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    Re: O.T.- Puzzle of a different sort
    From: Peter Hakel
    Date: 2013 Sep 25, 06:47 -0700
    In Hungary on August 11, 1999 I had the good fortune to observe many solar "crescents" on the ground created by a tree as the solar eclipse was approaching totality.


    Peter Hakel


    From: Frank Reed <FrankReed@HistoricalAtlas.com>
    To: pmh099@yahoo.com
    Sent: Wednesday, September 25, 2013 1:04 AM
    Subject: [NavList] Re: O.T.- Puzzle of a different sort


    I wouldn't even call this off-topic. Each of those circles is a "pinhole camera" image of the Sun. The gaps in the blinds projecting those images are not circular --it's the Sun that has a circular image. In addition to showing us the Sun's image, this gives us a very good tool for measuring distances. Since the Sun has an angular diameter of just over 32 minutes of arc, the size of each image is 108 times the distance to the rough pinhole that projected it (really, the size of the perpendicular projection, but not hard to correct for that). So next time you're walking under some trees, and you see that dappled light on the sidewalk, you can figure the height of the canopy of the trees overhead with considerable accuracy by measuring the dancing circles of light. If the circles are 8 inches across, or two-thirds of a foot, then the distance to the canopy of leaves is 108*(2/3) or about 70 feet. Here the distance to the blinds is no mystery, but imagine being down a hallway and seeing those little projected Sun images from a room that you cannot directly see off to one side. You could estimate the distance to the windows in a hidden room with good accuracy by observing the sizes of those images.
    Those images are not always circles or even foreshortened ellipses. The shapes reflect the apparent image of the Sun at some great distance (some distance much greater than other distances involved). So, for example, if an airplane passes in front of the Sun, you will see its silhouette in each and every one of those circles on your floor from each little "pinhole camera". Or if the Sun is undergoing a partial eclipse, and the image of the Sun is a circle with a circular bite taken out of it, then each of those images on your floor will be a similar circle with a circular bite taken out (probably elongated into an ellipse unless the surface happens to be close to perpendicular to the rays of sunlight). Or if the planet Venus should happen to be transiting the Sun (you'll have to wait a century to see this again), then each circle of light projected on your floor will have a little dot of darkness in it. And I did, in fact, observe the image of Venus in transit in patches of sunlight under maple trees in June of 2012, by the way, during the last transit. The circles on the ground were dancing as the wind blew, but each circle had a distinct dot of darkness --the image of Venus in transit.
    -FER

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