Sunday 29 March 2020

astrophysics - How do astronomers know what wavelength the body will emit when it is at rest?




In the book of The First Three Minutes by Weinberg, at page 21, he talks about how do astronomers measure the speed of a luminous body along the line of sight by Doppler affect, i.e. the fractional change in the wavelength of the incoming light will be proportional to the speed of the body to $c$, but to use this technique, we need to know the original wavelength, i.e the wavelength of the emitted light when the body is at rest, without it we cannot talk about any increase in the wavelength, so how do astronomers get this information prior to the measurement?



Answer



As an addition to the correct answer of @flippiefanus, consider the element sodium.


When excited at low pressure by an electric arc, sodium vapour emits a complex spectrum of discrete wavelengths, an atomic emission spectrum, dominated by two intense emission lines with slightly different wavelengths: one at $588.9950$ nanometres and the second at $589.5924$ nanometres. If you have ever tossed some salt (or salt water) into a Bunsen burner flame, or seen a low-pressure sodium street light, you've seen these two wavelengths.


In addition, if you pass a continuous spectrum through a cloud of unexcited sodium vapour, these same two wavelengths will be strongly absorbed in an atomic absorption spectrum.


The two wavelengths above have been very precisely measured for sodium atoms at rest in the lab framework. In addition, the ratio of the two wavelengths has been calculated: $1.00101427$.


If the sodium is moving towards or away from the observer at some unknown speed, the two emission lines will both be Doppler shifted by the same factor, but the ratio will stay the same!


So, if an astronomer takes a spectrum of a distant star and sees two very close, strong, emission or absorption lines, he/she will calculate the ratio of the two wavelengths. If the result is the same as the ratio above, then the original wavelengths are known, and the observed wavelengths, via the Doppler shift, will produce a velocity of recession or approach.


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