Rawlins' VA theory on Aristarchos
- Topic:
- Angles
'For the terminator to deviate more than 27″ ± 3″ from straightness, the line connecting the Moon’s horns must deviate 54″ ± 6″ from the middle of the terminator. The arcsine of the ratio of this to Aristarchos’ lunar semidiameter (0.5º) equals 2º38′ ≈ 3º. (Rawlins 1991:170’s analyses [in DIO 1.2-3 ‡9] used 0.4′ instead of 0.0001 radians, yielding 2º57′ by the same equation.) Note that DR has not arbitrarily conjured up [a visual acuity] α ≈ 24″ for the purposes of this paper: Rawlins (1982:263), in a quite different context, noted that the mean angular separation of the retina’s foveal cones is 24″ to 30″. (The arcsine of 0.45′/15′ is 3º26′ ≈ 3º). I found by experiment long ago that the eye’s primitive visual limit is about 1/3′. (The arcsine of this divided by 1/4º is 2º33′ ≈ 3º.) Aristarchos presumably performed just such an experiment to arrive at his value for α. These estimates agree closely with Dawes’ limit (consistent with diffractive Airy disk) for a human eye’s pupilsize, and all flutter around α ≈ 0.0001 radians, the value underlying all Aristarchan celestial scales.' (Excerpt from DIO 14 ‡2 by Rawlins, 2008:17.)