Khanh-Dang wrote:

Le 25 mai 2007, Ernie Wright a écrit :

yields a distance estimate of 404,897 km, for an error of only a
little more than 2%. That's pretty cool!

Well, actually, the 395,520 km Anthony gave is the geocentric distance
of the Moon, i.e. the distance from the center of the Earth to the
center of the Moon. In geocentric coordinates, the Moon is a little
closer. My ephemeris program tells me the real distance of the Moon from
Athens is 391,741 km, so that the error is around 3.4 %.

You're right, of course. And as it turns out, my first calculation,
which I did by hand, had an error in it (I switched sine and cosine in
the declination term of the coordinate conversions; I described this the
right way in my post but did it backwards). I've written a program to
run the calculation more rigorously and it finds a distance about 3%
*less* than the topocentric distance.

That's still cool, however ;-)

Doing this calculation gives one a renewed appreciation for what
Hipparchus was able to accomplish before trigonometry was invented.

- Ernie http://home.comcast.net/~erniew