• DOI:10.1177/002182867500600201
• Corpus ID: 125137430

Archimedes's Measurement of the Sun's Apparent Diameter

@article{Shapiro1975ArchimedessMO,
  title={Archimedes's Measurement of the Sun's Apparent Diameter},
  author={A. Eugene Shapiro},
  journal={Journal for the History of Astronomy},
  year={1975},
  volume={6},
  pages={75 - 83}
}

• A. Shapiro
• Published 1 June 1975
• Physics
• Journal for the History of Astronomy

Although Archimedes's principal concern in The sand-reckoner is arithmetical, the work is equally important for its astronomical contribution. Archimedes's goal in The sand-reckoner is to demonstrate that he can write a number so large that it will exceed even the number of grains of sand needed to fill the entire universe, so he must first find the size of the universe. It is at this point that Archimedes relates, in a well-known passage, Aristarchus's heliocentric theory. Since an heliocentric theory implies a much larger universe than a geocentric one, because of the absence of stellar parallax-and the larger a universe, the better for Archimedes's purpose-he chooses to fill Aristarchus's heliocentric universe with sand. To estimate the size of Aristarchus's universe Archimedes needs values for the circumference of the Earth, the relative sizes of the Earth, Sun and Moon, and the apparent diameter of the Sun. Archimedes is content to adopt his predecessors' results for all these parameters-but suitably adjusting them so that they always result in an overestimate for the size of the universeexcept that of the apparent diameter of the Sun, which he chooses to determine by his own observations. Archimedes may have chosen this parameter alone to redetermine, because it was in doubt: Aristarchus himself in his On the sizes and distances of the Sun and Moon accepted a value of 2° for the apparent diameter of the Sun, while Archimedes reported in The sand-reckoner that "Aristarchus discovered that the Sun appeared to be about 7hth part of the circle of the zodiac", i.e. a more reasonable to, which Archimedes's own observations would confirm.' Archimedes's description of his determination of the solar diameter is of interest from many aspects, especially since it is the earliest extant Greek account of an astronomical measurement. I will, however, consider it only as it relates to practical astronomy, and in particular to the measurement of small angles. I intend to show that, despite a lack of trigonometry and a table of chords, Archimedes was able to make do with an approximative procedure for calculating small angles from linear measurements. I have appended an English translation of this passage, since Heath unfortunately omitted its translation in his The works of Archimedes, because he judged it to be only a "rough experiment".» While Archimedes's account is rather terse and omits features which we would expect today, such as the dimensions of the instrument and the raw observational data, it is, nonetheless, a sophisticated piece of work: the procedure followed and apparatus used are described; correction factors are applied; and, most significantly, the result is given with an experimental error in the form of an upper and lower bound, rather than as a unique value. Archimedes was very much aware of the problem of precision in physical measurements, for "it is", he tells us, "not easy to measure this angle with precision, for neither the eye, nor the hands, nor the instruments for measuring it are reliable enough for determining it exactly". I will only briefly describe Archimedes's procedure and apparatus for