Editing Visual binary (section)

==Mass–luminosity relationship==
In order to find the [[luminosity]] of the stars, the rate of flow of [[radiant energy]], otherwise known as radiant flux, must be observed. When the observed luminosities and masses are graphed, the [[mass–luminosity relation]] is obtained. This relationship was found by Arthur Eddington in 1924.

:<math>\frac{L}{L_{\odot}} = \left(\frac{M}{M_{\odot}}\right)^\alpha</math>

Where L is the luminosity of the star and M is its mass. ''L''<sub>⊙</sub> and ''M''<sub>⊙</sub> are the luminosity and mass of the Sun.<ref name="evolutionofstars">{{cite book|last=Salaris|first=Maurizio|author2=Santi Cassisi |title=Evolution of stars and stellar populations |publisher=[[John Wiley & Sons]]|date=2005|pages=138–140|isbn=0-470-09220-3|url=https://books.google.com/books?id=r1dNzr8viRYC&q=Mass-Luminosity%20relation&pg=PA138}}</ref> The value ''<math>\alpha</math>''&nbsp;=&nbsp;3.5 is commonly used for [[main sequence|main-sequence]] stars.<ref>{{cite web|url=http://hyperphysics.phy-astr.gsu.edu/hbase/Astro/herrus.html#c3|title=Mass–luminosity relationship|publisher=Hyperphysics|access-date=2009-08-23}}</ref> This equation and the usual value of a = 3.5 only applies to main-sequence stars with masses 2''M''<sub>⊙</sub>&nbsp;<&nbsp;''M''&nbsp;<&nbsp;20''M''<sub>⊙</sub> and does not apply to red giants or white dwarfs. For these stars, the equation applies with different constants, since these stars have different masses. For the different ranges of masses, an adequate form of the Mass–Luminosity Relation is

:<math>\frac{L}{L_{\odot}} \approx .23\left(\frac{M}{M_{\odot}}\right)^{2.3}   \qquad (M < .43M_{\odot})</math>
:<math>\frac{L}{L_{\odot}} = \left(\frac{M}{M_{\odot}}\right)^4   \qquad\qquad      (.43M_{\odot} < M < 2M_{\odot})</math>
:<math>\frac{L}{L_{\odot}} \approx 1.5\left(\frac{M}{M_{\odot}}\right)^{3.5}   \qquad (2M_{\odot} < M < 20M_{\odot})</math>
:<math>\frac{L}{L_{\odot}} \varpropto \frac{M}{M_{\odot}}   \qquad (M > 20M_{\odot})</math>

The greater a star's luminosity, the greater its mass will be. The [[absolute magnitude]] or luminosity of a star can be found by knowing the distance to it and its [[apparent magnitude]]. The stars [[bolometric magnitude]] is plotted against its mass, in units of the Sun's mass. This is determined through observation and then the mass of the star is read of the plot. Giants and main sequence stars tend to agree with this, but super giants do not and neither do white dwarfs. The Mass–Luminosity Relation is very useful because, due to the observation of binaries, particularly the visual binaries since the masses of many stars have been found this way, astronomers have gained insight into the evolution of stars, including how they are born.<ref name="double"/><ref name="evolutionofstars"/><ref name="advanced">{{cite book|last=Duric|first=Nebojsa|author-link=Neb Duric|title=Advanced astrophysics|publisher=[[Cambridge University Press]]|date=2004|pages=19|isbn=978-0-521-52571-8|url=https://books.google.com/books?id=-ljdYMmI0EIC&q=Mass-luminosity%20relation&pg=PA19}}</ref>