Re: phases of moon, earth-sun system

["John S. Denker" <jsd@MONMOUTH.COM>]

At 08:24 PM 9/14/01 -0500, Jack Uretsky wrote:
> The Greeks measured the distance to the sun

One Greek in particular:
  http://www.perseus.tufts.edu/GreekScience/Students/Kristen/Aristarchus.html

>         Their number for the solar distance was not too good, as I recall,
> because the relevant angle is so close to pi/2.

If we look on the bright side (so to speak), Aristarchos was able to
demonstrate that the earth-sun distance is much much bigger than the
earth-moon distance.

I'm not sure measuring the angle was the limiting factor.
 -- Aristarchos mis-estimated the angle by 3 degrees.  Somebody as clever
as he was should have been able to measure it much more accurately than
that, if that were the only issue.  Probably more like 0.5 degrees.
 -- In contrast, judging the moment of dichotomy is not super-easy.  Try
it some time.

For homework:  Suggest a way of getting a more accurate result, using only
tools available in 300 BC.