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Apparent magnitude () is a measure of the brightness of a
star A star is an astronomical object comprising a luminous spheroid of plasma held together by its gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night, but their immense distances from Earth ...
or other astronomical object observed from Earth. An object's apparent magnitude depends on its intrinsic
luminosity Luminosity is an absolute measure of radiated electromagnetic power (light), the radiant power emitted by a light-emitting object over time. In astronomy, luminosity is the total amount of electromagnetic energy emitted per unit of time by a ...
, its distance from Earth, and any
extinction Extinction is the termination of a kind of organism or of a group of kinds (taxon), usually a species. The moment of extinction is generally considered to be the death of the last individual of the species, although the capacity to breed and ...
of the object's light caused by interstellar dust along the line of sight to the observer. The word ''magnitude'' in astronomy, unless stated otherwise, usually refers to a celestial object's apparent magnitude. The magnitude scale dates back to the ancient Roman astronomer
Claudius Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...
, whose star catalog listed stars from 1st magnitude (brightest) to 6th magnitude (dimmest). The modern scale was mathematically defined in a way to closely match this historical system. The scale is reverse logarithmic: the brighter an object is, the lower its
magnitude Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (mathematics), the relative size of an object *Norm (mathematics), a term for the size or length of a vector *Order of ...
number. A difference of 1.0 in magnitude corresponds to a brightness ratio of
Venus Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never far ...
at −4.2 or
Sirius Sirius is the brightest star in the night sky. Its name is derived from the Greek word , or , meaning 'glowing' or 'scorching'. The star is designated α Canis Majoris, Latinized to Alpha Canis Majoris, and abbreviated Alpha CMa ...
at −1.46. The faintest stars visible with the naked eye on the darkest night have apparent magnitudes of about +6.5, though this varies depending on a person's
eyesight Visual perception is the ability to interpret the surrounding environment through photopic vision (daytime vision), color vision, scotopic vision (night vision), and mesopic vision (twilight vision), using light in the visible spectrum reflec ...
and with
altitude Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context ...
and atmospheric conditions. The apparent magnitudes of known objects range from the Sun at −26.832 to objects in deep
Hubble Space Telescope The Hubble Space Telescope (often referred to as HST or Hubble) is a space telescope that was launched into low Earth orbit in 1990 and remains in operation. It was not the first space telescope, but it is one of the largest and most versa ...
images of magnitude +31.5. The measurement of apparent magnitude is called photometry. Photometric measurements are made in the
ultraviolet Ultraviolet (UV) is a form of electromagnetic radiation with wavelength from 10 nm (with a corresponding frequency around 30  PHz) to 400 nm (750  THz), shorter than that of visible light, but longer than X-rays. UV radiation i ...
, visible, or
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
wavelength bands using standard
passband A passband is the range of frequencies or wavelengths that can pass through a filter. For example, a radio receiver contains a bandpass filter to select the frequency of the desired radio signal out of all the radio waves picked up by its antenn ...
filters belonging to
photometric system In astronomy, a photometric system is a set of well-defined passbands (or optical filters), with a known sensitivity to incident radiation. The sensitivity usually depends on the optical system, detectors and filters used. For each photometric ...
s such as the UBV system or the Strömgren ''uvbyβ'' system. Absolute magnitude is a measure of the intrinsic luminosity of a celestial object, rather than its apparent brightness, and is expressed on the same reverse logarithmic scale. Absolute magnitude is defined as the apparent magnitude that a star or object would have if it were observed from a distance of . Therefore, it is of greater use in stellar astrophysics since it refers to a property of a star regardless of how close it is to Earth. But in observational astronomy and popular stargazing, unqualified references to "magnitude" are understood to mean apparent magnitude.

# History

The scale used to indicate magnitude originates in the
Hellenistic In Classical antiquity, the Hellenistic period covers the time in Mediterranean history after Classical Greece, between the death of Alexander the Great in 323 BC and the emergence of the Roman Empire, as signified by the Battle of Actium in ...
practice of dividing stars visible to the naked eye into six ''magnitudes''. The
brightest stars This is a list of stars arranged by their apparent magnitude – their brightness as observed from Earth. It includes all stars brighter than magnitude +2.50 in visible light, measured using a ''V''-band filter in the UBV photometric system. Sta ...
in the night sky were said to be of first magnitude ( = 1), whereas the faintest were of sixth magnitude ( = 6), which is the limit of human
visual perception Visual perception is the ability to interpret the surrounding environment through photopic vision (daytime vision), color vision, scotopic vision (night vision), and mesopic vision (twilight vision), using light in the visible spectrum refl ...
(without the aid of a
telescope A telescope is a device used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. Originally meaning only an optical instrument using lenses, curved mirrors, or a combination of both to observ ...
). Each grade of magnitude was considered twice the brightness of the following grade (a
logarithmic scale A logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way—typically the largest numbers in the data are hundreds or even thousands of times larger than the smallest numbers. Such a ...
), although that ratio was subjective as no
photodetector Photodetectors, also called photosensors, are sensors of light or other electromagnetic radiation. There is a wide variety of photodetectors which may be classified by mechanism of detection, such as photoelectric or photochemical effects, or ...
s existed. This rather crude scale for the brightness of stars was popularized by
Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...
in his ''
Almagest The ''Almagest'' is a 2nd-century Greek-language mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy ( ). One of the most influential scientific texts in history, it canoni ...
'' and is generally believed to have originated with
Hipparchus Hipparchus (; el, Ἵππαρχος, ''Hipparkhos'';  BC) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equ ...
. This cannot be proved or disproved because Hipparchus's original star catalogue is lost. The only preserved text by Hipparchus himself (a commentary to Aratus) clearly documents that he did not have a system to describe brightness with numbers: He always uses terms like "big" or "small", "bright" or "faint" or even descriptions such as "visible at full moon". In 1856,
Norman Robert Pogson Norman Robert Pogson, CIE (23 March 1829 – 23 June 1891) was an English astronomer who worked in India at the Madras observatory. He discovered several minor planets and made observations on comets. He introduced a mathematical scale of st ...
formalized the system by defining a first magnitude star as a star that is 100 times as bright as a sixth-magnitude star, thereby establishing the logarithmic scale still in use today. This implies that a star of magnitude is about 2.512 times as bright as a star of magnitude . This figure, the fifth root of 100, became known as Pogson's Ratio. The zero point of Pogson's scale was originally defined by assigning
Polaris Polaris is a star in the northern circumpolar constellation of Ursa Minor. It is designated α Ursae Minoris ( Latinized to ''Alpha Ursae Minoris'') and is commonly called the North Star or Pole Star. With an apparent magnitude tha ...
a magnitude of exactly 2. Astronomers later discovered that Polaris is slightly variable, so they switched to
Vega Vega is the brightest star in the northern constellation of Lyra. It has the Bayer designation α Lyrae, which is Latinised to Alpha Lyrae and abbreviated Alpha Lyr or α Lyr. This star is relatively close at only from the Sun, ...
as the standard reference star, assigning the brightness of Vega as the definition of zero magnitude at any specified wavelength. Apart from small corrections, the brightness of Vega still serves as the definition of zero magnitude for visible and
near infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
wavelengths, where its spectral energy distribution (SED) closely approximates that of a
black body A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. The name "black body" is given because it absorbs all colors of light. A black body ...
for a temperature of . However, with the advent of infrared astronomy it was revealed that Vega's radiation includes an
infrared excess An infrared excess is a measurement of an astronomical source, typically a star, that in their spectral energy distribution has a greater measured infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) wi ...
presumably due to a circumstellar disk consisting of
dust Dust is made of fine particles of solid matter. On Earth, it generally consists of particles in the atmosphere that come from various sources such as soil lifted by wind (an aeolian process), volcanic eruptions, and pollution. Dust in ho ...
at warm temperatures (but much cooler than the star's surface). At shorter (e.g. visible) wavelengths, there is negligible emission from dust at these temperatures. However, in order to properly extend the magnitude scale further into the infrared, this peculiarity of Vega should not affect the definition of the magnitude scale. Therefore, the magnitude scale was extrapolated to ''all'' wavelengths on the basis of the black-body radiation curve for an ideal stellar surface at uncontaminated by circumstellar radiation. On this basis the
spectral irradiance In radiometry, irradiance is the radiant flux ''received'' by a ''surface'' per unit area. The SI unit of irradiance is the watt per square metre (W⋅m−2). The CGS unit erg per square centimetre per second (erg⋅cm−2⋅s−1) is often used ...
(usually expressed in
jansky The jansky (symbol Jy, plural ''janskys'') is a non- SI unit of spectral flux density, or spectral irradiance, used especially in radio astronomy. It is equivalent to 10−26 watts per square metre per hertz. The ''flux density'' or ''mono ...
s) for the zero magnitude point, as a function of wavelength, can be computed. Small deviations are specified between systems using measurement apparatuses developed independently so that data obtained by different astronomers can be properly compared, but of greater practical importance is the definition of magnitude not at a single wavelength but applying to the response of standard spectral filters used in photometry over various wavelength bands. With the modern magnitude systems, brightness over a very wide range is specified according to the logarithmic definition detailed below, using this zero reference. In practice such apparent magnitudes do not exceed 30 (for detectable measurements). The brightness of Vega is exceeded by four stars in the night sky at visible wavelengths (and more at infrared wavelengths) as well as the bright planets Venus, Mars, and Jupiter, and these must be described by ''negative'' magnitudes. For example,
Sirius Sirius is the brightest star in the night sky. Its name is derived from the Greek word , or , meaning 'glowing' or 'scorching'. The star is designated α Canis Majoris, Latinized to Alpha Canis Majoris, and abbreviated Alpha CMa ...
, the brightest star of the celestial sphere, has a magnitude of −1.4 in the visible. Negative magnitudes for other very bright astronomical objects can be found in the
table Table may refer to: * Table (furniture), a piece of furniture with a flat surface and one or more legs * Table (landform), a flat area of land * Table (information), a data arrangement with rows and columns * Table (database), how the table data ...
below. Astronomers have developed other photometric zero point systems as alternatives to the Vega system. The most widely used is the
AB magnitude The AB magnitude system is an astronomical magnitude system. Unlike many other magnitude systems, it is based on flux measurements that are calibrated in absolute units, namely spectral flux densities. Definition The ''monochromatic'' AB magni ...
system, in which photometric zero points are based on a hypothetical reference spectrum having constant flux per unit frequency interval, rather than using a stellar spectrum or blackbody curve as the reference. The AB magnitude zero point is defined such that an object's AB and Vega-based magnitudes will be approximately equal in the V filter band.

# Measurement

Precision measurement of magnitude (photometry) requires calibration of the photographic or (usually) electronic detection apparatus. This generally involves contemporaneous observation, under identical conditions, of standard stars whose magnitude using that spectral filter is accurately known. Moreover, as the amount of light actually received by a telescope is reduced due to transmission through the
Earth's atmosphere The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing for ...
, the
airmass In astronomy, air mass or airmass is a measure of the amount of air along the line of sight when observing a star or other celestial source from below Earth's atmosphere ( Green 1992). It is formulated as the integral of air density along the ...
es of the target and calibration stars must be taken into account. Typically one would observe a few different stars of known magnitude which are sufficiently similar. Calibrator stars close in the sky to the target are favoured (to avoid large differences in the atmospheric paths). If those stars have somewhat different
zenith angle The zenith (, ) is an imaginary point directly "above" a particular location, on the celestial sphere. "Above" means in the vertical direction (plumb line) opposite to the gravity direction at that location (nadir). The zenith is the "highest" ...
s (
altitudes Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context ...
) then a correction factor as a function of airmass can be derived and applied to the airmass at the target's position. Such calibration obtains the brightness as would be observed from above the atmosphere, where apparent magnitude is defined. For those new to astronomy, Apparent Magnitude scales with the received power (as opposed to amplitude), so for astrophotography you can use the relative brightness measure to scale the exposure times between stars. Apparent magnitude also adds up (integrates) over the entire object, so it is focus independent. This needs to be taken into account when scaling exposure times for objects with significant apparent size, like the Sun, Moon and planets. For example, directly scaling the exposure time from the Moon to the Sun works, because they are approximately the same size in the sky, but scaling the exposure from the Moon to Saturn would result in an overexposure, if the image of Saturn takes up a smaller area on your sensor than the Moon did (at the same magnification or more generally f/#).

# Calculations

The dimmer an object appears, the higher the numerical value given to its magnitude, with a difference of 5 magnitudes corresponding to a brightness factor of exactly 100. Therefore, the magnitude , in the
spectral band Spectral bands are parts of the electromagnetic spectrum of specific wavelengths, which can be filtered by a standard filter. In nuclear physics, spectral bands are referred to the emission of polyatomic systems, including condensed materials, larg ...
, would be given by $m_= -5 \log_ \left(\frac \right),$ which is more commonly expressed in terms of common (base-10) logarithms as $m_ = -2.5 \log_ \left(\frac \right),$ where is the observed
irradiance In radiometry, irradiance is the radiant flux ''received'' by a ''surface'' per unit area. The SI unit of irradiance is the watt per square metre (W⋅m−2). The CGS unit erg per square centimetre per second (erg⋅cm−2⋅s−1) is often used ...
using spectral filter , and is the reference flux (zero-point) for that photometric filter. Since an increase of 5 magnitudes corresponds to a decrease in brightness by a factor of exactly 100, each magnitude increase implies a decrease in brightness by the factor (Pogson's ratio). Inverting the above formula, a magnitude difference implies a brightness factor of $\frac = 100^\frac = 10^ \approx 2.512^.$

## Example: Sun and Moon

''What is the ratio in brightness between the
Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared r ...
and the full
Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
?'' The apparent magnitude of the Sun is −26.832 (brighter), and the mean magnitude of the
full moon The full moon is the lunar phase when the Moon appears fully illuminated from Earth's perspective. This occurs when Earth is located between the Sun and the Moon (when the ecliptic longitudes of the Sun and Moon differ by 180°). This mean ...
is −12.74 (dimmer). Difference in magnitude: $x = m_1 - m_2 = (-12.74) - (-26.832) = 14.09.$ Brightness factor: $v_b = 10^ = 10^ \approx 432\,513.$ The Sun appears about times as bright as the full Moon.

Sometimes one might wish to add brightness. For example, photometry on closely separated double stars may only be able to produce a measurement of their combined light output. To find the combined magnitude of that double star knowing only the magnitudes of the individual components, this can be done by adding the brightness (in linear units) corresponding to each magnitude. $10^ = 10^ + 10^.$ Solving for $m_f$ yields $m_f = -2.5\log_ \left(10^ + 10^ \right),$ where is the resulting magnitude after adding the brightnesses referred to by and .

## Apparent bolometric magnitude

While magnitude generally refers to a measurement in a particular filter band corresponding to some range of wavelengths, the apparent or absolute bolometric magnitude (mbol) is a measure of an object's apparent or absolute brightness integrated over all wavelengths of the electromagnetic spectrum (also known as the object's
irradiance In radiometry, irradiance is the radiant flux ''received'' by a ''surface'' per unit area. The SI unit of irradiance is the watt per square metre (W⋅m−2). The CGS unit erg per square centimetre per second (erg⋅cm−2⋅s−1) is often used ...
or power, respectively). The zero point of the apparent bolometric magnitude scale is based on the definition that an apparent bolometric magnitude of 0 mag is equivalent to a received irradiance of 2.518×10−8
watt The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James Wat ...
s per square metre (W·m−2).

## Absolute magnitude

While apparent magnitude is a measure of the brightness of an object as seen by a particular observer, absolute magnitude is a measure of the ''intrinsic'' brightness of an object. Flux decreases with distance according to an inverse-square law, so the apparent magnitude of a star depends on both its absolute brightness and its distance (and any extinction). For example, a star at one distance will have the same apparent magnitude as a star four times as bright at twice that distance. In contrast, the intrinsic brightness of an astronomical object, does not depend on the distance of the observer or any
extinction Extinction is the termination of a kind of organism or of a group of kinds (taxon), usually a species. The moment of extinction is generally considered to be the death of the last individual of the species, although the capacity to breed and ...
. The absolute magnitude , of a star or astronomical object is defined as the apparent magnitude it would have as seen from a distance of . The absolute magnitude of the Sun is 4.83 in the V band (visual), 4.68 in the Gaia satellite's G band (green) and 5.48 in the B band (blue). In the case of a planet or asteroid, the absolute magnitude rather means the apparent magnitude it would have if it were from both the observer and the Sun, and fully illuminated at maximum opposition (a configuration that is only theoretically achievable, with the observer situated on the surface of the Sun).

# Standard reference values

The magnitude scale is a reverse logarithmic scale. A common misconception is that the logarithmic nature of the scale is because the
human eye The human eye is a sensory organ, part of the sensory nervous system, that reacts to visible light and allows humans to use visual information for various purposes including seeing things, keeping balance, and maintaining circadian rhythm. T ...
itself has a logarithmic response. In Pogson's time this was thought to be true (see
Weber–Fechner law The Weber–Fechner laws are two related hypotheses in the field of psychophysics, known as Weber's law and Fechner's law. Both laws relate to human perception, more specifically the relation between the actual change in a physical stimulus an ...
), but it is now believed that the response is a
power law In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one q ...
. Magnitude is complicated by the fact that light is not
monochromatic A monochrome or monochromatic image, object or palette is composed of one color (or values of one color). Images using only shades of grey are called grayscale (typically digital) or black-and-white (typically analog). In physics, monoc ...
. 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 (UV) is a form of electromagnetic radiation with wavelength from 10 nm (with a corresponding frequency around 30  PHz) to 400 nm (750  THz), shorter than that of visible light, but longer than X-rays. UV radiation i ...
), 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 human eye. When an apparent magnitude is discussed without further qualification, the V magnitude is generally understood. Because cooler stars, such as red giants and
red dwarf ''Red Dwarf'' is a British science fiction comedy franchise created by Rob Grant and Doug Naylor, which primarily consists of a television sitcom that aired on BBC Two between 1988 and 1999, and on Dave since 2009, gaining a cult following ...
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 stars have an estimated magnitude of well over 100, because they emit extremely little visible light, but are strongest in
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
. Measures of magnitude need cautious treatment and it is extremely important to measure like with like. On early 20th century and older orthochromatic (blue-sensitive) photographic film, the relative brightnesses of the blue
supergiant Supergiants are among the most massive and most luminous stars. Supergiant stars occupy the top region of the Hertzsprung–Russell diagram with absolute visual magnitudes between about −3 and −8. The temperature range of supergiant stars s ...
Rigel Rigel is a blue supergiant star in the constellation of Orion. It has the Bayer designation β Orionis, which is Latinized to Beta Orionis and abbreviated Beta Ori or β Ori. Rigel is the brightest and most massive componentand ...
and the red supergiant Betelgeuse irregular variable star (at maximum) are reversed compared to what human eyes perceive, because this archaic film is more sensitive to blue light than it is to red light. Magnitudes obtained from this method are known as
photographic magnitude Photographic magnitude ( or ) is a measure of the relative brightness of a star or other astronomical object as imaged on a photographic film emulsion with a camera attached to a telescope. An object's apparent photographic magnitude depends on i ...
s, and are now considered obsolete. For objects within the
Milky Way The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye. ...
with a given absolute magnitude, 5 is added to the apparent magnitude for every tenfold increase in the distance to the object. For objects at very great distances (far beyond the Milky Way), this relationship must be adjusted for redshifts and for
non-Euclidean In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean g ...
distance measures due to general relativity. For planets and other Solar System bodies, the apparent magnitude is derived from its phase curve and the distances to the Sun and observer.

# List of apparent magnitudes

Some of the listed magnitudes are approximate. Telescope sensitivity depends on observing time, optical bandpass, and interfering light from scattering and airglow.