star Distances to the starsastronomy

Distances to stars were first determined by the technique of trigonometric parallax, a method still used for nearby stars. When the position of a nearby star is measured from two points on opposite sides of Earth’s orbit (i.e., six months apart), a small angular (artificial) displacement is observed relative to a background of very remote (essentially fixed) stars. Using the radius of Earth’s orbit as the baseline, the distance of the star can be found from the parallactic angle, p. If p = 1″ (one second of arc), the distance of the star is 206,265 times Earth’s distance from the Sun—namely, 3.26 light-years. This unit of distance is termed the parsec, defined as the distance of an object whose parallax equals one arc second. Therefore, one parsec equals 3.26 light-years. Since parallax is inversely proportional to distance, a star at 10 parsecs would have a parallax of 0.1″. The nearest star to Earth, Proxima Centauri (a member of the triple system of Alpha Centauri), has a parallax of 0.7723″, meaning that its distance is ¹/_0.7723, or 1.295, parsecs, which equals 4.22 light-years. The parallax of Barnard’s star, the next closest after the Alpha Centauri system, is 0.549″, so that its distance is nearly 6 light-years. Errors of such parallaxes are now typically 0.005″, meaning that there is a 50 percent probability that a star whose parallax is 0.065″ lies between 14.3 and 16.7 parsecs (corresponding to parallaxes of 0.070″ and 0.060″, respectively), and an equal chance that it lies outside that range. Thus, measurements of trigonometric parallaxes are useful for only the nearby stars within a few hundred light-years. In fact, of the approximately 100 billion stars in the Milky Way Galaxy (also simply called the Galaxy), only about 700 are close enough to have their parallaxes measured with useful accuracy. For more distant stars indirect methods are used; most of them depend on comparing the intrinsic brightness of a star (found, for example, from its spectrum or other observable property) with its apparent brightness.