Stellar radii — common mistakes

Pay close attention to units! Ensure all distances are in metres, temperatures in Kelvin, and wavelengths in metres. Mistakes in unit conversion are a common pitfall in these calculations. Remember to use the correct constants for Wien's and Stefan-Boltzmann's laws. Ratio questions, like the second worked example, are common as they test your ability to manipulate formulas and cancel constants.

While stars aren't perfect blackbodies, their emission spectra are very close to the theoretical blackbody curve. This approximation simplifies calculations and allows us to apply powerful laws like Wien's and Stefan-Boltzmann's to estimate their properties with good accuracy.

The biggest challenge is accurately determining a star's distance from Earth. Errors in distance measurement directly affect the calculated luminosity (L) and subsequently the radius (r). This is why 'standard candles' are so crucial in astronomy.

A star's temperature has a huge impact on its luminosity, as L is proportional to T⁴. So, even a slightly hotter star is significantly more luminous. For a given luminosity, a hotter star must have a smaller radius, and a cooler star must have a larger radius to emit the same total power. This relationship is visualized on the H-R diagram.