A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2016 Nov 17, 12:38 -0800
Brad Morris, you wrote:
"I wonder how your result compares to the exact apparent diameter, given your precise location and time. "
Let's ignore refraction for the moment. The apparent semi-diameter of the Moon is then
SD = 0.2724·HP + 0.3·sin(altitude),
so not at all difficult to get the correct value given the time within a few hours (since the HP is slowly changing close to the time of full moon) and given the Moon's altitude within ten degrees. Assuming Greg took his photo within a few hours of perigee, the HP was 61.50. And if the Moon was above 60 degrees or so, the augmentation was 0.26 to 0.3 minutes yielding a diameter of 34.0 to 34.1 minutes of arc.
When the Moon is low in the sky, refraction can significantly reduce the Moon's diameter in the vertical direction. You can work out how much by looking at the refraction tables and seeing how much it changes in half a degree. The lower limb will be elevated by refraction more than the upper limb, yielding that slightly flattened, "oval" shape of the Moon when it's very low in the sky. The Moon's diameter is also slightly reduced by refraction in the horizontal direction, which might be a bit surprising. Treated as a lens, the optical effect of the atmosphere is to shrink all of the constellations and celestial bodies, including the Moon, by a small amount. As I have described before, for altitudes about 45°, the reduction in size is nearly linear for all angular sizes and directions and shrinks the constellations, and the Moon, by one part in 3000. That amounts to 0.7 seconds of arc reduction at perigee for both the vertical and horizontal semi-diameter of the Moon --insignificant for any sextant observations but observable with proper instrumentation.