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

## Answer #1

Level 2 (without higher mathematics)

Answered by Alexander Fufaev

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 so-called **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**:

**Wien's Displacement Law**$$ \begin{align} T ~=~ \frac{ 2897.8 \,\cdot\, 10^{-6} \text{mK} }{ \class{blue}{ \lambda_{\text{max}}} } \end{align} $$