# Calculating radius of a blackbody

1. Oct 31, 2011

### the riddick25

1. The problem statement, all variables and given/known data
We are asked to calculate the flux at a specific wavelength (f_5500), the surface flux(F) and the radius of a star (Sirius A and then B)
We are given the following:
Brightness of Sirius A: V=-1.47
Effective temperature: 9870K
Central wavelength: 5510 Angstroms
Filter constant: Cv=3.58 x 10^-2 W m^-2 m^-1

We calculated distance earlier to be: 8.14 x 10^16 m

2. Relevant equations
f_5500=Cv x 10^-0.4V
F=((2hc^2)/(lambda)^5)(1/(exp(hc/lambda k T)-1))

3. The attempt at a solution
I calculated the first two parts correctly, getting values of:
f_5500=1.37x10^-1 W/m^2 m
F=1.804x10^14 W/m^2m

I am stuck on how to calculate the radius, as i thought have thought taking a ratio of the two fluxes would work, but i end up with R= d sqrt (f_5500/F)
This gives the wrong answer, the correct answer is found by using the same equation but with the F being (pi F)
I am unsure as to how this equation can be found, and so have no idea how to continue with the question

Any help would be greatly appreciated :D

Thanks