The Race Toward Stellar Distances

During his short life, Joseph von Fraunhofer made important advances to telescopes. He constructed a stand on which the telescope could rotate equatorially, with the axis of rotation pointing at the North Pole. It had a clock mechanism keeping the correct rate of rotation so that the desired star remained in the field of view and its position could be carefully measured by an astronomer. He also manufactured a special kind of refracting telescope, so-called heliometer, which was very suitable for precision measurements of angles between two stars.

Fraunhofer's skill of making instruments led to the first reliable measurement of a star's parallax by Friedrich Bessel (1784-1846). This director of the Observatory of Konigsberg was a self-made man, whose teenage dream had been to go on a trading expedition to China and the East Indies. In preparation for this trip he desired to add some acquaintance with the art of taking observations at sea. He was thus led from navigation to astronomy and from astronomy to mathematics.

Fraunhofer built the first heliometer for Bessel's observatory. However, it was completed only after the death of the master optician and was mounted in 1829. Bessel was well aware of the high quality of the instrument but only in 1837 did he find time to make a serious attack on the problem of parallax. Unlike Herschel, he did not use stellar brightness as a criterion of closeness; rather he reasoned that a star with a rapid motion across the sky should be nearby. One century earlier the British astronomer Edmond Halley (1656-1742) had shown that stars are not fixed on the celestial sphere, but move slowly. For example, since the time of Ptolemy, Sirius had shifted its position by half a degree (the diameter of the full Moon). These proper motions reflect the motion of both our Sun in space and the intrinsic motion of the star itself. In any case, it is expected that a distant star has a small proper motion, while nearby stars would appear to move more swiftly (similarly when sitting in a moving train the things close to you seem to move quickly while the distant landscape is crawling slowly). Bessel's criterion explains why he chose a rather inconspicuous star, 61 Cygni, at the back edge of the "wing" of the Swan (the constellation Cygnus). This star is actually a "sprinter" among stars, as it moves more than three diameters of the full Moon during one thousand years (the record-holder is Barnard's star in Ophiuchus, running across one Moon diameter in 180 years; in fact, it is the second nearest star).

Bessel measured for over one year the angular distance of 61 Cygni from three faint comparison stars. His careful analysis of the measurements revealed that the star had a parallax of 0.3136 ± 0.0202 arcsec. A parallax of one second of arc corresponds to a distance of 206,265 radii of the Earth's orbit (Box 8.1), Bessel's result put 61 Cygni at a distance of about 650,000 times the Sun-Earth distance.2

The first measurement of a star's distance aroused much attention, being an important breakthrough in astronomy. The tiny effect, to which Ptolemy and Galileo had referred to, was finally observed, and determination of cosmic distances had moved from the Solar System to the realm of the stars (Fig. 8.4).

Just 2 months after Bessel had communicated his result, the Scottish Thomas Henderson (1798-1844) informed the astronomy community that he had measured the parallax of the bright southern star alpha Centauri. The result, based on his observations several years earlier at the Observatory of the Cape of Good Hope in South Africa, was 0.98 ± 0.09 arcsec. The modern value for this nearest of all stars (excepting our Sun, of course) is 0.75 arcsec. In fact, alpha Centauri is made of three stars revolving around each other, of which Proxima Centauri is the nearest one. Its distance is 1.3 parsec.

In fact, the question of stellar distances was much "in the air." The head of Dorpat (Tartu) observatory Friedrich Struve (1793-1864) had ordered from Utzschneider and Fraunhofer a high-class telescope. Its 24-cm objective lens made it the largest refractor in the world, when it started operating in 1824. Among other objects, Struve focused the telescope on the brightest star of the northern heavens, Vega. Observations in 1835-36 put its parallax into the range 0.10-0.18 arcsec, as he reported to St. Petersburg Academy of Science in 1837. His notice was read in the meeting of the Academy, but it got buried in the archives. The modern value for Vega's parallax

2 The modern looking "plus/minus" error estimate in Bessel's result was calculated by the new recipe by mathematician Carl Friedrich Gauss, who had found out how one can derive from observations not only an average value for the result, but also an estimate for its accuracy. Modern measurements have given for the parallax of 61 Cygni the value 0.299 ± 0.0045 arcsec, so Bessel's measurement was not far from the true value.

Fig. 8.4 Fraunhofer heliometer at the Royal Observatory of Königsberg which was used to make the first measurement of the parallax (distance) of a star. In 1838, Bessel determined that the distance of 61 Cygni is about 650,000 times the distance to the Sun

is 0.12 arcsec (distance = 8pc), so Struve was on the right track. However, he was not yet satisfied by the result and continued with the observations. When he finally published, in 1840, his final results, he derived the parallax 0.26 ± 0.03 arcsec. For some reason he had got twice the true value, or the distance 50% too short.

After these pioneering efforts by three astronomers, parallax measurement was a demonstrated technique of obtaining star distances and became an important specialty in astronomy. The large distances proved that stars are so remote that to be visible in our sky, they must be pouring out as much or even more light than the Sun. If one gives stellar distances in kilometers, cumbersomely large numbers appear, since 1pc is about 3 x 1013km. Even the nearest star is 3.9 x 1013km away, an immense distance. If stars were squeezed down into the size of an apple, they would still be separated by some 20,000 km. Stars are really very sparsely scattered in space and collisions between them are extremely rare!

The parsec unit is comparable to the huge distances between stars and is directly related to the method of measuring star distances. Astronomers usually express cosmic distances in parsecs. In this book we also use the light year (remember that 1 parsec is about 3.3 light years).

At first the number of stars having their parallax measured grew quite slowly. At the end of the 1870s only around 20 parallaxes were known, because visual measurements through the telescope were tedious. But when astronomical photography matured in the 1880s, astronomers started to make also parallax measurements from photographs, which speeded up the process. By the present day more than 7,000 parallaxes have been measured with ground-based telescopes.

All known stars are more distant than 1 parsec, so the parallax shift in the sky is always less than one second of arc. Such very small shifts are difficult to detect even with the widely separated astronomer's "eyes" (the diameter of the Earth's orbit). The restless air spreads the image of a star into a fuzzy dot, which limits ground-based parallax measurements to stars closer than 50 parsec.

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