Measuring stellar orbital velocity in a binary star system
In order to understand how the orbital velocities of stars in a binary
system are determined, you must first understand the Doppler effect.
The light that we see can be thought of as waves in the electromagnetic
field. The wavelength (or distance from one wave crest to the next) of light
is very small... ranging from four to seven ten-millionths of a meter. The
different wavelengths of light are what the human eye sees as different
colors, with the longest wavelengths appearing at the red end of the
spectrum and the shortest wavelengths at the blue end.
Now imagine a source of light at a constant distance from us... say a star.
The star emits light at a constant wavelength and we receive the light here on
Earth at the same constant wavelength. Now suppose that the star starts to
move toward us. When the source emits the next wave, it will be slightly
nearer to us, so the distance between wave crests will be smaller than when
the star was stationary. This means that the wavelength of the waves we
receive on Earth is shorter than what we saw from the stationary star.
Correspondingly, if the star is moving away from us, the wavelength of the
waves we receive will be slightly longer. In the case of light, this means
that a star moving toward us will have its spectrum shifted toward the blue
end of the spectrum (blue-shifted) and stars moving away from us will have
their spectrum red-shifted. The relationship between the amount of the shift
and the velocity at which the source is moving is called the Doppler equation.
When the velocity is small (relative to the speed of light), the
equation simplifies to:
source velocity/speed of light = change in wavelength/rest wavelength
Now let us think about two stars in a binary system. Let us take a
"bird's eye" view, that is, let us look down from above the
system and the Earth-observer. It might look something like this:
On one side of the orbit, the star is moving toward us and on the other
side of the orbit, it is moving away from us. This is all we need to have a
Doppler shift, which can then tell us how fast the star is moving!