# How Big is That Star?

## 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 = change in wavelength speed of light 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!

 A service of the High Energy Astrophysics Science Archive Research Center (HEASARC), Dr. Alan Smale (Director), within the Astrophysics Science Division (ASD) at NASA/GSFC