Editing Absolute magnitude (section)

=== Cometary magnitudes ===
The brightness of [[comet]]s is given separately as ''total magnitude'' (<math>m_{1}</math>, the brightness integrated over the entire visible extend of the [[Coma (cometary)|coma]]) and ''nuclear magnitude'' (<math>m_{2}</math>, the brightness of the core region alone).<ref name="MPES"/> 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 {{mvar|H}}.

The activity of comets varies with their distance from the Sun. Their brightness can be approximated as
<math display="block">m_{1} = M_{1} + 2.5\cdot K_{1}\log_{10}{\left(\frac{d_{BS}}{d_0}\right)} + 5\log_{10}{\left(\frac{d_{BO}}{d_0}\right)}</math>
<math display="block">m_{2} = M_{2} + 2.5\cdot K_{2}\log_{10}{\left(\frac{d_{BS}}{d_0}\right)} + 5\log_{10}{\left(\frac{d_{BO}}{d_0}\right)},</math>
where <math>m_{1,2}</math> are the total and nuclear apparent magnitudes of the comet, respectively, <math>M_{1,2}</math> are its "absolute" total and nuclear magnitudes, <math>d_{BS}</math> and <math>d_{BO}</math> are the body-sun and body-observer distances, <math>d_{0}</math> is the [[Astronomical Unit]], and <math>K_{1,2}</math> are the slope parameters characterising the comet's activity. For <math>K=2</math>, this reduces to the formula for a purely reflecting body (showing no cometary activity).<ref name="Meisel1976"/>

For example, the lightcurve of comet [[C/2011 L4|C/2011 L4 (PANSTARRS)]] can be approximated by <math>M_{1}=5.41\text{, }K_{1}=3.69.</math><ref name="COBS 2011L4"/> On the day of its perihelion passage, 10 March 2013, comet PANSTARRS was <math>0.302\text{ AU}</math> from the Sun and <math>1.109\text{ AU}</math> from Earth. The total apparent magnitude <math>m_{1}</math> is predicted to have been <math>m_1 = 5.41 + 2.5\cdot3.69\cdot\log_{10}{\left(0.302\right)}+5\log_{10}{\left(1.109\right)} = +0.8</math> at that time. The Minor Planet Center gives a value close to that, <math>m_{1} = +0.5</math>.<ref name="MPC2011L4"/>

{| class="wikitable sortable" style="font-size: 0.9em;"
|+Absolute magnitudes and sizes of comet nuclei
! Comet
! Absolute<br />magnitude <math>M_{1}</math><ref name="kidger"/>
! Nucleus<br />diameter
|-
|[[Comet Sarabat]] || −3.0 || ≈100&nbsp;km?
|-
|[[Comet Hale-Bopp]] || −1.3 || 60 ± 20&nbsp;km
|-
|[[Comet Halley]] || 4.0 || 14.9 x 8.2&nbsp;km
|-
|average new comet || 6.5 || ≈2&nbsp;km<ref name="Hughes"/>
|-
|[[C/2014 UN271 (Bernardinelli-Bernstein)|C/2014 UN<sub>271</sub> (Bernardinelli-Bernstein)]] || 6.7<ref name="Bernardinelli">{{cite web|type = 2021-08-08 last obs.|title = JPL Small-Body Database Browser: (2014 UN271)|url = https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=54161348|publisher = [[Jet Propulsion Laboratory]]|accessdate = 15 September 2021}}</ref> || 60–200&nbsp;km?<ref>{{cite news |title=The Largest Comet Ever Found Is Making Its Move Into a Sky Near You |url=https://www.nytimes.com/2021/06/28/science/comet-largest-ever-seen.html|date=28 June 2021 |work=[[The New York Times]]|accessdate=1 July 2021 }}</ref><ref name="ATel14759">{{cite web|title = Comet C/2014 UN271 (Bernardinelli-Bernstein) exhibited activity at 23.8 au |url = https://www.astronomerstelegram.org/?read=14759|first1 = Tony|last1 = Farnham|work = The Astronomer's Telegram|date = 6 July 2021|accessdate = 6 July 2021}}</ref>
|-
|[[289P/Blanpain]] (during 1819 outburst) || 8.5<ref name="Yoshida"/> || 320 m<ref name="Jewitt"/>
|-
|289P/Blanpain (normal activity) || 22.9<ref name="JPL_289"/> || 320 m
|}

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 <math>M_{1} = 8.5</math>.<ref name="Yoshida"/> It was subsequently lost and was only rediscovered in 2003. At that time, its absolute magnitude had decreased to <math>M_{1} = 22.9</math>,<ref name="JPL_289"/> 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.<ref name="Yoshida"/><ref name="Jewitt"/>

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.<ref name="Lamy2004"/>