Radius of the Sun from Doppler Shift

Since the Sun is rotating on its axis, half of its body is rotating towards us while half of it is rotating away from us. This results in a measurable Doppler shift in the emission spectra from the two sides of the sun. Such a spectrum is shown below. The red line is the spectrum from a point on the Sun rotating away from Earth, the black line is from the center of the Sun, and the green line is from a point on the Sun rotating towards Earth. Note the trough at 6224.75 wavenumbers. This indicates the wavelength that is most readily absorbed by the Earth's atmosphere, and has been used to align the three curves.

Our reference wavelength will be the one from the center of the Sun (black line), because the center of the Sun is not rotating and thus this wavelength is not Doppler shifted. Our change in wavelength is approximately the same for the parts of the sun that are moving towards and away from us (as we would expect). We will calculate the values of the reference wavelength and the change in wavelength:

Using the Doppler shift equation, we can solve for the speed at the surface of the Sun:

If we know the angular frequency of the Sun's rotation, we can find the radius. Consider these two images of a particular sunspot (labeled "George") taken 7 days apart. 

We see that the labeled sunspot rotates about a quarter of a turn in this much time. Thus, we can find the angular frequency of the Sun's rotation as follows:

Now, we can solve for radius:

This is the same order of magnitude as the accepted value of