Apparent magnitude

Asteroid 65 Cybele and two stars, with their magnitudes labeled

The apparent magnitude ( $m$ ) of an astronomical object is a number that is a measure of its brightness as seen by an observer on Earth. The brighter an object appears, the lower its magnitude value (i.e. inverse relation). The Sun, at apparent magnitude of −26.7, is the brightest object in the sky. It is adjusted to the value it would have in the absence of the atmosphere. Furthermore, the magnitude scale is logarithmic. A difference of 1 in magnitude corresponds to a change in brightness by a factor of ⁵√100, or about 2.512.

The measurement of apparent magnitudes or brightnesses of celestial objects is known as photometry. Apparent magnitudes are used to quantify the brightness of sources at ultraviolet, visible, and infrared wavelengths. An apparent magnitude is usually measured in a specific passband corresponding to some photometric system such as the UBV system. In standard astronomical notation, an apparent magnitude in the V ("visual") filter band would be denoted either as m_V or often simply as V, as in "m_V = 15" or "V = 15" to describe a 15th-magnitude object.

History[edit]

Visible to typical human eye^[1]	Apparent magnitude	Bright- ness relative to Vega	Number of stars brighter than apparent magnitude^[2] in the night sky
Yes	−1.0	250%	1 (Sirius)
	00.0	100%	4
	01.0	40%	15
	02.0	16%	48
	03.0	6.3%	171
	04.0	2.5%	513
	05.0	1.0%	7003160200000000000♠1602
	06.0	0.4%	7003480000000000000♠4800
	06.5	0.25%	7003910000000000000♠9100^[3]
No	07.0	0.16%	7004140000000000000♠14000
	08.0	0.063%	7004420000000000000♠42000
	09.0	0.025%	7005121000000000000♠121000
	10.0	0.010%	7005340000000000000♠340000

The scale used to indicate magnitude originates in the Hellenistic practice of dividing stars visible to the naked eye into six magnitudes. The brightest stars in the night sky were said to be of first magnitude ( $m$ = 1), whereas the faintest were of sixth magnitude ( $m$ = 6), which is the limit of human visual perception (without the aid of a telescope). Each grade of magnitude was considered twice the brightness of the following grade (a logarithmic scale), although that ratio was subjective as no photodetectors existed. This rather crude scale for the brightness of stars was popularized by Ptolemy in his Almagest and is generally believed to have originated with Hipparchus.

In 1856, Norman Robert Pogson 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 $m$ is about 2.512 times as bright as a star of magnitude $m + 1$ . This figure, the fifth root of 100, became known as Pogson's Ratio.^[4] The zero point of Pogson's scale was originally defined by assigning Polaris a magnitude of exactly 2. Astronomers later discovered that Polaris is slightly variable, so they switched to Vega 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 wavelengths, where its spectral energy distribution (SED) closely approximates that of a black body for a temperature of 7004110000000000000♠11000 K. However, with the advent of infrared astronomy it was revealed that Vega's radiation includes an Infrared excess presumably due to a circumstellar disk consisting of dust 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 7004110000000000000♠11000 K uncontaminated by circumstellar radiation. On this basis the spectral irradiance (usually expressed in janskys) for the zero magnitude point, as a function of wavelength, can be computed.^[5] 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, the brightest star of the celestial sphere, has an apparent magnitude of −1.4 in the visible. Negative magnitudes for other very bright astronomical objects can be found in the table below.

Astronomers have developed other photometric zeropoint systems as alternatives to the Vega system. The most widely used is the AB magnitude system,^[6] in which photometric zeropoints 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 zeropoint is defined such that an object's AB and Vega-based magnitudes will be approximately equal in the V filter band.

Calculations[edit]

30 Doradus image taken by ESO's VISTA. This nebula has an apparent magnitude of 8.

A graph of apparent magnitude against brightness

As the amount of light actually received by a telescope is reduced by transmission through the Earth's atmosphere, any measurement of apparent magnitude is corrected for what it would have been as seen from above the atmosphere. The dimmer an object appears, the higher the numerical value given to its apparent magnitude, with a difference of 5 magnitudes corresponding to a brightness factor of exactly 100. Therefore, the apparent magnitude $m$ , in the spectral band $x$ , would be given by

{displaystyle m_{x}=-5log _{100}left({frac {F_{x}}{F_{x,0}}}right),}

which is more commonly expressed in terms of common (base-10) logarithms as

{displaystyle m_{x}=-2.5log _{10}left({frac {F_{x}}{F_{x,0}}}right),}

where $F x$ is the observed flux density using spectral filter $x$ , and $F x,0$ 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 ⁵√100 ≈ 2.512 (Pogson's ratio). Inverting the above formula, a magnitude difference $m 1 - m 2 = Δ m$ implies a brightness factor of

{displaystyle {frac {F_{2}}{F_{1}}}=100^{frac {Delta m}{5}}=10^{0.4Delta m}approx 2.512^{Delta m}.}

Example: Sun and Moon[edit]

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

The apparent magnitude of the Sun is −26.74 (brighter), and the mean apparent magnitude of the full moon is −12.74 (dimmer).

Difference in magnitude:

{displaystyle x=m_{1}-m_{2}=(-12.74)-(-26.74)=14.00.}

Brightness factor:

{displaystyle v_{b}=10^{0.4x}=10^{0.4times 14.00}approx 398,107.17.}

The Sun appears about 7005400000000000000♠400000 times brighter than the full moon.

Magnitude addition[edit]

Sometimes one might wish to add brightnesses. For example, photometry on closely separated double stars may only be able to produce a measurement of their combined light output. How would we reckon the combined magnitude of that double star knowing only the magnitudes of the individual components? This can be done by adding the brightnesses (in linear units) corresponding to each magnitude.^[7]

{displaystyle 10^{-m_{f}times 0.4}=10^{-m_{1}times 0.4}+10^{-m_{2}times 0.4}.}

Solving for $m_{f}$ yields

{displaystyle m_{f}=-2.5log _{10}left(10^{-m_{1}times 0.4}+10^{-m_{2}times 0.4}right),}

where $m f$ is the resulting magnitude after adding the brightnesses referred to by $m 1$ and $m 2$ .

Absolute magnitude[edit]

Since flux decreases with distance according to the inverse-square law, a particular apparent magnitude could equally well refer to a star at one distance, or a star four times brighter at twice that distance, and so on. When one is not interested in the brightness as viewed from Earth, but the intrinsic brightness of an astronomical object, then one refers not to the apparent magnitude but the absolute magnitude. The absolute magnitude $M$ , of a star or astronomical object is defined as the apparent magnitude it would have as seen from a distance of 10 parsecs (about 32.6 light-years). The absolute magnitude of the Sun is 4.83 in the V band (yellow) and 5.48 in the B band (blue).^[8] In the case of a planet or asteroid, the absolute magnitude $H$ rather means the apparent magnitude it would have if it were 1 astronomical unit from both the observer and the Sun, and fully illuminated (a configuration that is only theoretically achievable, with the observer situated on the surface of the Sun).

Standard reference values[edit]

Standard apparent magnitudes and fluxes for typical bands^[9]
Band	$λ$ (μm)	$Δ λ / λ$ (FWHM)	Flux at $m = 0$ , $F x,0$
Band	$λ$ (μm)	$Δ λ / λ$ (FWHM)	Jy	10⁻²⁰ erg/(s·cm²·Hz)
U	0.36	0.15	1810	1.81
B	0.44	0.22	4260	4.26
V	0.55	0.16	3640	3.64
R	0.64	0.23	3080	3.08
I	0.79	0.19	2550	2.55
J	1.26	0.16	1600	1.60
H	1.60	0.23	1080	1.08
K	2.22	0.23	0670	0.67
L	3.50
g	0.52	0.14	3730	3.73
r	0.67	0.14	4490	4.49
i	0.79	0.16	4760	4.76
z	0.91	0.13	4810	4.81

It is important to note that the scale is logarithmic: 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 approximately 19.05.

A common misconception is that the logarithmic nature of the scale is because the human eye 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 (see Stevens' power law).^[10]

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), 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.

Because cooler stars, such as red giants and red dwarfs, 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.

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 Rigel 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 magnitudes, and are now considered obsolete.

For objects within the Milky Way 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 distance measures due to general relativity.^[11]^[12]

For planets and other Solar System bodies the apparent magnitude is derived from its phase curve and the distances to the Sun and observer.

Table of notable celestial objects[edit]

Apparent visual magnitudes of known celestial objects
App. mag. (V)	Celestial object ...	... as seen from
−67.57	gamma-ray burst GRB 080319B	as seen from 1 AU.
−44.00	star R136a1	as seen from 1 AU.
−40.07	star Zeta1 Scorpii	as seen from 1 AU.
−38.00	star Rigel	as seen from 1 AU. It would be seen as a large very bright bluish disk of 35° apparent diameter.
−30.30	star Sirius	as seen from 1 AU.
−29.30	star Sun	as seen from Mercury at perihelion
−27.40	star Sun	as seen from Venus at perihelion
−26.74	star Sun	as seen from Earth (about 400,000 times brighter than mean full moon)^[13]
−25.60	star Sun	as seen from Mars at aphelion
−25.00	Minimum brightness that causes the typical eye slight pain to look at
−23.00	star Sun	as seen from Jupiter at aphelion
−21.70	star Sun	as seen from Saturn at aphelion
−20.20	star Sun	as seen from Uranus at aphelion
−19.30	star Sun	as seen from Neptune
−18.20	star Sun	as seen from Pluto at aphelion
−16.70	star Sun	as seen from Eris at aphelion
−14.20	An illumination level of 1 lux^[14]^[15]
−12.90	full moon	maximum brightness of perigee+perihelion full moon (mean distance value is −12.74,^[16] though both values are about 0.18 magnitude brighter when including the opposition effect)
−11.20	star Sun	as seen from Sedna at aphelion
−10.00	Comet Ikeya–Seki (1965)	which was the brightest Kreutz Sungrazer of modern times^[17]
0−9.50	Iridium (satellite) flare	maximum brightness
0−7.50	supernova of 1006	the brightest stellar event in recorded history (7200 light-years away)^[18]
0−6.50	The total integrated magnitude of the night sky	as seen from Earth
0−6.00	Crab Supernova of 1054	(6500 light-years away)^[19]
0−5.90	International Space Station	when the ISS is at its perigee and fully lit by the Sun^[20]
0−4.92	planet Venus	maximum brightness ^[21] when illuminated as a crescent
0−4.14	planet Venus	mean brightness ^[21]
0−4	Faintest objects observable during the day with naked eye when Sun is high
0−3.99	star Epsilon Canis Majoris	maximum brightness of 4.7 million years ago, the historical brightest star of the last and next five million years
0−2.98	planet Venus	minimum brightness when it is on the far side of the Sun ^[21]
0−2.94	planet Jupiter	maximum brightness ^[21]
0−2.94	planet Mars	maximum brightness ^[21]
0−2.5	Faintest objects visible during the day with naked eye when Sun is less than 10° above the horizon
0−2.50	new moon	minimum brightness
0−2.48	planet Mercury	maximum brightness 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) ^[21]
0−2.20	planet Jupiter	mean brightness ^[21]
0−1.66	planet Jupiter	minimum brightness ^[21]
0−1.47	star Sirius	Brightest star (except for the Sun) at visible wavelengths^[22]
0−0.83	star Eta Carinae	apparent brightness as a supernova impostor in April 1843
0−0.72	star Canopus	2nd brightest star^[23]
0−0.55	planet Saturn	maximum brightness near opposition and perihelion when the rings are wide open ^[21]
0−0.3	Halley's comet	Expected apparent magnitude at 2061 passage
0−0.27	star system Alpha Centauri AB	The total magnitude (3rd brightest star to the naked eye)
0−0.04	star Arcturus	4th brightest star to the naked eye ^[24]
0−0.01	star Alpha Centauri A	4th brightest individual star visible telescopically in the sky
0+0.03	star Vega	which was originally chosen as a definition of the zero point^[25]
0+0.23	planet Mercury	mean brightness ^[21]
0+0.50	star Sun	as seen from Alpha Centauri
0+0.46	planet Saturn	mean brightness ^[21]
0+0.71	planet Mars	mean brightness ^[21]
0+1.17	planet Saturn	minimum brightness ^[21]
0+1.86	planet Mars	minimum brightness ^[21]
0+3.03	supernova SN 1987A	in the Large Magellanic Cloud (160,000 light-years away)
0 3...4	Faintest stars visible in an urban neighborhood with naked eye
003.44	Andromeda Galaxy	M31^[26]
004.38	moon Ganymede	maximum brightness^[27] (moon of Jupiter and the largest moon in the Solar System)
004.50	open cluster M41	an open cluster that may have been seen by Aristotle^[28]
005.20	asteroid Vesta	maximum brightness
005.38	planet Uranus	maximum brightness ^[21]
005.68	planet Uranus	mean brightness ^[21]
005.72	spiral galaxy M33	which is used as a test for naked eye seeing under dark skies^[29]^[30]
005.8	gamma-ray burst GRB 080319B	Peak visual magnitude (the "Clarke Event") seen on Earth on March 19, 2008 from a distance of 7.5 billion light-years.
006.03	planet Uranus	minimum brightness ^[21]
006.49	asteroid Pallas	maximum brightness
006.5	Approximate limit of stars observed by a mean* naked eye observer under very good conditions. There are about 9,500 stars visible to mag 6.5.^[1]*
006.64	dwarf planet Ceres	maximum brightness
006.75	asteroid Iris	maximum brightness
006.90	spiral galaxy M81	This is an extreme naked-eyetarget that pushes human eyesight and the Bortle scale to the limit^[31]
0 7...8	Extreme naked-eye limit, Class 1 on Bortle scale, the darkest skies available on Earth^[32]
007.25	planet Mercury	minimum brightness ^[21]
007.67	planet Neptune	maximum brightness ^[21]
007.78	planet Neptune	mean brightness ^[21]
008.00	planet Neptune	minimum brightness ^[21]
008.10	moon Titan	maximum brightness of largest moon of Saturn^[33]^[34] mean opposition magnitude 8.4^[35]
008.94	asteroid 10 Hygiea	maximum brightness^[36]
009.50	Faintest objects visible using common 7×50 binoculars under typical conditions^[37]
010.20	moon Iapetus	maximum brightness^[34], brightest when west of Saturn and takes 40 days to switch sides
012.91	quasar 3C 273	brightest (luminosity distance of 2.4 billion light-years)
013.42	moon Triton	Maximum brightness^[35]
013.65	dwarf planet Pluto	maximum brightness^[38], 725 times fainter than magnitude 6.5 naked eye skies
015.4	centaur Chiron	maximum brightness^[39]
015.55	moon Charon	maximum brightness (the large moon of Pluto)
016.8	dwarf planet Makemake	Current opposition brightness^[40]
017.27	dwarf planet Haumea	Current opposition brightness of^[41]
018.7	dwarf planet Eris	Current opposition brightness
020.7	moon Callirrhoe	(small ~8 km satellite of Jupiter)^[35]
022	Faintest objects observable in visible light with a 600 mm (24″) Ritchey-Chrétien telescope with 30 minutes of stacked images (6 subframes at 5 minutes each) using a CCD detector^[42]
022.91	moon Hydra	maximum brightness of Pluto's moon
023.38	moon Nix	maximum brightness of Pluto's moon
025.0	moon Fenrir	(small ~4 km satellite of Saturn)^[43]
027.6	planet Jupiter	if it were located 5,000 AU (750 billion km) from the Sun^[44]
027.7	Faintest objects observable with an 8-meter class ground-based telescope such as the Subaru Telescope in a 10-hour image^[45]
028.2	Halley's Comet	in 2003 when it was 28 AU from the Sun^[46]
028.4	asteroid 2003 BH91	observed magnitude of ~15-kilometer Kuiper belt object Seen by the Hubble Space Telescope (HST) in 2003, dimmest known directly-observed asteroid.
031.5	Faintest objects observable in visible light with Hubble Space Telescope^[47]
034	Faintest objects observable in visible light with James Webb Space Telescope^[48]
035	unnamed asteroid	expected magnitude of dimmest known asteroid, a 950-meter Kuiper belt object discovered by the HST passing in front of a star in 2009.^[49]
035	star LBV 1806-20	a luminous blue variable star, expected magnitude at visible wavelengths due to interstellar extinction
See also: List of brightest stars

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

References[edit]

^ ^a^b "Vmag<6.5". SIMBAD Astronomical Database. Retrieved 2010-06-25..mw-parser-output cite.citation{font-style:inherit}.mw-parser-output q{quotes:"""""""'""'"}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-limited a,.mw-parser-output .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}

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^ Magnitude difference is 2.512 log₁₀[(5000/5)² × (4999/4)²] ˜ 30.6, so Jupiter is 30.6 magnitudes fainter at 5000 AU

^ What is the faintest object imaged by ground-based telescopes?, by: The Editors of Sky Telescope, July 24, 2006

^ "New Image of Comet Halley in the Cold". ESO. 2003-09-01. Archived from the original on 1 March 2009. Retrieved 2009-02-22.

^ Illingworth, G. D.; Magee, D.; Oesch, P. A.; Bouwens, R. J.; Labbé, I.; Stiavelli, M.; van Dokkum, P. G.; Franx, M.; Trenti, M.; Carollo, C. M.; Gonzalez, V. (21 October 2013). "The HST eXtreme Deep Field XDF: Combining all ACS and WFC3/IR Data on the HUDF Region into the Deepest Field Ever". The Astrophysical Journal Supplement Series. 209 (1): 6. arXiv:1305.1931. Bibcode:2013ApJS..209....6I. doi:10.1088/0067-0049/209/1/6.

^ http://www.jaymaron.com/telescopes/telescopes.html (retrieved Sep 14 2017)

^ "NASA - Hubble Finds Smallest Kuiper Belt Object Ever Seen". www.nasa.gov. NASA. Retrieved 16 March 2018.

External links[edit]

"The astronomical magnitude scale". International Comet Quarterly.

[SIMBAD-mag6.5-1] "Vmag<6.5". SIMBAD Astronomical Database. Retrieved 2010-06-25..mw-parser-output cite.citation{font-style:inherit}.mw-parser-output q{quotes:"""""""'""'"}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-limited a,.mw-parser-output .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}

[2] "Magnitude". National Solar Observatory—Sacramento Peak. Archived from the original on 2008-02-06. Retrieved 2006-08-23.

[3] Bright Star Catalogue

[4] Pogson, N. (1856). "Magnitudes of Thirty-six of the Minor Planets for the first day of each month of the year 1857". MNRAS. 17: 12. Bibcode:1856MNRAS..17...12P. doi:10.1093/mnras/17.1.12.

[5] See [1].

[6] Oke, J. B.; Gunn, J. E. (March 15, 1983). "Secondary standard stars for absolute spectrophotometry". The Astrophysical Journal. 266: 713–717. Bibcode:1983ApJ...266..713O. doi:10.1086/160817.

[7] "Magnitude Arithmetic". Weekly Topic. Caglow. Retrieved 30 January 2012.

[Bband-8] Evans, Aaron. "Some Useful Astronomical Definitions" (PDF). Stony Brook Astronomy Program. Retrieved 2009-07-12.

[UTmags-9] Huchra, John. "Astronomical Magnitude Systems". Harvard-Smithsonian Center for Astrophysics. Retrieved 2017-07-18.

[10] Schulman, E.; Cox, C. V. (1997). "Misconceptions About Astronomical Magnitudes". American Journal of Physics. 65 (10): 1003. Bibcode:1997AmJPh..65.1003S. doi:10.1119/1.18714.

[umeh-11] Umeh, Obinna; Clarkson, Chris; Maartens, Roy (2014). "Nonlinear relativistic corrections to cosmological distances, redshift and gravitational lensing magnification: II. Derivation". Classical and Quantum Gravity. 31 (20): 205001. arXiv:1402.1933. Bibcode:2014CQGra..31t5001U. doi:10.1088/0264-9381/31/20/205001.

[hogg-12] Hogg, David W.; Baldry, Ivan K.; Blanton, Michael R.; Eisenstein, Daniel J. (2002). "The K correction". arXiv:astro-ph/0210394.

[sun-fact-13] Williams, David R. (2004-09-01). "Sun Fact Sheet". NASA (National Space Science Data Center). Archived from the original on 15 July 2010. Retrieved 2010-07-03.

[14] Dufay, Jean (2012-10-17). Introduction to Astrophysics: The Stars. p. 3. ISBN 9780486607719.

[IM08-15] McLean, Ian S. (2008). Electronic Imaging in Astronomy: Detectors and Instrumentation. Springer. p. 529. ISBN 978-3-540-76582-0.

[moon-fact-16] Williams, David R. (2010-02-02). "Moon Fact Sheet". NASA (National Space Science Data Center). Archived from the original on 23 March 2010. Retrieved 2010-04-09.

[brightest-17] "Brightest comets seen since 1935". International Comet Quarterly. Retrieved 18 December 2011.

[SN1006-18] Winkler, P. Frank; Gupta, Gaurav; Long, Knox S. (2003). "The SN 1006 Remnant: Optical Proper Motions, Deep Imaging, Distance, and Brightness at Maximum". The Astrophysical Journal. 585 (1): 324–335. arXiv:astro-ph/0208415. Bibcode:2003ApJ...585..324W. doi:10.1086/345985.

[SN1054-19] "Supernova 1054 – Creation of the Crab Nebula". SEDS.

[20] "ISS Information - Heavens-above.com". Heavens-above. Retrieved 2007-12-22.

[Mallama_and_Hilton-21] ⁱ^j^k^l^mⁿ^o^p^q^r^s^t^u Mallama, A.; Hilton, J.L. (2018). "Computing Apparent Planetary Magnitudes for The Astronomical Almanac". Astronomy and Computing. 25: 10–24. Bibcode:2018A&C....25...10M. doi:10.1016/j.ascom.2018.08.002.

[SIMBAD-Sirius-22] "Sirius". SIMBAD Astronomical Database. Retrieved 2010-06-26.

[SIMBAD-Canopus-23] "Canopus". SIMBAD Astronomical Database. Retrieved 2010-06-26.

[SIMBAD-Arcturus-24] "Arcturus". SIMBAD Astronomical Database. Retrieved 2010-06-26.

[SIMBAD-Vega-25] "Vega". SIMBAD Astronomical Database. Retrieved 2010-04-14.

[SIMBAD-M31-26] "SIMBAD-M31". SIMBAD Astronomical Database. Retrieved 2009-11-29.

[horizons-Ganymede-27] Yeomans; Chamberlin. "Horizon Online Ephemeris System for Ganymede (Major Body 503)". California Institute of Technology, Jet Propulsion Laboratory. Retrieved 2010-04-14. (4.38 on 1951-Oct-03)

[Aristotle-28] "M41 possibly recorded by Aristotle". SEDS (Students for the Exploration and Development of Space). 2006-07-28. Retrieved 2009-11-29.

[SIMBAD-M33-29] "SIMBAD-M33". SIMBAD Astronomical Database. Retrieved 2009-11-28.

[M33-30] Lodriguss, Jerry (1993). "M33 (Triangulum Galaxy)". Retrieved 2009-11-27. (Shows bolometric magnitude not visual magnitude.)

[SEDS-31] "Messier 81". SEDS (Students for the Exploration and Development of Space). 2007-09-02. Retrieved 2009-11-28.

[Bortle-32] John E. Bortle (February 2001). "The Bortle Dark-Sky Scale". Sky & Telescope. Retrieved 2009-11-18.

[horizons-Titan-33] Yeomans; Chamberlin. "Horizon Online Ephemeris System for Titan (Major Body 606)". California Institute of Technology, Jet Propulsion Laboratory. Retrieved 2010-06-28.
(8.10 on 2003-Dec-30) Archived November 13, 2012, at the Wayback Machine.

[arval-34] "Classic Satellites of the Solar System". Observatorio ARVAL. Archived from the original on 31 July 2010. Retrieved 2010-06-25.

[jpl-sat-35] "Planetary Satellite Physical Parameters". JPL (Solar System Dynamics). 2009-04-03. Archived from the original on 23 July 2009. Retrieved 2009-07-25.

[AstDys-Hygiea-36] "AstDys (10) Hygiea Ephemerides". Department of Mathematics, University of Pisa, Italy. Retrieved 2010-06-26.

[binoculars-37] Zarenski, Ed (2004). "Limiting Magnitude in Binoculars" (PDF). Cloudy Nights. Retrieved 2011-05-06.

[pluto-38] Williams, David R. (2006-09-07). "Pluto Fact Sheet". National Space Science Data Center. NASA. Archived from the original on 1 July 2010. Retrieved 2010-06-26.

[AstDys-Chiron-39] "AstDys (2060) Chiron Ephemerides". Department of Mathematics, University of Pisa, Italy. Retrieved 2010-06-26.

[AstDys-Makemake-40] "AstDys (136472) Makemake Ephemerides". Department of Mathematics, University of Pisa, Italy. Retrieved 2010-06-26.

[AstDys-Haumea-41] "AstDys (136108) Haumea Ephemerides". Department of Mathematics, University of Pisa, Italy. Retrieved 2010-06-26.

[24inch-42] Steve Cullen (sgcullen) (2009-10-05). "17 New Asteroids Found by LightBuckets". LightBuckets. Archived from the original on 2010-01-31. Retrieved 2009-11-15.

[sheppard-saturn-43] Sheppard, Scott S. "Saturn's Known Satellites". Carnegie Institution (Department of Terrestrial Magnetism). Retrieved 2010-06-28.

[44] Magnitude difference is 2.512 log₁₀[(5000/5)² × (4999/4)²] ˜ 30.6, so Jupiter is 30.6 magnitudes fainter at 5000 AU

[45] What is the faintest object imaged by ground-based telescopes?, by: The Editors of Sky Telescope, July 24, 2006

[ESO2003-46] "New Image of Comet Halley in the Cold". ESO. 2003-09-01. Archived from the original on 1 March 2009. Retrieved 2009-02-22.

[47] Illingworth, G. D.; Magee, D.; Oesch, P. A.; Bouwens, R. J.; Labbé, I.; Stiavelli, M.; van Dokkum, P. G.; Franx, M.; Trenti, M.; Carollo, C. M.; Gonzalez, V. (21 October 2013). "The HST eXtreme Deep Field XDF: Combining all ACS and WFC3/IR Data on the HUDF Region into the Deepest Field Ever". The Astrophysical Journal Supplement Series. 209 (1): 6. arXiv:1305.1931. Bibcode:2013ApJS..209....6I. doi:10.1088/0067-0049/209/1/6.

[maron-48] ttp://www.jaymaron.com/telescopes/telescopes.html (retrieved Sep 14 2017)

[hstoccultation-49] "NASA - Hubble Finds Smallest Kuiper Belt Object Ever Seen". www.nasa.gov. NASA. Retrieved 16 March 2018.

v t e Star
Formation	Accretion Molecular cloud Bok globule Young stellar object Protostar Pre-main-sequence star Herbig Ae/Be Orion T Tauri FU Orionis Herbig–Haro object Hayashi track Henyey track
Evolution	Main sequence Red-giant branch Horizontal branch Red clump Asymptotic giant branch Protoplanetary nebula Planetary nebula PG1159 star Dredge-up Instability strip Luminous blue variable Blue straggler Stellar population Supernova Supernova impostor Hypernova Hertzsprung–Russell diagram Color–color diagram
Luminosity class	Subdwarf Dwarf Blue Red White Yellow Brown Subgiant Giant Blue Red Yellow Bright giant Supergiant Blue Red Yellow Hypergiant Yellow
Spectral classification	O B A F G K M WR Be OB Subdwarf O Subdwarf B Late-type Chemically peculiar Am Ap/Bp Oscillating Barium Carbon CH CN Extreme helium Lambda Boötis Lead HgMn S Technetium Shell
Remnants	White dwarf Helium planet Neutron star Radio-quiet Pulsar Binary X-ray Magnetar Stellar black hole X-ray binary Burster
Hypothetical stars	Boson star Black dwarf Exotic Electroweak star Quark Strange Preon Planck Dark matter star Dark-energy star Black star Gravastar Frozen star Q star Quasi-star Thorne–Żytkow object Iron star Blitzar
Nucleosynthesis	Deuterium burning Lithium burning Proton–proton chain CNO cycle Helium flash Triple-alpha process Alpha process Carbon burning Neon burning Oxygen burning Silicon burning S-process R-process Fusor Nova Symbiotic Remnant Luminous red nova
Structure	Core Convection zone Microturbulence Oscillations Radiation zone Atmosphere Photosphere Starspot Chromosphere Corona Stellar wind Bubble Bipolar outflow Accretion disk Asteroseismology Helioseismology Eddington luminosity Kelvin–Helmholtz mechanism
Properties	Designation Dynamics Effective temperature Kinematics Magnetic field Absolute magnitude Mass Metallicity Rotation UBV color Variable star Mira variable
Star systems	Binary Contact Common envelope Eclipsing Symbiotic Multiple Star cluster Open cluster Globular cluster Super star cluster Planetary system Earth's Solar System
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Lists	Star names Arabic Chinese Extremes Most massive Highest temperature Largest volume Smallest volume Brightest Historical Most luminous Nearest Nearest bright Stars with exoplanets Brown dwarfs White dwarfs Milky Way novae Notable supernovae Supernova candidates Supernova remnants Planetary nebulae Timeline of stellar astronomy
Related articles	Substellar object Brown dwarf Sub-brown dwarf Planet Galactic year Galaxy Supercluster Guest star Gravity Icarus (most distant individual star) Intergalactic star Infrared dark cloud Starfield
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