# 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 $$5630\, ^{\circ}\mathrm{C}$$.

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