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Thanks Frank I had forgot about Augmentation (and you explain it
nicely here http://reednavigation.com/lunars/easylun.html )

I am not very experienced at observations of the moon and I was
surprised how difficult it was for me to judge when the two images of
the moon where just touching. When you look closely the edges are
quite fuzzy.

I thought about this as well a while ago when we were considering
taking sun sights with a camera and deciding what counts as the edge
of the sun and the line of the horizon using image processing. But
with a visual observation it is different as our visual system
enhances edges (Tolhurst discovered this mechanism in the 1970s). The
problem is does it enhance it in such a way the edges appear in the
right place.

Given that we know the angular diameter of the moon (..with
augmentation!) presumably the best thing to do is practice until we
calibrate our visual system to get the right answer!

On 19 November 2016 at 02:43, Frank Reed  wrote:
> While we're at it, measuring the angular diameter of the Sun or Moon with a
> sextant is the flip side of the coin from measuring index error using the
> Sun or Moon. Bring the Sun's reflected and direct images together with the
> reflected image above, limbs perfectly touching. Note this on-arc angle. It
> should be around half a degree. Let's suppose it's 32.1' for a specific
> example; call that D1. Then reverse the images so that the reflected image
> is below the direct image, again with the limbs in perfect contact. Record
> this off-arc angle. Let's suppose it's 30.8' for a specific; call that D2.
> The angular diameter of the Sun or Moon is then just the average of the two
> values:
>   DIA = (D1+D2)/2
> while the index error is half the difference:
>   IE = (D1-D2)/2.
> In the specific numerical example, I have given here, the diameter is then
> 31.45' while the IE is 0.65' (implying that the index correction is -0.65'
> and you could either round up or down). Normally the diameter is thrown out,
> but if you divide it by two and compare with some known value for the SD
> from a Nautical Almanac or some other source (making sure you account for
> the augmentation), then you have a nice check on your observations and work.
> Half the diameter in this case rounds to 15.7', and if that's what your
> source says for the augmented SD, you can have good confidence in your IE
> value as well.
>
> You can detect the changes in the Moon's size directly and easily using this
> method, corresponding to changes in distance of just a few hundred miles.
> Note that with the Moon, you have to make sure you make the measurement
> along the line of the Moons horns, which is nearly pole-to-pole.
>
> Frank Reed
>
> 



--
Professor of Applied Mathematics
http://www.maths.manchester.ac.uk/bl

   

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