Stellar Distances

The first attempts to estimate distances to stars proceeded on the assumption that the stars were roughly the same brightness as the Sun so that their distance could be determined by comparing their brightness with the brightness of the Sun. The task of determining the relative brightness of a star and the Sun was not completely straightforward, and the assumption that all stars possessed the same brightness as the Sun was later shown to be false. Hence the estimates that were obtained were quite crude, although they produced values that formed the basis for the first stage in charting the dimensions of the stellar universe.

Accurate distances would only be achieved with the measurement of trigonometric annual parallax. In the first few decades of the nineteenth century, advances in the grinding of lenses and the mounting of the telescope tubes permitted much greater accuracy in the determination of stellar positions. The refracting telescope was better suited to such work than the reflector and throughout the century was the instrument of choice for research at the leading observatories of Europe and America. A special type of refractor, called a heliometer, was built by the Munich instrument maker Joseph Fraunhofer (1787-1826). This instrument was used to measure the diameter of the Sun— hence its name—and could also be used to find the diameters of planets as well as the angular separation between stars. The objective lens of the refracting telescope was split in half, and the two semicircular halves were allowed to move with respect to each other. Two neighboring stars were sighted in the telescope, the first in one half of the lens and the second in the other half. By measuring the amount the two halves had to be moved in order to make the two images coincide, one obtained a very accurate value for the angular separation between the stars. The Konigsberg astronomer Friedrich Bessel (1784-1846) selected the star 61 Cygni as a candidate to measure parallax because its large proper motion indicated that it must be fairly close to the Sun. Working at his observatory with a 6.25-inch-aperture Fraunhofer heliometer, Bessel observed 61 Cygni over an 18-month period and documented small shifts in its position relative to two nearby faint and more distant stars. In 1838 he obtained a value for its parallax of approximately 0.314 seconds of arc, indicating that the star was at a distance of 10.3 light-years. (Later observation would increase this value to 11.2 light-years.) Subsequently, Thomas Henderson (1798-1844) of the Cape Observatory in South Africa obtained a parallax for a Centauri that was twice as large as 61 Cygni's, indicating that it was twice as close to the Sun.

In 1834 small variations in the proper motion of the dog star Sirius led Bessel to conclude that it had a companion star revolving about it. A similar conclusion followed from close observation of Procyon, Sirius's neighbor in the Little Dog. In 1862 Alvan Graham Clark (1832-1897) visually sighted Sirius's companion using an 18-inch refractor, and astronomers at the end of the century at the Lick Observatory sighted Procyon's companion. It was possible to calculate the masses of the companions, and these were found to be in the range of 10 percent of the mass of the primary star. It was clear that while the brightness of two stars may differ by a factor of thousands, their masses need differ only by only a factor of two or three.

The method of trigonometric parallax only gave distances for stars that were relatively close to the Sun, out to a distance of about 50 light-years. By the time photographic astrometry was introduced in the 1880s the parallax of 90 stars had been determined. Although limited in scope, the trigonometric method provides the essential base line for all further estimations of distance, enabling one to bootstrap from nearby stars to groups of stars more distant, whose distances are obtained by some other method. Distance methods involving variable stars that were developed in the twentieth century would prove to be crucial in the modern revolution in cosmology and are described in more detail in chapter 7.

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