## Motions

Stars have a space velocity, or motion through space with respect to the Sun, of many kilometers a second.

Space velocity has two components, which are measured independently: radial velocity, or speed toward or away from us along the line of sight; and proper motion, or the amount of angular change in a star's position per year (Figure 3.10).

A star's radial velocity is determined from analysis of its spectrum. The Doppler shift is an effect, discovered by Austrian physicist Christian Doppler (1803-1853), that applies to all wave motion. When a source of waves and an

Star first observed here.

Star first observed here.

2nd position of star

Proper motion

Figure 3.10. Space velocity has two components—radial velocity and proper motion.

Proper motion

2nd position of star

Figure 3.10. Space velocity has two components—radial velocity and proper motion.

observer are approaching or receding from each other, the observed wavelengths are changed.

A star's spectral lines (wavelengths) for any given element, such as iron, are compared with a reference spectrum. The star's wavelengths are shorter (blueshift) or longer (redshift) according to whether the star is moving toward or away from us (Figure 3.11).

The change in wavelength (AX) divided by the wavelength from a stationary source (X) is proportional to the relative velocity (v) (unless v is comparable to the velocity of light, c). The formula is:

Proper motion is measured over an interval of 20 to 30 years. The average proper motion for all visible stars is less than 0.1 second of arc (0".1) per year. At that rate you won't notice any change in the appearance of your favorite constellation during your lifetime. But if you could return to observe the sky 50,000 years from now, it would look very different (Figure 3.12).

Reference lines Object stationary

Reference lines Object stationary

Figure 3.11. Doppler shift. A sky object's spectral lines for any given element are compared with reference lines. Redshifted spectral lines indicate that the object is moving away from us.

Today

Today

50,000 years from now

Figure 3.12. Measured proper motion of the Big Dipper today indicates that the grouping will have a whole new look far in the future.

What is the angular change in an average visible star's position after 50,000 years?_

Answer: 5000 seconds of arc, or 1.39° (almost three times the Moon's angular diameter, which is 12°).

Solution: 0".1 per year x 50,000 years = 5000"

Other information about stars is obtained from careful measurements of spectral line shape.

Gas density, the mass per unit volume, is indicated by collisional broadening. A broadened spectral line is produced when atoms collide more frequently in higher-density stars.

Axial rotation, the rotation of a star around its axis, is indicated by rotational broadening. If observable, a broadened line can yield a lower limit to the star's rate of rotation on its axis.

A splitting or broadening of spectral lines occurs in the presence of a magnetic field, a region where magnetic forces are detected, which is called the Zeeman effect. The amount of splitting depends on the magnetic field strength.

These different kinds of broadening are not distinguishable to the unaided eye but are determined by careful analysis of the shape of the line using sensitive spectrometers.

List three properties of a star connected to its spectral line shape.