# absolute magnitude

In astronomy, absolute magnitude is the apparent magnitude, m, an object would have if it were at a standard luminosity distance away from us, in the absence of interstellar extinction. It allows the overall brightnesses of objects to be compared without regard to distance.

The absolute magnitude uses the same convention as the visual magnitude, with a ~2.512 difference in brightness between step rates (because 2.5125 ≈ 100). The Milky Way, for example, has an absolute magnitude of about -20.5. So a quasar at an absolute magnitude of -25.5 is 100 times brighter than our galaxy. If this particular quasar and our galaxy could be seen side by side at the same distance, the quasar would be 5 magnitudes (or 100 times) brighter than our galaxy.

## Absolute magnitude for stars and galaxies (M)

In stellar and galactic astronomy, the standard distance is 10 parsecs (about 32.616 light years, or 3×1014 kilometres). A star at ten parsecs has a parallax of 0.1" (100 milli arc seconds).

In defining absolute magnitude it is necessary to specify the type of electromagnetic radiation being measured. When referring to total energy output, the proper term is bolometric magnitude. The bolometric magnitude can be computed from the visual magnitude plus a bolometric correction, . This correction is needed because very hot stars radiate mostly ultraviolet radiation, while very cool stars radiate mostly infrared radiation (see Planck's law). The dimmer an object (at a distance of 10 parsecs) would appear, the higher its absolute magnitude. The lower an object's absolute magnitude, the higher its luminosity. A mathematical equation relates apparent magnitude with absolute magnitude, via parallax.

Many stars visible to the naked eye have an absolute magnitude which is capable of casting shadows from a distance of 10 parsecs; Rigel (-7.0), Deneb (-7.2), Naos (-6.0), and Betelgeuse (-5.6).

For comparison, Sirius has an absolute magnitude of 1.4 and the Sun has an absolute visual magnitude of 4.83 (it actually serves as a reference point). The Sun's absolute bolometric magnitude is 4.75.

Absolute magnitudes for stars generally range from -10 to +17. The absolute magnitude for galaxies can be much lower (brighter). For example, the giant elliptical galaxy M87 has an absolute magnitude of -22.

### Computation

One can compute the absolute magnitude of an object given its apparent magnitude and luminosity distance :

where is the star's luminosity distance in parsecs, which are (≈ 3.2616 light-years)

For nearby astronomical objects (such as stars in our galaxy) the luminosity distance DL is almost identical to the real distance to the object, because spacetime within our galaxy is almost Euclidean. For much more distant objects the Euclidean approximation is not valid, and General Relativity must be taken into account when calculating the luminosity distance of an object.

In the Euclidean approximation for nearby objects, the absolute magnitude of a star can be calculated from its apparent magnitude and parallax:

where π is the star's parallax in arcseconds.

You can also compute the absolute magnitude of an object given its apparent magnitude and distance modulus :

#### Example

Rigel has a visual magnitude of mV=0.18 and distance about 773 light-years.
: MVRigel = 0.18 + 5*(1 + log10(3.2616/773)) = -6.7
Vega has a parallax of 0.133", and an apparent magnitude of +0.03
: MVVega = 0.03 + 5*(1 + log10(0.133)) = +0.65
Alpha Centauri has a parallax of 10.750" and an apparent magnitude of -0.01
: MVα Cen = -0.01 + 5*(1 + log10(10.750)) = +4.37
Black Eye Galaxy has a visual magnitude of mV=+9.36 and a distance modulus of 31.06.
: MVBlack Eye Galaxy = 9.36 - 31.06 = -21.7

### Apparent magnitude

Given the absolute magnitude , for objects within our galaxy you can also calculate the apparent magnitude from any distance :

For objects at very great distances (outside our galaxy) the luminosity distance DL must be used instead of d.

Given the absolute magnitude , you can also compute apparent magnitude from its parallax :

Also calculating absolute magnitude from distance modulus :

## Absolute magnitude for planets (H)

For planets, comets and asteroids a different definition of absolute magnitude is used which is more meaningful for nonstellar objects.

In this case, the absolute magnitude is defined as the apparent magnitude that the object would have if it were one astronomical unit (au) from both the Sun and the Earth and at a phase angle of zero degrees. This is a physical impossibility, as it requires the observing telescope to be at the centre of the Sun, but it is convenient for purposes of calculation.

To convert a stellar or galactic absolute magnitude into a planetary one, subtract 31.57. This factor also corresponds to the difference between the Sun's visual magnitude of -26.8 and its (stellar) absolute magnitude of +4.8. Thus, the Milky Way (galactic absolute magnitude -20.5) would have a planetary absolute magnitude of -52.

### Apparent magnitude

The absolute magnitude can be used to help calculate the apparent magnitude of a body under different conditions.

where

is 1 au, is the phase angle, the angle between the Sun-Body and Body-Observer lines; by the law of cosines, we have:

is the phase integral (integration of reflected light; a number in the 0 to 1 range)
Example: (An ideal diffuse reflecting sphere) - A reasonable first approximation for planetary bodies

A full-phase diffuse sphere reflects ⅔ as much light as a diffuse disc of the same diameter
Distances:
: is the distance between the observer and the body
: is the distance between the Sun and the body
: is the distance between the observer and the Sun

#### Example

Moon
= +0.25
= = 1 au
= 384.5 Mm = 2.57 mau

How bright is the Moon from Earth?
: Full Moon: = 0, ( ≈ 2/3)
::
:: (Actual -12.7) A full Moon reflects 30% more light at full phase than a perfect diffuse reflector predicts.
: Quarter Moon: = 90°, (if diffuse reflector)
::
:: (Actual approximately -11.0) The diffuse reflector formula does better for smaller phases.

## External links

Absolute Magnitude may also refer to a science fiction magazine of that name.
Astronomy is the scientific study of celestial objects (such as stars, planets, comets, and galaxies) and phenomena that originate outside the Earth's atmosphere (such as the cosmic background radiation).
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The apparent magnitude (m) of a celestial body is a measure of its brightness as seen by an observer on Earth, normalized to the value it would have in the absence of the atmosphere.
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Luminosity distance DL is defined in terms of the relationship between the absolute magnitude M and apparent magnitude m of an astronomical object.
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Extinction is a term used in astronomy to describe the absorption and scattering of light emitted by astronomical objects by matter (dust and gas) between the emitting object and the observer.
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Brightness is an attribute of visual perception in which a source appears to emit a given amount of light. In other words, brightness is the perception elicited by the luminance of a visual target. This is a subjective attribute/property of an object being observed.
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Milky Way (a translation of the Latin Via Lactea, in turn derived from the Greek Γαλαξίας (Galaxias) sometimes referred to simply as "the Galaxy"), is a barred spiral galaxy that lies with the Local Group of galaxies
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quasar (contraction of QUASi-stellAR radio source) is an extremely bright and distant active galactic nucleus. They were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light that were point-like, similar to stars,
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A galaxy (from the Greek root γαλαξίας, meaning "milky", a reference to our own Milky Way) is a massive, gravitationally bound system consisting of stars, an interstellar medium of gas and dust, and dark matter.
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Distance is a numerical description of how far apart objects are at any given moment in time. In physics or everyday discussion, distance may refer to a physical length, a period of time, or an estimation based on other criteria (e.g. "two counties over").
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parsec (symbol pc) is a unit of length used in astronomy. The length of the parsec is based on the method of trigonometric parallax, one of the oldest methods for measuring the distances to stars.
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1 light-year =
SI units
01015 m 01012 km
Astronomical units
0103 AU 0 pc
US customary / Imperial units
01015 ft 01012 mi
A light-year or lightyear (symbol:
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1 kilometre =
SI units
0 m 0106 mm
US customary / Imperial units
0 ft 0 mi
A kilometre (American spelling: kilometer, symbol km
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Parallax, or more accurately motion parallax (Greek: παραλλαγή (parallagé) = alteration) is the change of angular position of two stationary points relative to each other as seen by an observer, caused by the motion of an
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Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. These components oscillate at right angles to each other and to the direction of propagation, and are in phase with each other.
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Measurement is the estimation of the magnitude of some attribute of an object, such as its length or weight, relative to a unit of measuremnt. Measurement usually involves using a measuring instrument, such as a ruler or scale, which is calibrated to compare the object to some
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energy (from the Greek ενεργός, energos, "active, working")[1] is a scalar physical quantity that is a property of objects and systems of objects which is conserved by nature.
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For a general introduction, see black body.

In physics, Planck's law describes the spectral radiance of electromagnetic radiation at all wavelengths from a black body at temperature .
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Luminosity has different meanings in several different fields of science.

## In photometry and color imaging

Main article: luminance
In photometry, luminosity
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Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions".
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equation is a mathematical statement, in symbols, that two things are the same (or equivalent). Equations are written with an equal sign, as in
.

The equation above is an example of an equality: a proposition which states that two constants are equal.
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relation or relationship is a generalization of 2-place relations, such as the relation of equality, denoted by the sign "=" in a statement like "5 + 7 = 12," or the relation of order,
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A shadow is a region of darkness where light is blocked. It occupies all of the space behind an opaque object with light in front of it. The cross section of a shadow is a two-dimensional silhouette, or reverse projection of the object blocking the light.
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Rigel (pronounced IPA: /ˈraɪʤəl/) (β Orionis) is the brightest star in the constellation Orion and the sixth brightest star in the sky, with visual magnitude 0.12.
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Deneb (α Cyg / α Cygni / Alpha Cygni) is the brightest star in the constellation Cygnus and one of the vertices of the Summer Triangle. The 19th brightest star in the night sky, with an apparent magnitude of 1.25, Deneb is also one of the most luminous stars known.
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Zeta Puppis (ζ Pup / ζ Puppis) is a star in the constellation of Puppis. It also has traditional names Naos (nay'-os, from the Greek ναύς
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Betelgeuse (Alpha (α) Orionis) is a semiregular variable star located 427 light-years away.<ref name="SIMBAD" /> It is the second brightest star in the constellation Orion, and the ninth brightest star in the night sky.
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Sirius (α CMa / α Canis Majoris / Alpha Canis Majoris) (IPA: /ˈsɪriəs/) is the brightest star in the night-time sky with a visual apparent magnitude of −1.47.
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The Sun

Observation data
Mean distance
from Earth 1.4961011 m
(8.31 min at light speed)
Visual brightness (V) −26.74m [1]
Absolute magnitude 4.
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In descriptive statistics, the range is the length of the smallest interval which contains all the data. It is calculated by subtracting the smallest observations from the greatest and provides an indication of statistical dispersion.
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elliptical galaxy is a galaxy belonging to one of the three main classes of galaxy originally described by Edwin Hubble in his 1936 work “The Realm of the Nebulae”[1] and, as such, forms part of the Hubble sequence.
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