The Nonrelativistic Doppler Effect

As we saw in our discussion of the properties of electromagnetic radiation (Chapter 5), relative motion of a source creates a shift in the frequency of light (or any other wave) called the Doppler effect. The adjacent right figure illustrates, as does this animation. The Doppler effect for light leads to a displacement in the position of spectral lines. Motion of the source away from the observer causes a shift to longer wavelengths that is termed a red shift. Motion of the source toward the observer causes a shift to shorter wavelengths that is termed a blue shift.

Importance of Doppler Shifts
The Doppler effect is particularly important in astronomy because it allows a rather simple determination of the radial velocity (velocity along the line of sight) for a source emitting electromagnetic waves. Since binary stars are in orbit around their center of mass, the measurement of Doppler shifts in the light coming from binary systems provides an important way to learn about this motion.

The Doppler Shift Formula
In nonrelativistic approximation, the radial velocity and the Doppler shift of spectral lines are related by the formulas given in the adjacent left figure. The nonrelativistic approximation is valid when the velocities v are much less than the speed of light c. If v is comparable to c, a slightly more complex formula must be used but the effect is still to allow a velocity to be computed from a Doppler shift. (We shall have need of the more complex formula when we consider the expansion of the Universe in later chapters.) The radial velocities in all normal binary star systems are much smaller than the speed of light, so the simpler nonrelativistic form of the Doppler shift is adequate for our discussion in this chapter.