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.