1.1.5. How Far to the Nearest Star?
For the next two centuries cosmological advances were tied to determining how big the Universe is (note that this effort continues today). During much of the eighteenth century a significant effort was made toward producing stellar catalogs with accurate positions from which determinations of stellar parallax could be made. This was an age of great anticipation, for the first accurate measurement of the stellar parallax of even just one star would provide the first observational determination of the size of the universe. The original stellar catalog of Tycho had a positional accuracy of 1 arcminute and the catalog of Edmund Halley (1656-1752) did not improve upon this, although Halley was able to detect the proper motion of nearby stars thus at least identifying good candidates for parallax measurements. These efforts continued largely through the work of James Bradley (1693-1762) and William Herschel (1738-1822). Many attempts were made to use these data to make stellar parallax measurements but the results were not very consistent or accurate. The first accurate stellar parallax measurement of 0.32 seconds of arc for the star 61 Cygni was published by the F.W. Bessel in 1838. This was followed in 1839 by Thomas Henderson's measurement of about 1 arc-second for Cen and the 1840 measurement of Lyrae (Vega) at 0.26 arcseconds. With these three measurements, it now became clear that the distance to even the closest stars was about one million times larger than the earth-sun distance. Such vast distances imply that the energy outputs of stars had to be huge.
The accurate observations of double star motions by Herschel now took on added meaning since these motions were accurately described by Newtonian gravity and hence the same force that held over the (by now) small scale of the Solar System, also held over very much larger scales. This is perhaps the first verification of an important principle, known as the Cosmological principle, which asserts that the Universe must be homogeneous and isotropic. Put another way, the Cosmological principle demands that the Universe is not arbitrary and hence any local physics must hold on larger scales. The motions of binary stars, therefore showed that the same physics which held the solar system together also occurred at a location many millions of times farther away.