# How to calculate the size of a star with just temperature

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1. May 2, 2016

### timnswede

1. The problem statement, all variables and given/known data
This isn't a specific problem, but my professor told us that we can calculate the size of a star if we know the temperature of it.

2. Relevant equations
Stefan-Boltzmann Law, Wien's displacement law.

3. The attempt at a solution
With the temperature i can also get the intensity with Stefan-Boltzmann law and intensity is power over area and area is what i want. But I don't see how I am supposed to be able to calculate area without also knowing the power. My professor also mentioned wavelength which I know I can calculate with Wien's displacement law if i know the temperature, but I can't figure out how that will help me.

2. May 2, 2016

### drvrm

with the temperature of a star-T known
the amount of radiation emitted can be estimated using the famous Stefan- Boltzmann law.

therefore if one can estimate the Luminosity ,there are methods using H-R diagrams that its size can be estimated..
Energy radiated per sec per unit area is equivalent to stefan's constant x T^4 and
if the star has radius R
then one can relate energy radiated per sec to temp..
and if comparison is made with other steller radiators one can have some idea about its size

3. May 2, 2016

### timnswede

So without knowing luminosity (which is just power?) then the area can't be found?

4. May 2, 2016

### drvrm

its difficult as some size effects must be there to be observed -apart from temperature!
at least for single stars.

for binary stars some eclipse method gives an estimate of size -
as binary stars move about its center of mass and can eclipse each other and during eclipse the emitted spectral line Doppler shift can be related to their speed
and the time of eclipse can be used to estimate their size.