(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The monochromatic flux emitted from unit surface area of a black body is given by

[tex] F_{\lambda}(T) = \frac{2h\pi c^{2}}{\lambda^{5}} \frac{1}{exp(hc/\lambda KT)-1} Wm^{-2}m^{-1} [/tex]

If the distance to star X is 620 parsecs, calculate:

(a) the radius of star X, in Solar radii; [3]

(b) the bolometric luminosity of star X, in units of Solar luminosity. [1]

2. Relevant equations

OK so I know if we integrate the given equation between 0 and infintiy we get the bolometric flux for F(T). When we perform this integration we end up with the stefan boltzmann equation:

[tex]F(T) = \sigma T^{4} Wm^{-2}[/tex]

this enables me to calulate the bolometric surface flux, great.

Now i want the radius of star X. I am aware that

[tex]F^{bol} = (\frac{R}{d})^{2}\sigma T^{4}[/tex]

where R is the stellar radius and d the distance to the star.

My problem comes here. I can't calculate the flux from the stefan boltzmann equation and use it in this last equation because I will always have the distance to the star equal to the radius, which cannot be correct.

Any help would be greatly appreciated

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# Calculating Stellar radius from bolometric flux

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