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    Re: The Orion North Arrow
    From: Frank Reed
    Date: 2017 Feb 12, 11:20 -0800

    David Pike, you wrote:
    "The Arrow always points to the North Pole, true, but the projection of its meridian onto the observers northern horizon moves from west of north to east of north throughout the evening. "

    Yikes. You have confused yourself mightily! I have taught this idea to children in the past month, and they get it right away and have no problem understanding how it works. But naturally the pre-conceived notions that are the baggage and burden of great wisdom and experience, such as you certainly have, can sometimes get in our way. All this business about projecting meridians and such is simply irrelevant. Maybe it would help if we talk about sundials for a bit...

    Ordinary sundials are accurately aligned with the elevated celestial pole --nearly enough the North Star in the northern hemisphere-- and when we look at a properly-aligned sundial, even on a cloudy day, we can see both the compass direction of the pole as well as the latitude by looking at the sundial's gnomon. The gnomon (pronounced like "know-mun") is the shadow-casting element. I'll limit myself to certain kinds of simple cylindrical sundials. These have a simple stick or rod for the gnomon. That rod is centered in a circular arc on which the hours of the day are marked. Here's an example from Wikipedia and another neat one from a Dutch website:


    During the day the Sun moves across the sky, and the gnomon casts a shadow on the scale with a one-to-one direct correspondence between angles on the scale and hour angles in the sky. This works throughout the day and year without adjustment (except for the usual time-related issues of the equation of time and time zone issues) so long as the gnomon is pointed at the celestial pole. In the northern hemisphere, this means that the gnomon points almost exactly at the North Star. When you walk up to a sundial you can instantly see the direction of north by looking at it (from any side, but certainly also from behind it). At the same time you can see the latitude by looking at the inclination of the gnomon relative to the local horizontal. I do hope we can all agree that these are straight-forward, true statements, right? The azimuthal orientation of the gnomon yields true north, and the inclination of the gnomon displays true latitude. It does so because it has been built that way. If you disagree with any of this, then we have a huge problem. So please, if anyone doesn't see this, just say so -- we have to all agree on this first.

    Now let's return to the Orion North Arrow. It yields exactly the same geometric relationship as the gnomon of a sundial. When you "shoot it" with your hand, assuming you're able to hold your thumb perpendicular to your index finger, it has exactly the same orientation as the gnomon of a sundial. I need to emphasize here that it is not just "kind of" like the orientation of the gnomon or similar in some latitudes --it is identical to the orientation of a sundial's gnomon, both in azimuth and elevation. Indeed you could test out the orientation of the gnomon of a sundial using the Orion North Arrow hand trick. Your thumb points to the north celestial pole (that's a slight difference from a sundial where no distinction is normally drawn between the two poles and we see the gnomon as pointing to the elevated pole). Its azimuthal orientation indicates true north. Its elevation relative to the horizon indicates latitude.

    The nice thing about a trick that involves your hand is that we all have our fingers and thumbs with us all the time, excluding injury. Of course, your thumb isn't especially accurate. But I want to make sure that we all see that a rough check on direction and latitude is highly valuable in the modern world. Computer systems with electronic sensors work beautifully, but when they go wrong or when they are mis-used the errors are usually substantial --you're not half a degree off in course, you're thirty degrees wrong, for example. If you're aboard a vessel, and an incorrect waypoint has been set, and you are sailing southeast in the middle of the night instead of south, a quick hand shot check on Orion will reveal this error immediately. More exotic and disturbing, if you're in an aircraft that has been hijacked, you can look out the window, and if you can see Orion you'll be able to follow changes in bearing and latitude through the night, until Orion sets (and within the visibility limitations of whatever windows are available on the aircraft).

    Can we go beyond the lowly thumb? This hand-based trick is extremely useful for a quick check on direction and latitude. But the nice thing about this method is that it is open and accessible to a high degree of improvement in accuracy, if that floats your boat. I already described this briefly. Get yourself an index card or any other piece of cardstock with a right-angle corner. You'll also want something to mount it in place if you're aiming for accuracy. This may stretch your resources and circumstances: can you find a paper clip? With an index card and a paper clip, you are now equipped to get true north and latitude within a few degrees, maybe better. Attach the paper clip to some convenient fixed support. Insert the index card in the paper clip so that it is sticking up and oriented roughly toward Orion. The long edge of the card should be aligned with Mintaka. You can do this by twisting the paper clip as necessary. Now you need to align the plane of the index card with the orientation of the North Arrow. You can do this by bending the card just above the spot where it sits in the paper clip. Bend it until it aligns with the axis of the North Arrow, and then rotate it a bit more, eight degrees counter-clockwise to the "truer" axis, as described in my first message on this. When the card is properly aligned, upper edge pointing at Mintaka, axis aligned with the "truer" axis of the North Arrow, it is then guaranteed that either short edge of the index card is now pointing right at the north celestial pole. Its orientation is identical to the orientation of the gnomon of the sundial; both are parallel (in three dimensions) to the Earth's axis of rotation. Note that this works if you can't see Polaris (because of an obstruction, skies too bright, wrong hemisphere, clouds). Although I haven't tried it in person, it would clearly be an excellent method for finding the southern celestial pole, which otherwise has no prominent "south star". The execution can be made as exact as you require. If you want to "nerd out" over this, your wish is granted! You can indeed make this more accurate if that's what you desire. But I must emphasize that the goal of a method like this is instant use, a quick check on the gross compass orientation and approximate latitude. Yes, you can squeeze accuracy out of it, but that's not a critical goal.

    Frank Reed
    Conanicut Island, New England

    PS: The interesting Dutch sundial in the image above is detailed here.

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