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    Re: Lunars and pixels
    From: John Huth
    Date: 2010 Dec 13, 07:39 -0500
    On the sunstone - I have a longish personal history with the darn thing.    I, too, am skeptical that there it was used, but it may very well have been that some lucky Norse found one and was also seduced by the cool factor - that is to say, the birefringent properties, and it found its way into a minor snippet of sagas after a lot of misinterpretation or exaggeration.   

    When I was 12 years old, my 6th grade teacher gave me the assignment of describing the sunstone to my class.  I believe that the proposition that this was used was only two years old at that point.   Even then, I wondered if it was really in use.

    Many years later, when I visited the Viking Ship Museum in Roskilde, Denmark, there was a small exhibit on sunstones.   I tried to dig up someone who might debate the details with me, but I was made to feel like a heretic.

    Recently, after contacting David Burch, he got me in touch with Leif Karlsen, who wrote "Secrets of Viking Navigation", where he presses the sunstone issue and did somewhat extensive testing and has more quotes on the topic.   E.g. he talks about a piece of calcite found in a wrecked ship off Great Britain.

    I hold out the possibility that perhaps some Norseman had one of these things, and there was a "gee whiz" factor associated with it even back then.

    Whatever the history, it makes for a nice little project for students to do, as they have to understand some physics and do some testing on it.

    Best,

    John H. 


    On Sun, Dec 12, 2010 at 10:47 PM, Frank Reed <FrankReed@historicalatlas.com> wrote:

    Thank you very much for the background, John. I can now see how this went down with the student "camera lunars".

    Regarding one of the other experiments, you wrote:
    "The sunstone seemed to work to a precision of about +/- 5 degrees, which, as a rough and ready compass seemed to me to be quite good. They also measured angles using their bodies, and I suspect they could easily improve on the precision. The sunstone is an interesting piece of history. Calcite is birefringent, and will refract light differently depending on the polarization state. In cases where the sun is low on the horizon and is obscured by clouds or fog, but you can see some blue sky, the sunstone can indicate the direction of the sun from the polarization of the sky. I imagine if it was really used by Norse sailors that this would be the only condition under which it was useful. On completely cloudy days, it would be useless. On days when the sun is visible, it's not needed, so there's only that one case where blue sky is available, but the Sun is obscured when it would work."

    This level of accuracy sounds very believable. As for navigational use, I've become more and more convinced that we are being "seduced by the dark side" here. It's the physics "cool" factor that makes us want to believe in it. The practical cases where it might have been useful are just too rare. And of course, there's nearly zero historical evidence that it was an actual method of navigation.

    For satellite dishes, you wrote:
    "For example, I believe that DirectTV has one that hovers over 113 degrees W, or something close to that. The satellites also hover over the Earth's equator. Glossing over some details, if you know the longitude of the satellite, you can deduce your longitude from the azimuthal orientation of the satellite dish, and the latitude from the elevation angle."

    Yep. You sure can! To get the azimuth and the elevation given the longitude of the satellite in geostationary orbit, you might do something like this:
    "Height = 22300
    Radius = 3975
    A1 = (long0 - longitude)/degtorad
    cosbet = SIN(pio2 - latitude)*COS(A1)
    slanth = SQR((Radius + Height)^2 + Radius^2 - 2*(Radius + Height)*Radius*cosbet)
    bet = arccos(cosbet)
    DSSazm = 180 + degtorad*arcsin(SIN(A1)/SIN(bet))
    DSSelev = degtorad*arccos(SIN(bet)*(Radius + Height)/slanth)"

    That's a little sample of some old code I just found in a file called "SunDSS.bas" that I last modified in February of 1995. LOL. Back then, aligning one of those satellite dishes was annoyingly difficult. They had a crude protractor scale on the mounting hardware for elevation, but for azimuth the installer (few professionals back then) had to guess. So I wrote this software that calculated the exact azimuth of the Sun for the observer's latitude and longitude and output the time when the arm of the dish would be aligned with the Sun and the satellite at once. Then all you had to do was go to the dish at the right time of day, aim it so that the shadow of the arm disappeared, and it was instantly pointed correctly in azimuth. I uploaded the software as a freebie to good old Compuserve and it was very popular for a couple of years... That was all in the before time, when dinosaurs ruled the Earth.

    And yes, it's a genuine means of position-finding which can be refined quite a bit. For example, with a medium-sized telescope it's possible to observe the satellites directly. Since they're way up there, at a tenth of the distance to the Moon, the position derived isn't all that great. If I can observe the position in RA and Dec of a geostationary satellite to the nearest tenth of a minute of arc (reasonable if the telescope is big enough to see them) then the position is accurate to about half a mile --no significant improvement over ordinary celestial navigation and it requires a large aperture telescope. Might as well use a sextant and shoot lunar distances for a position fix. It's the same principle. By contrast, with visual observation of bright satellites in Low Earth Orbit, which I have suggested as a modern means of backup navigation a few times, you can get a position accurate to 50-100 feet if you can observe the positions of the satellites to the nearest tenth of a minute of arc. This is feasible, with some hard work, with a "prosumer" grade digital camera and it's competitive with GPS accuracy if we average many observations.

    -FER


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