Re: Historical determination of the astronomical unit (again)

[DrArthurCarlson]

Thanks for the replies, but ...   The geometry and the calculations are not hard, but I question the possibility of a significant observation. Aristarchus of Samos claims 18 < D < 20. That implies an astounding ability to determine when the Moon is exactly halved. If you draw a line between the poles of the Moon, then the shadow cannot depart from this line by more than 1/800th of its length!* Does anyone out there believe that Aristarchus was capable of observations with this kind of accuracy? (By daylight, I might add.) To distinguish the true value of 1/400 within a factor of two requires the same accuracy. Maybe the observation was misreported and was intended to be a lower limit, 19 < D, but then we still have the question of how Copernicus and Halley did so well.   Still unhappy,   Art Carlson   * The mathematical details: The method assumes that the angle Earth-Moon-Sun is 90 deg. An error in this angle translates directly into an error in the angle Moon-Sun-Earth, reported to be between 1/18 and 1/20 (radians), that is, 1/19 +/- 1/400. If the angle Earth-Moon-Sun is off by 1/400, then the center of the shadow line is 1/400th of a Moon radius to the left or right of the straight line.