Astrophysics: how hard can it be?

 

Today, let’s calculate the surface temperature of a star.

Physicists like to use the Kelvin temperature because it is convenient. Just imagine a black rock in the middle of nowhere in the universe. It’s very cold because nothing warms it up. So we say it’s at 0 degrees Kelvin. 0°K! In the more familiar Celsius scale, it would be -273°C.

That black rock at 0°K does not emit any radiation. But if we warm it up, it will start to emit some weak infrared light. If we heat it hard, it will glow red, then yellow, then white…

Now let’s look at the light. It is an electromagnetic wave, and its wavelength defines its colour. The wavelength is expressed in nanometers. FYI 1 nm is 1/1000th of a micron. Visible light ranges from 400nm (deep red) to 700nm (violet).

Physicists found out that the light spectrum emitted by a black body has always the same shape. As the black body gets hotter, the peak of the spectrum curve shifts towards the short wavelengths. At 4,000°K, it looks red with a peak around 700nm. At 18,000°K, it Peaks around 400 nm (blue).

So to measure the temperature of a star, you point your spectrometer at it and plot its emission curve. Then you find out where the peak wavelength is and apply Wien’s law:

T = 2,900,000 / top wavelength in nm.

Try it on the Sun: it peaks at 500nm, So T = 2,900000 / 500 = 5,800°K.

How hard was that?

References:

Wien’s law: https://en.wikipedia.org/wiki/Wien%27s_displacement_law