RE: Historical determination of the astronomical unit (again)

[Roger Bailey]

I have two questions on this technique.   1. How does it solve for the astronomical unit, the absolute distance from the earth to the sun? I understand that it solves for the ratio of the distances earth to sun and earth to moon, but not the absolute distance. There is no base line to triangulate for actual distance.   2. How does it demonstrate heliocentricity? The moon rotates around the earth but are not the triangles the same if the sun revolves around the earth or the earth resolves around the sun?   I have shifted the topic to the Copernican Challenge (again).   Regards,   Roger Bailey Walking Shadow Designs N 48.6  W 123.4  -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]On Behalf Of [EMAIL PROTECTED] Sent: June 13, 2004 8:54 AM To: sundial@rrz.uni-koeln.de Subject: Re: Historical determination of the astronomical unit (again) 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.