Absolute magnitude () is a measure of the
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 s ...
of a
celestial object
An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often us ...
on an inverse
logarithmic Logarithmic can refer to:
* Logarithm, a transcendental function in mathematics
* Logarithmic scale, the use of the logarithmic function to describe measurements
* Logarithmic spiral,
* Logarithmic growth
* Logarithmic distribution, a discrete pr ...
astronomical magnitude
In astronomy, magnitude is a unitless measure of the brightness of an object in a defined passband, often in the visible or infrared spectrum, but sometimes across all wavelengths. An imprecise but systematic determination of the magnitude of o ...
scale. An object's absolute magnitude is defined to be equal to the
apparent magnitude
Apparent magnitude () is a measure of the brightness of a star or other astronomical object observed from Earth. An object's apparent magnitude depends on its intrinsic luminosity, its distance from Earth, and any extinction of the object's li ...
that the object would have if it were viewed from a distance of exactly , without
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 ...
(or dimming) of its light due to absorption by
interstellar matter and
cosmic dust. By hypothetically placing all objects at a standard reference distance from the observer, their luminosities can be directly compared among each other on a magnitude scale.
As with all astronomical
magnitudes, the absolute magnitude can be specified for different
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...
ranges corresponding to specified
filter bands or
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 anten ...
s; for stars a commonly quoted absolute magnitude is the absolute visual magnitude, which uses the visual (V) band of the spectrum (in the
UBV photometric system
The UBV photometric system (from ''Ultraviolet, Blue, Visual''), also called the Johnson system (or Johnson-Morgan system), is a photometric system usually employed for classifying stars according to their colors.
It was the first standardized ...
). Absolute magnitudes are denoted by a capital M, with a subscript representing the filter band used for measurement, such as M
V for absolute magnitude in the V band.
The more luminous an object, the smaller the numerical value of its absolute magnitude. A difference of 5 magnitudes between the absolute magnitudes of two objects corresponds to a ratio of 100 in their luminosities, and a difference of n magnitudes in absolute magnitude corresponds to a luminosity ratio of 100
n/5. For example, a star of absolute magnitude M
V = 3.0 would be 100 times as luminous as a star of absolute magnitude M
V = 8.0 as measured in the V filter band. The
Sun has absolute magnitude M
V = +4.83.
Highly luminous objects can have negative absolute magnitudes: for example, 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 ey ...
galaxy has an absolute
B magnitude of about −20.8.
An object's absolute ''bolometric'' magnitude (M
bol) represents its total
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 s ...
over all
wavelengths, rather than in a single filter band, as expressed on a logarithmic magnitude scale. To convert from an absolute magnitude in a specific filter band to absolute bolometric magnitude, a
bolometric correction (BC) is applied.
For
Solar System
The Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar ...
bodies that shine in reflected light, a different definition of absolute magnitude (H) is used, based on a standard reference distance of one
astronomical unit
The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbi ...
.
Stars and galaxies
In stellar and galactic astronomy, the standard distance is 10 parsecs (about 32.616 light-years, 308.57 petameters or 308.57
trillion kilometres). A star at 10 parsecs has a
parallax of 0.1″ (100 milli
arcseconds
A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The na ...
). Galaxies (and other
extended objects) are much larger than 10 parsecs, their light is radiated over an extended patch of sky, and their overall brightness cannot be directly observed from relatively short distances, but the same convention is used. A galaxy's magnitude is defined by measuring all the light radiated over the entire object, treating that integrated brightness as the brightness of a single point-like or star-like source, and computing the magnitude of that point-like source as it would appear if observed at the standard 10 parsecs distance. Consequently, the absolute magnitude of any object ''equals'' the apparent magnitude it ''would have'' if it were 10 parsecs away.
Some stars visible to the naked eye have such a low absolute magnitude that they would appear bright enough to outshine the
planet
A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a ...
s and cast shadows if they were at 10 parsecs from the Earth. Examples include
Rigel (−7.0),
Deneb (−7.2),
Naos (−6.0), and
Betelgeuse (−5.6). For comparison,
Sirius has an absolute magnitude of only 1.4, which is still brighter than the
Sun, whose absolute visual magnitude is 4.83. The Sun's absolute bolometric magnitude is set arbitrarily, usually at 4.75.
Absolute magnitudes of stars generally range from approximately −10 to +20. The absolute magnitudes of galaxies can be much lower (brighter). For example, the giant
elliptical galaxy M87 has an absolute magnitude of −22 (i.e. as bright as about 60,000 stars of magnitude −10). Some
active galactic nuclei (
quasars like
CTA-102
CTA 102, also known by its B1950 coordinates as 2230+114 (QSR B2230+114) and its J2000 coordinates as J2232+1143 (QSO J2232+1143), is a blazar-type quasar discovered in the early 1960s by a radio survey carried out by the California Institute of T ...
) can reach absolute magnitudes in excess of −32, making them the most luminous persistent objects in the observable universe, although these objects can vary in brightness over astronomically short timescales. At the extreme end, the optical afterglow of the gamma ray burst
GRB 080319B reached, according to one paper, an absolute
r magnitude brighter than −38 for a few tens of seconds.
Apparent magnitude
The Greek astronomer
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 ...
established a numerical scale to describe the brightness of each star appearing in the sky. The brightest stars in the sky were assigned an apparent magnitude , and the dimmest stars visible to the naked eye are assigned .
The difference between them corresponds to a factor of 100 in brightness. For objects within the immediate neighborhood of the Sun, the absolute magnitude and apparent magnitude from any distance (in
parsec
The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to or (au), i.e. . The parsec unit is obtained by the use of parallax and trigonometry, a ...
s, with 1 pc = 3.2616
light-year
A light-year, alternatively spelled light year, is a large unit of length used to express astronomical distances and is equivalent to about 9.46 trillion kilometers (), or 5.88 trillion miles ().One trillion here is taken to be 101 ...
s) are related by
where is the radiant flux measured at distance (in parsecs), the radiant flux measured at distance . Using the
common logarithm
In mathematics, the common logarithm is the logarithm with base 10. It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered ...
, the equation can be written as
where it is assumed that
extinction from gas and dust is negligible. Typical extinction rates 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 ey ...
galaxy are 1 to 2 magnitudes per kiloparsec, when
dark clouds are taken into account.
For objects at very large distances (outside the Milky Way) the luminosity distance (distance defined using luminosity measurements) must be used instead of , because the
Euclidean approximation is invalid for distant objects. Instead,
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. ...
must be taken into account. Moreover, the
cosmological redshift complicates the relationship between absolute and apparent magnitude, because the radiation observed was shifted into the red range of the spectrum. To compare the magnitudes of very distant objects with those of local objects, a
K correction might have to be applied to the magnitudes of the distant objects.
The absolute magnitude can also be written in terms of the apparent magnitude and
stellar parallax :
or using apparent magnitude and
distance modulus :
Examples
Rigel has a visual magnitude of 0.12 and distance of about 860 light-years:
Vega
Vega is the brightest star in the northern
Northern may refer to the following:
Geography
* North, a point in direction
* Northern Europe, the northern part or region of Europe
* Northern Highland, a region of Wisconsin, United Sta ...
has a parallax of 0.129″, and an apparent magnitude of 0.03:
The
Black Eye Galaxy has a visual magnitude of 9.36 and a distance modulus of 31.06:
Bolometric magnitude
The
bolometric absolute magnitude , takes into account
electromagnetic radiation
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible ...
at all
wavelengths. It includes those unobserved due to instrumental
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 anten ...
, the Earth's atmospheric absorption, and
extinction by interstellar dust. It is defined based on the
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 s ...
of the stars. In the case of stars with few observations, it must be computed assuming an
effective temperature
The effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation. Effective temperature is often used as an estimate of a body's surface temperature ...
.
Classically, the difference in bolometric magnitude is related to the luminosity ratio according to:
which makes by inversion:
where
* is the Sun's luminosity (bolometric luminosity)
* is the star's luminosity (bolometric luminosity)
* is the bolometric magnitude of the Sun
* is the bolometric magnitude of the star.
In August 2015, the
International Astronomical Union
The International Astronomical Union (IAU; french: link=yes, Union astronomique internationale, UAI) is a nongovernmental organisation with the objective of advancing astronomy in all aspects, including promoting astronomical research, outreach ...
passed Resolution B2
defining the
zero points of the absolute and apparent
bolometric magnitude scales in SI units for power (
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 Wa ...
s) and irradiance (W/m
2), respectively. Although bolometric magnitudes had been used by astronomers for many decades, there had been systematic differences in the absolute magnitude-luminosity scales presented in various astronomical references, and no international standardization. This led to systematic differences in bolometric corrections scales.
Combined with incorrect assumed absolute bolometric magnitudes for the Sun, this could lead to systematic errors in estimated stellar luminosities (and other stellar properties, such as radii or ages, which rely on stellar luminosity to be calculated).
Resolution B2 defines an absolute bolometric magnitude scale where corresponds to luminosity , with the zero point
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 s ...
set such that the Sun (with nominal luminosity ) corresponds to absolute
bolometric magnitude . Placing a
radiation
In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes:
* ''electromagnetic radiation'', such as radio waves, microwaves, infrared, vi ...
source (e.g. star) at the standard distance of 10
parsecs
The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to or (au), i.e. . The parsec unit is obtained by the use of parallax and trigonometry, a ...
, it follows that the zero point of the apparent bolometric magnitude scale corresponds to
irradiance . Using the IAU 2015 scale, the nominal total
solar irradiance
Solar irradiance is the power per unit area ( surface power density) received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument.
Solar irradiance is measured in watts per square metr ...
("
solar constant
The solar constant (''GSC'') is a flux density measuring mean solar electromagnetic radiation ( total solar irradiance) per unit area. It is measured on a surface perpendicular to the rays, one astronomical unit (au) from the Sun (roughly the ...
") measured at 1
astronomical unit
The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbi ...
() corresponds to an apparent bolometric magnitude of the
Sun of .
Following Resolution B2, the relation between a star's absolute bolometric magnitude and its luminosity is no longer directly tied to the Sun's (variable) luminosity:
where
* is the star's luminosity (bolometric luminosity) in
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 Wa ...
s
* is the zero point luminosity
* is the bolometric magnitude of the star
The new IAU absolute magnitude scale permanently disconnects the scale from the variable Sun. However, on this SI power scale, the nominal solar luminosity corresponds closely to , a value that was commonly adopted by astronomers before the 2015 IAU resolution.
The luminosity of the star in watts can be calculated as a function of its absolute bolometric magnitude as:
using the variables as defined previously.
Solar System bodies ()
For
planet
A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a ...
s and
asteroid
An asteroid is a minor planet of the Solar System#Inner solar system, inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic o ...
s, a definition of absolute magnitude that is more meaningful for non-stellar objects is used. The absolute magnitude, commonly called
, is defined as the
apparent magnitude
Apparent magnitude () is a measure of the brightness of a star or other astronomical object observed from Earth. An object's apparent magnitude depends on its intrinsic luminosity, its distance from Earth, and any extinction of the object's li ...
that the object would have if it were one
astronomical unit
The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbi ...
(AU) from both the
Sun and the observer, and in conditions of ideal solar opposition (an arrangement that is impossible in practice).
Because Solar System bodies are illuminated by the Sun, their brightness varies as a function of illumination conditions, described by the
phase angle. This relationship is referred to as the
phase curve. The absolute magnitude is the brightness at phase angle zero, an arrangement known as
opposition, from a distance of one AU.
Apparent magnitude

The absolute magnitude
can be used to calculate the apparent magnitude
of a body. For an object
reflecting sunlight,
and
are connected by the relation
where
is the
phase angle, the angle between the body-Sun and body–observer lines.
is the
phase integral (the
integration
Integration may refer to:
Biology
* Multisensory integration
* Path integration
* Pre-integration complex, viral genetic material used to insert a viral genome into a host genome
*DNA integration, by means of site-specific recombinase technolo ...
of reflected light; a number in the 0 to 1 range).
By the
law of cosines
In trigonometry, the law of cosines (also known as the cosine formula, cosine rule, or al-Kashi's theorem) relates the lengths of the sides of a triangle to the cosine of one of its angles. Using notation as in Fig. 1, the law of cosines stat ...
, we have:
Distances:
* is the distance between the body and the observer
* is the distance between the body and the Sun
* is the distance between the observer and the Sun
* , a
unit conversion factor, is the constant 1
AU, the average distance between the Earth and the Sun
Approximations for phase integral
The value of
depends on the properties of the reflecting surface, in particular on its
roughness. In practice, different approximations are used based on the known or assumed properties of the surface. The surfaces of terrestrial planets are generally more difficult to model than those of gaseous planets, the latter of which have smoother visible surfaces.
Planets as diffuse spheres

Planetary bodies can be approximated reasonably well as
ideal diffuse reflecting sphere
A sphere () is a Geometry, geometrical object that is a solid geometry, three-dimensional analogue to a two-dimensional circle. A sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...
s. Let
be the phase angle in
degrees, then
A full-phase diffuse sphere reflects two-thirds as much light as a diffuse flat disk of the same diameter. A quarter phase (
) has
as much light as full phase (
).
By contrast, a ''diffuse disk reflector model'' is simply
, which isn't realistic, but it does represent the
opposition surge for rough surfaces that reflect more uniform light back at low phase angles.
The definition of the
geometric albedo , a measure for the reflectivity of planetary surfaces, is based on the diffuse disk reflector model. The absolute magnitude
, diameter
(in
kilometers) and geometric albedo
of a body are related by
Example: The
Moon's absolute magnitude
can be calculated from its diameter
and
geometric albedo :
We have
,
At
quarter phase,
(according to the diffuse reflector model), this yields an apparent magnitude of
The actual value is somewhat lower than that,
The phase curve of the Moon is too complicated for the diffuse reflector model.
A more accurate formula is given in the following section.
More advanced models
Because Solar System bodies are never perfect diffuse reflectors, astronomers use different models to predict apparent magnitudes based on known or assumed properties of the body.
For planets, approximations for the correction term
in the formula for have been derived empirically, to match
observations at different phase angles. The approximations recommended by the
Astronomical Almanac
''The Astronomical Almanac''The ''Astronomical Almanac'' for the Year 2015, (United States Naval Observatory/Nautical Almanac Office, 2014) . is an almanac published by the United States Naval Observatory (USNO) and His Majesty's Nautical Almana ...
are (with
in degrees):
Here
is the effective inclination of
Saturn's rings (their tilt relative to the observer), which as seen from Earth varies between 0° and 27° over the course of one Saturn orbit, and
is a small correction term depending on Uranus' sub-Earth and sub-solar latitudes.
is the
Common Era
Common Era (CE) and Before the Common Era (BCE) are year notations for the Gregorian calendar (and its predecessor, the Julian calendar), the world's most widely used calendar era. Common Era and Before the Common Era are alternatives to the ...
year. Neptune's absolute magnitude is changing slowly due to seasonal effects as the planet moves along its 165-year orbit around the Sun, and the approximation above is only valid after the year 2000. For some circumstances, like
for Venus, no observations are available, and the phase curve is unknown in those cases. The formula for the Moon is only applicable to the
near side of the Moon, the portion that is visible from the Earth.
Example 1: On 1 January 2019,
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 f ...
was
from the Sun, and
from Earth, at a phase angle of
(near quarter phase). Under full-phase conditions, Venus would have been visible at
Accounting for the high phase angle, the correction term above yields an actual apparent magnitude of
This is close to the value of
predicted by the Jet Propulsion Laboratory.
Example 2: At
first quarter phase, the approximation for the Moon gives
With that, the apparent magnitude of the Moon is
close to the expected value of about
. At
last quarter
Concerning the lunar month of ~29.53 days as viewed from Earth, the lunar phase or Moon phase is the shape of the Moon's directly sunlit portion, which can be expressed quantitatively using areas or angles, or described qualitatively using th ...
, the Moon is about 0.06 mag fainter than at first quarter, because that part of its surface has a lower albedo.
Earth's
albedo varies by a factor of 6, from 0.12 in the cloud-free case to 0.76 in the case of
altostratus cloud. The absolute magnitude in the table corresponds to an albedo of 0.434. Due to the variability of the
weather
Weather is the state of the atmosphere, describing for example the degree to which it is hot or cold, wet or dry, calm or stormy, clear or cloudy. On Earth, most weather phenomena occur in the lowest layer of the planet's atmosphere, the ...
, Earth's apparent magnitude cannot be predicted as accurately as that of most other planets.
Asteroids

If an object has an atmosphere, it reflects light more or less isotropically in all directions, and its brightness can be modelled as a diffuse reflector. Bodies with no atmosphere, like asteroids or moons, tend to reflect light more strongly to the direction of the incident light, and their brightness increases rapidly as the phase angle approaches
. This rapid brightening near opposition is called the
opposition effect. Its strength depends on the physical properties of the body's surface, and hence it differs from asteroid to asteroid.
In 1985, the
IAU adopted the
semi-empirical -system, based on two parameters
and
called ''absolute magnitude'' and ''slope'', to model the opposition effect for the
ephemerides published by the
Minor Planet Center
The Minor Planet Center (MPC) is the official body for observing and reporting on minor planets under the auspices of the International Astronomical Union (IAU). Founded in 1947, it operates at the Smithsonian Astrophysical Observatory.
Function
...
.
where
*the phase integral is
and
*
for
or
,
,
,
and
.
This relation is valid for phase angles
, and works best when
.
The slope parameter
relates to the surge in brightness, typically , when the object is near opposition. It is known accurately only for a small number of asteroids, hence for most asteroids a value of
is assumed.
In rare cases,
can be negative.
An example is
101955 Bennu
101955 Bennu (provisional designation ) is a carbonaceous asteroid in the Apollo group discovered by the LINEAR Project on 11 September 1999. It is a potentially hazardous object that is listed on the Sentry Risk Table and has the highest cumu ...
, with
.
In 2012, the
-system was officially replaced by an improved system with three parameters
,
and
, which produces more satisfactory results if the opposition effect is very small or restricted to very small phase angles. However, as of 2022, this
-system has not been adopted by either the Minor Planet Center nor
Jet Propulsion Laboratory
The Jet Propulsion Laboratory (JPL) is a federally funded research and development center and NASA field center in the City of La Cañada Flintridge, California, United States.
Founded in the 1930s by Caltech researchers, JPL is owned by NASA ...
.
The apparent magnitude of asteroids
varies as they rotate, on time scales of seconds to weeks depending on their
rotation period
The rotation period of a celestial object (e.g., star, gas giant, planet, moon, asteroid) may refer to its sidereal rotation period, i.e. the time that the object takes to complete a single revolution around its axis of rotation relative to the ...
, by up to
or more.
In addition, their absolute magnitude can vary with the viewing direction, depending on their
axial tilt
In astronomy, axial tilt, also known as obliquity, is the angle between an object's rotational axis and its orbital axis, which is the line perpendicular to its orbital plane; equivalently, it is the angle between its equatorial plane and orb ...
. In many cases, neither the rotation period nor the axial tilt are known, limiting the predictability. The models presented here do not capture those effects.
Cometary magnitudes
The brightness of
comet
A comet is an icy, small Solar System body that, when passing close to the Sun, warms and begins to release gases, a process that is called outgassing. This produces a visible atmosphere or Coma (cometary), coma, and sometimes also a Comet ta ...
s is given separately as ''total magnitude'' (
, the brightness integrated over the entire visible extend of the
coma) and ''nuclear magnitude'' (
, the brightness of the core region alone).
Both are different scales than the magnitude scale used for planets and asteroids, and can not be used for a size comparison with an asteroid's absolute magnitude .
The activity of comets varies with their distance from the Sun. Their brightness can be approximated as
where
are the total and nuclear apparent magnitudes of the comet, respectively,
are its "absolute" total and nuclear magnitudes,
and
are the body-sun and body-observer distances,
is the
Astronomical Unit
The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbi ...
, and
are the slope parameters characterising the comet's activity. For
, this reduces to the formula for a purely reflecting body (showing no cometary activity).
For example, the lightcurve of comet
C/2011 L4 (PANSTARRS) can be approximated by
On the day of its perihelion passage, 10 March 2013, comet PANSTARRS was
from the Sun and
from Earth. The total apparent magnitude
is predicted to have been
at that time. The Minor Planet Center gives a value close to that,
.
The absolute magnitude of any given comet can vary dramatically. It can change as the comet becomes more or less active over time or if it undergoes an outburst. This makes it difficult to use the absolute magnitude for a size estimate. When comet
289P/Blanpain was discovered in 1819, its absolute magnitude was estimated as
.
It was subsequently lost and was only rediscovered in 2003. At that time, its absolute magnitude had decreased to
,
and it was realised that the 1819 apparition coincided with an outburst. 289P/Blanpain reached naked eye brightness (5–8 mag) in 1819, even though it is the comet with the smallest nucleus that has ever been physically characterised, and usually doesn't become brighter than 18 mag.
For some comets that have been observed at heliocentric distances large enough to distinguish between light reflected from the coma, and light from the nucleus itself, an absolute magnitude analogous to that used for asteroids has been calculated, allowing to estimate the sizes of their nuclei.
Meteors
For a
meteor
A meteoroid () is a small rocky or metallic body in outer space.
Meteoroids are defined as objects significantly smaller than asteroids, ranging in size from grains to objects up to a meter wide. Objects smaller than this are classified as mic ...
, the standard distance for measurement of magnitudes is at an altitude of at the observer's
zenith
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 "high ...
.
See also
*
Araucaria Project
*
Hertzsprung–Russell diagram – relates absolute magnitude or
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 s ...
versus spectral color or surface
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied on ...
.
*
Jansky radio astronomer's preferred unit – linear in power/unit area
*
List of most luminous stars
*
Photographic magnitude
*
Surface brightness – the ''magnitude'' for extended objects
*
Zero point (photometry) – the typical calibration point for star flux
References
External links
Reference zero-magnitude fluxes
International Astronomical UnionAbsolute Magnitude of a Star calculatorAbout stellar magnitudesObtain the magnitude of any star–
SIMBAD
Converting magnitude of minor planets to diameter
{{DEFAULTSORT:Absolute Magnitude
Observational astronomy