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**Stellar radius determination** is generally approximated
by the formula relating luminosity, temperature, and radius:

L = 4πR²sT^{4}

- L,R,T - luminosity, radius, temperature.
- s - Stefan-Boltzmann constant

Or if the values are known in terms of the Sun's values:

R/R_{Sun}=(T_{Sun}/T)²(L/L_{Sun})^{1/2}

Both L and T need to be measured or estimated. Temperature is generally related to the B-V color index. With a parallax distance measurement, L is related to the apparent magnitude. This yields a very rough estimate: merely basing the temperature on b-v can result in a radius off by as much as 50%.

When a parallax distance is not available, an even rougher estimate can be made using the mass-luminosity relation and mass-radius relation.

More accurate determination uses:

- eclipsing binary stars: if their radial velocities can be determined, e.g., by Doppler shift, their separation can be derived and the eclipse yields information about their radii.
- Interferometry (for nearby stars).
- asteroseismology (for stars with observable vibrations): a relatively accurate method for the distances it covers, useful in calibrating other methods.
- Lunar occultation observations.

Only a few hundred stars have been measured by these more accurate methods. Using the more accurate radius in the above formula can sometimes yield a more accurate temperature determination.

One use for the radius is in the study of transiting extra-solar planets, to determine characteristics of the planet's orbit.

http://skyserver.sdss.org/dr1/en/proj/advanced/hr/radius1.asp

http://star-www.st-and.ac.uk/~kdh1/sea/sea09.pdf

asteroseismology

California-Kepler Survey (CKS)

Palomar Testbed Interferometer (PTI)

stellar luminosity determination

stellar parameter determination