the constellation Orion and the sixth brightest star in the sky, with visual magnitude 0.18...

 and the red supergiant 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...

 irregular variable star (at maximum) are reversed compared to what our eyes see since this archaic film is more sensitive to blue light than it is to red light. Magnitudes obtained from this method are known as 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...

s, and are now considered obsolete.

For objects within our Galaxy with a given 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...

, 5 is added to the apparent magnitude for every tenfold increase in the distance to the object. This relationship does not apply for objects at very great distances (far beyond our galaxy), since a correction for General Relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

 must then be taken into account due to the non-Euclidean nature of space.

For planets and other Solar System bodies the apparent magnitude is derived from its phase curve
Phase curve (astronomy)
In astronomy a phase curve describes the brightness of a reflecting body as a function of its phase angle. The brightness usually refers the object’s absolute magnitude which, in turn, is its apparent magnitude at a distance of one astronomical unit from the Earth and Sun...

 and the distances to the Sun and observer.

See also


  • Magnitude (astronomy)
    Magnitude (astronomy)
    Magnitude is the logarithmic measure of the brightness of an object, in astronomy, measured in a specific wavelength or passband, usually in optical or near-infrared wavelengths.-Background:...

  • 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...

  • Luminosity in astronomy
  • List of brightest stars
  • List of nearest bright stars
  • List of nearest stars
  • Lux
    Lux
    The lux is the SI unit of illuminance and luminous emittance, measuring luminous flux per unit area. It is used in photometry as a measure of the intensity, as perceived by the human eye, of light that hits or passes through a surface...

  • Surface brightness
    Surface brightness
    The overall brightness of an extended astronomical object such as a galaxy, star cluster, or nebula, can be measured by its total magnitude, integrated magnitude or integrated visual magnitude; a related concept is surface brightness, which specifies the brightness of a standard-sized piece of an...

  • 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...



External links