Wonders: Netting the Deep Sky; May 2000; Scientific American Magazine; by Morrison, Morrison; 3 Page(s)
Held up at arm's length, your forefinger blocks out more than half a degree, enough to obscure the half-degree moon. No one imagines that the luminary is finger-size nor that your fist is in outer space. The match fixes neither distance nor size but only their ratio, as some fraction of a full circle. Angles have a history so long that Babylonian units are still used to describe them. In a full circle of 360 equal degrees, each degree is divided into 60 equal arc minutes, then each minute into 60 arc seconds. (We include the word "arc" with the unit to minimize confusion with the familiar measures of time.) Notice that we don't even need to know how far away the moon is to define its angular width. The length of that distant arc segment is simply proportional to its distance.
It is no surprise that astronomy and angles are old intimates. Celestial times, distances, sizes and maps largely arise from the notion of angle. The first detailed catalogue of some 1,000 star positions was reliable to about 20 arc minutes. It was made around 150 B.C. by Hipparchus of Rhodes: he probably used a tabletop brass dial. Around 1600 Tycho Brahe, with wall-size circles and metal sights without lenses, set a new accuracy record of around one minute in his list of 1,000 stars. In 1712 the first British Astronomer Royal, John Flamsteed, an ingenious pioneer of systematic telescopeaided mapping, finished his catalogue of more than 3,000 stars to an accuracy of about 10 arc seconds.