CHAPTER 7 | ATOMS AND STARLIGHT 139
much too small to change the color of a star, but they are easily
detected in spectra.
Th e terms redshift and blueshift are used to refer to any range
of wavelengths. Th e light does not actually have to be red or blue,
and the terms apply equally to wavelengths in other parts of the
electromagnetic spectrum such as X-rays and radio waves. Red
and blue refer to the direction of the shift, not to actual color.
Th e amount of change in wavelength, and thus the magnitude
of the Doppler shift, depends on the velocity of the source. A mov-
ing car has a smaller Doppler shift than a jet plane, and a slow-
moving star has a smaller Doppler shift than one that is moving
more quickly. You can measure the velocity of a star by measuring
the size of its Doppler shift. If a star is moving toward Earth, it has
a blue shift and each of its spectral lines is shifted very slightly
toward shorter wavelengths. If it is receding from Earth, it has a
red shift. Th e next section will show how astronomers can convert
Doppler shifts into velocities.
When you think about the Doppler eff ect, it is important to
understand two things. Earth itself moves, so a measurement of
a Doppler shift really measures the relative motion between
Earth and the star. Figure 7-11c shows the Doppler eff ect in two
spectra of the star Arcturus. Lines in the top spectrum are slightly
blueshifted because the spectrum was recorded when Earth, in
the course of its orbit, was moving toward Arcturus. Lines in the
bottom spectrum are redshifted because it was recorded six
months later, when Earth was moving away from Arcturus. To
fi nd the true motion of Arcturus, astronomers must subtract the
motion of Earth.
Th e second point to remember is that the Doppler shift is
sensitive only to the part of the velocity directed away from you
or toward you—the radial velocity (V r) (■ Figure 7-12a). You
cannot use the Doppler eff ect to detect any part of the velocity
that is perpendicular to your line of sight. A star moving to the
left, for example, would have no blueshift or redshift because its
distance from Earth would not be decreasing or increasing. Th is
is why police using radar guns park right next to the highway
(Figure 7-12b). Th ey want to measure your full velocity as you
drive past, not just part of your velocity.
Calculating the Doppler Velocity
It is easy to calculate the radial velocity of an object from its
Doppler shift. Th e formula is a simple proportion relating the
■ Figure 7-12
(a) From Earth, astronomers can use the Doppler effect to measure the radial
velocity (Vr ) of a star, but they cannot measure its true velocity, V, through
space. (b) Police radar can measure only the radial part of your velocity (Vr )
as you drive down the highway, not your true velocity along the pavement
(V). That is why police using radar should never park far from the highway.
This police car is poorly placed to make a good measurement.EarthVVrbVVraradial velocity Vr divided by the speed of light c, to the change in
wavelength, , divided by the un-shifted wavelength, 0 :
Vr
__c Δ___
0
For example, suppose you observed a line in a star’s spec-
trum with a wavelength of 600.1 nm. Laboratory measurements
show that the line should have a wavelength of 600 nm. Th at is,
its un-shifted wavelength is 600 nm. What is the star’s radial
velocity? First note that the change in wavelength is 0.1 nm:
Vr
__
c ____0.1
600 0.000167Multiplying by the speed of light, 3.00 × 105 km/s, gives the
radial velocity, 50 km/s. Because the wavelength is shifted to the
red (lengthened), the star must be receding.