Subject: Re: Stereo of the Moon

[P3D john bercovitz <bercov@xxxxxxxxxxx>]

I just did some back-of-the-envelope figuring and I must agree 
with Mugnier now.  What I was really basing my earlier statement 
on was having looked at an old moon stereo and not seeing any 
depth in the craters/mountains.  But!  The pair was of very poor 
resolution.  That thought set me to scribbling:
 
Mugnier says parallax is visible in stereo pairs of the moon.  
My question is, "At what magnification?"  Using rough guesses:
 
Moon distance is 238 000 mi ? (+/- 5%?).
 
Crater wall height ~ 3 mi ?
 
Mugnier indicates max libration ~ 15 degrees, 
the tangent of which is about 1 part in 4
 
So shift of top of crater wall relative to bottom of crater wall 
is 1/4 * 3 = 3/4 mile
 
At a distance of 238 000 mi, this is 
1 part in (238 000/(3/4)) = 320 000
 
Eyes' sensitivity to parallax is 10" of arc or 1 part in 20 000
 
So minimum magnification is 320K/20K = 16X !!
 
Moon subtends 1/2 degree but needs to subtend 
16 * 1/2 degree = 8 degrees, the tangent of which is about 1/8
 
In a 45 mm ocular viewer, 8 degrees would come from an image size 
of 45 * (1/8) or 6 mm
 
The moon subtends 1/2 degree which is 1 part in ~100.
 
To get a 6 mm image diameter, you would need a 6 * 100 or 600 mm 
lens on your camera.  And that's to get minimally-detectable 
parallax.  Probably it would be better to go for some overkill and 
use at least a 2000 mm camera lens.
 
John B


------------------------------