22 Degrees
Death Valley National Park, California
2024
I checked with Wikipedia to see what the “official” name of this phenomenon is and was surprised to find out that it is called a
- θ deviation = θ incidence + sin − 1 [ n sin ( π 3 − sin − 1 sin θ incidence n ) ] − π 3 .
![{\displaystyle \theta _{\text{deviation}}=\theta _{\text{incidence}}+\sin ^{-1}\left[n\sin \left({\frac {\pi }{3}}-\sin ^{-1}{\frac {\sin \theta _{\text{incidence}}}{n}}\right)\right]-{\frac {\pi }{3}}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c1e13e38fb397c2c5a79e4be8b8ded67f9dfbbbe)
Hah, just kidding, I don’t understand it either. To add insult to injury the Wikipedia article then goes on to explain how to “intuitively” understand what all the calculations mean. All I was able to glean from that further explanation was that the author (most likely a physicist of some ilk) doesn’t really understand what intuitive means.
But one small illustration in the article did confirm that my own “intuitive” idea of the what the angle in question is. Imagine a stick pointing from your eye to the sun (don’t use a real stick for obvious reasons). Then imagine a second stick pointing from your eye to the halo ring. Grab that protractor (plastic, or metal if you’re really old) you’ve been saving since your school days and measure that angle and it should come out to be about . The proof, as they often say in the math world, is left to the reader, or Wikipedia.
Straws (sticks) and protractors, now you are talking my level of understanding science….I believe my 7th grade science teacher Ed Jones (Lt. Col., USAF retired), had his class out one cold January evening measuring angles of the rising moon above the horizon vs. the apparent measure of the moons diameter as measured by a protractor and straw. Yup, it measured the same low on the horizon and overhead, even though it “looks” much larger at the horizon. Now his spirit probably travels among the stars concocting mind experiments…
With apologies to the memory of the Lt. Col., I’ve done a more crude version of the moon size test by just extending my arm out fully and comparing the moon to my thumbnail. Not particularly accurate but enough so that I came to the conclusion that the size doesn’t change. Or at least logically I have concluded that. On any given moonrise my eyes still would swear otherwise.