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The "brightness" of a star is actually measured in terms of the radiant flux $ F $ received from the star. The radiant flux is the total amount of light energy of all wavelengths that crosses a unit area oriented perpendicular to the direction of the light's travel per unit time.

Units of FluxEdit

$ F = \frac {[energy]}{[time][distance]^2} $

Relationship to LuminosityEdit

Flux

A visual depiction of the flux with respect to luminosity of a star

Imagine a star of luminosity $ L $ surrounded by a huge spherical shell of $ r $. Then, assuming that no light is absorbed during its journey out to the shell, the radiant flux $ F $, measured at a distance $ r $ follows the equation detailed below

$ F = \frac {L}{4 \pi r^2} $





Reliance on Surface AreaEdit

Half flux

This diagram shows the effects when the energy from the luminosity is not directed into the full celestial sphere, but rather into half

The flux changes depending on how much surface area the luminosity is being directed towards.

When the luminosity is being directed into half the celestial sphere, the flux can be described with:

$ F = \frac {L}{2 \pi r^2} $






Luminosity of an Object Receiving FluxEdit

When an object receives flux and reflects it, it will inherently have some luminosity. Assuming that an object receives $ F _r $ and reflects with some factor $ \alpha $ (0 is total absorbing, 1 is total reflecting) and the object has some cross sectional area $ A $, then it's luminosity can be expressed as:

$ L = \alpha A F _r $

Blackbody Surface FluxEdit

The amount of surface flux emitted by a blackbody can be characterized with the following equation:

$ F _{blackbody} = \sigma T^4 $

Flux Retained Through a MediumEdit

Whenever flux goes through some medium, there is some of it that will inevitably be absorbed. The equation that governs how much flux will leave the medium is described below:

$ F = F_o e ^ {-\tau} $