Recall from Chapter 1 how we can use parallax to measure distances to terrestrial and solar system objects. Parallax is an object's apparent shift relative to some more distant background as the observer's point of view changes. 
(Sec. 1.5) To measure parallax, we must observe the object from either end of some baseline and measure the angle through which the line of sight to the object shifts. In astronomical contexts, we determine the parallax by comparing photographs made from the two ends of the baseline.
As the distance to the object increases or the baseline shrinks, the parallax becomes smaller and therefore harder to measure. Accordingly, a large baseline is essential for measuring the distance to a very remote object. The stars are so far away from us that even Earth's diameter is too short to use as a baseline in determining their distance. Their apparent shift, as seen from different points on Earth, is too small to measure. However, by comparing observations made of a star at different times of the year, as shown in Figure 17.1, we effectively extend the baseline to the diameter of Earth's orbit around the Sun, 2 A.U. Only with this enormously longer baseline do some stellar parallaxes become measurable. As indicated in the figure, a star's parallactic angle—or, more commonly, just its "parallax"—is conventionally defined to be half its apparent shift relative to the background as we move from one side of Earth's orbit to the other.
Figure 17.1 (a) The geometry of stellar parallax. For observations made 6 months apart, the baseline is twice the Earth—Sun distance, or 2 A.U. (b) The parallactic angle is usually measured photographically (the shift is greatly exaggerated in this drawing) .
The parallaxes of even the closest stars are very small, so astronomers generally find it convenient to measure parallax in arc seconds rather than in degrees. If we ask at what distance a star must lie in order for its observed parallax to be exactly 1", we get an answer of 206,265 A.U., or 3.1 
1016 m. Astronomers call this distance 1 parsec (1 pc), from "parallax in arc seconds." Because parallax decreases as distance increases, we can relate a star's parallax to its distance by the following simple formula:
Thus, a star with a measured parallax of 1" lies at a distance of 1 pc from the Sun. The parsec is defined so as to make the conversion between distance and parallactic angle easy. An object with a parallax of 0.5" lies at a distance of 2 pc; an object with a parallax of 0.1" lies at 10 pc, and so on. One parsec is approximately equal to 3.3 light years.
The closest star to Earth (excluding the Sun) is called Proxima Centauri. This star is a member of a triple-star system (three separate stars orbiting one another, bound together by gravity) known as the Alpha Centauri complex. Proxima Centauri displays the largest known stellar parallax, 0.76", which means that it is about 1.3 pc away—about 270,000 A.U., or 4.3 light years. That's the nearest star to Earth—at almost 300,000 times the distance from Earth to the Sun! This is a fairly typical interstellar distance in the Milky Way Galaxy.
Vast distances can sometimes be grasped by means of analogies. Imagine Earth as a grain of sand that orbits a golfball-sized Sun at a distance of about 1 m. The nearest star, also a golfball-sized object, is then more than 270 kilometers away. Except for the other planets in our solar system, themselves ranging in size from grains of sand to small marbles and all lying within 50 m of the "Sun," nothing else of consequence exists in the 270 km separating the two stars. Such is the void of interstellar space.
The next nearest neighbor to the Sun beyond the Alpha Centauri system is called Barnard's Star. Its parallax is 0.55", so it lies at a distance of 1.8 pc, or 6.0 light years—370 km in our model. Figure 17.2 is a map of our nearest galactic neighbors—the 30 or so stars lying within 4 pc of Earth.
Figure 17.2 A plot of the 30 closest stars to the Sun, projected so as to reveal their three-dimensional relationships. Notice that many are members of multiple-star systems. All lie within 4 pc (about 13 light years) of Earth.
As mentioned in Chapter 5, ground-based images of stars are generally smeared out into a disk of radius 1" or so by turbulence in Earth's atmosphere. (Sec. 5.3) However, astronomers have special equipment that can routinely measure stellar parallaxes of 0.03" or less, corresponding to stars within about 30 pc (100 light years) of Earth. Several thousand stars lie within this range, most of them much dimmer than the Sun and invisible to the naked eye. As discussed in more detail in Interlude 17-1, recently released data from the European Hipparcos satellite have extended the range of accurately measured parallaxes to well over 100 pc, encompassing nearly a million stars. Even so, the vast majority of stars in our galaxy are far more distant than this.
