# How do astronomers use the Doppler effect to determine the velocities of astronomical objects?

Nov 21, 2015

Astronomers analyze the shift of spectral patterns of the light emitted or absorbed by those objects.

#### Explanation:

One of the problems which prompted Einstein's work on relativity was the constant speed of light in a vacuum. Classical physics would expect that even if the emission speed of light, $c$, were a constant, the observed speed would change with the relative velocity, $v$, of the light emitting object.

Laboratory observations, however, consistently measured the speed of light to be $3 \cdot {10}^{8} \text{ m/s}$. It turns out that the speed remains the same, but the wavelength is compressed or stretched depending on whether the object is moving toward or away from the observer.

Since the wavelength of light determines its color, we call this change "blueshift" for objects moving toward the observer, and "redshift" for objects moving away. Edwin Hubble derived a formula for measuring velocity based on the change in wavelength.

$v = \frac{\lambda - {\lambda}_{o}}{\lambda} _ o \cdot c$

This means that we need to know the emitted wavelength of the light in order to calculate the velocity. This is where spectroscopy comes in.

Every element on the periodic table has its own unique emission spectrum. This spectrum is formed when electrons within the atoms of these elements are excited to higher energies and then relax back to the ground state. In order to relax the atoms give off light. Because of quantum mechanics, however, electrons can only exist in specific orbital energies, so the atoms can only emit photons with wavelengths that correspond to the energies of these transitions.

Hydrogen is a convenient element to use for spectroscopy because not only does it have a fairly simple emission spectrum, it is abundant throughout the universe. If we analyze the light spectrum of a galaxy, we would expect to find an emission line at $656 \text{ nm}$. If instead we find that line at $670 \text{ nm}$, then the star is moving relative to us at a velocity of;

$v = \left(670 \cdot {10}^{-} 9 \text{ m" - 656* 10^-9 " m")/(656 * 10^-9 " m")(3*10^8 " m/s}\right)$

$= 6.4 \cdot {10}^{6} \text{ m/s}$

That's $6.4 \text{ million m/s}$ away from us. A similar process can be used to determine the speed of stars relative to us, but it involves absorption spectrums. The absorption spectrum of an element is the same as the emission spectrum except that instead of photons being emitted, they are subtracted from a background light source.