How to Determine the Temperature of the Sun without Touching it?

Video: Temperature of the Sun: how to determine

To calculate the temperature \( T \) of the Sun from Earth, one must first find out what light the Sun emits. The Sun emits a polychromatic light, that is, infrared light, visible light, and even X-rays and gamma rays. You need to figure out the wavelengths \( \lambda \) of each of these radiations and with what intensity ("how bright"?) they are emitted. If you plot all wavelengths with their intensities in a diagram, you get a spectral intensity distribution of the sun. From this distribution, you have to read off the wavelength \( \class{blue}{\lambda_{\text{max}}} \) which has the highest intensity (maximum of the function).

Then you can calculate the temperature of the sun with the Wien's displacement law:

In the case of the sun, the maximum is within the blue light spectrum at the wavelength \( \lambda_{\text{max}} = 490 \, \mathrm{nm} = 490 \cdot 10^{-9}\, \mathrm{m} \). This results in a temperature of \( T = 5900 \, \mathrm{K}\) or \( 5630\, ^{\circ}\mathrm{C} \).