In addition to the apparent motion caused by parallax, stars have real motion, too. In other words, stars travel through space. This stellar motion has two components. (Sec. 3.5) The transverse component measures a star's motion perpendicular to our line of sight—in other words, its motion across the sky. The radial component measures a star's movement along our line of sight—toward us or away from us.

The annual movement of a star across the sky, as seen from Earth (and corrected for parallax), is called proper motion. It describes the transverse component of a star's velocity relative to the Sun. Like parallax, proper motion is measured in terms of angular displacement. Since the angles involved are typically very small, proper motion is usually expressed in arc seconds per year. Stars' velocities through space can be quite large—tens or even hundreds of kilometers per second. However, because of their great distances, it usually takes many years for us to be able to discern their movement.

Figure 17.3 compares two photographs of the sky around Barnard's Star. They were made on the same day of the year, but 22 years apart. As the photographs show, Barnard's Star moved during this interval. If the two images were superimposed, the images of the other stars in the field of view would coincide, but those of Barnard's Star would not—Barnard's Star moved during this time interval. Because Earth was at the same point in its orbit when these photographs were taken, the displacement cannot be due to parallax caused by Earth's motion around the Sun. We conclude that the observed displacement indicates real space motion of Barnard's Star relative to the Sun.

Figure 17.3 Comparison of two photographic plates taken 22 years apart shows evidence of real space motion for Barnard's Star (denoted by an arrow).

Careful measurements show that Barnard's Star moved 227" during the 22-year interval. The proper motion of Barnard's Star is therefore 227" /22 years, or 10.3" /yr. This is the largest known proper motion of any star. Only a few hundred stars have proper motions greater than 1" /yr.

A star's transverse velocity is easily calculated once its proper motion and its distance are known. At the distance of Barnard's Star (1.8 pc), an angle of 10.3" corresponds to a physical displacement of 0.00009 pc, or about 2.8 billion km. Barnard's Star takes a year (3.2 10⁷ s) to travel this distance, so its transverse velocity is 2.8 billion km/3.2 10⁷ s, or 88 km/s.

As another example, consider the three-dimensional motion of our nearest neighbor, the Alpha Centauri system, sketched in Figure 17.4 in relation to our own solar system. Alpha Centauri's proper motion has been measured, relative to more distant background stars, at about 3.5" /yr. At Alpha Centauri's distance of 1.3 pc, this implies a transverse velocity of 22 km/s. We can determine the other component of motion—the radial velocity—using the Doppler effect. Spectral lines from Alpha Centauri are slightly blueshifted, allowing astronomers to measure the star system's radial velocity (relative to the Sun) as 20 km/s toward us. (Sec. 3.5)

Figure 17.4 The motion of the Alpha Centauri star system drawn relative to our solar system. The transverse component of the velocity has been determined by observing the system's proper motion. The radial component is measured using the Doppler shift of lines in Alpha Centauri's spectrum. The true space velocity, indicated by the red arrow, results from the combination of the two.

What is the true space motion of Alpha Centauri? Will this alien system collide with our own some time in the future? The answer is no—Alpha Centauri's transverse velocity will steer it well clear of the Sun. We can combine the transverse and radial velocities according to the Pythagorean theorem. The total velocity is or about 30 km/s, in the direction shown by the horizontal red arrow in Figure 17.4. As that figure indicates, Alpha Centauri will get no closer to us than about 1 pc, and that won't happen until 280 centuries from now.