Editing Luminosity (section)

== Luminosity formulae ==
{{More citations needed section|date=July 2023}}
[[File:Inverse square law.svg|right|thumb|Point source ''S'' is radiating light equally in all directions. The amount passing through an area ''A'' varies with the distance of the surface from the light.]]

The [[Stefan–Boltzmann law|Stefan–Boltzmann]] equation applied to a [[black body]] gives the value for luminosity for a black body, an idealized object which is perfectly opaque and non-reflecting:<ref name="AUSTRALIA2004"/>
<math display="block">L = \sigma A T^4,</math>
where ''A'' is the surface area, ''T'' is the temperature (in kelvins) and {{math|''σ''}} is the [[Stefan–Boltzmann constant]], with a value of {{physconst|sigma|after=.}}

Imagine a point source of light of luminosity <math>L</math> that radiates equally in all directions. A hollow [[sphere]] centered on the point would have its entire interior surface illuminated. As the radius increases, the surface area will also increase, and the constant luminosity has more surface area to illuminate, leading to a decrease in observed brightness.

<math display="block">F = \frac{L}{A},</math>
where
*<math>A</math> is the area of the illuminated surface.
*<math>F</math> is the [[flux density]] of the illuminated surface.

The surface area of a sphere with radius ''r'' is <math>A = 4\pi r^2</math>, so for stars and other point sources of light: 
<math display="block">F = \frac{L}{4\pi r^2} \,,</math>
where <math>r</math> is the distance from the observer to the light source.

For stars on the [[main sequence]], luminosity is also [[mass–luminosity relation|related to mass]] approximately as below:
<math display="block">\frac{L}{L_{\odot}} \approx {\left ( \frac{M}{M_{\odot}} \right )}^{3.5}.</math>