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Bouguer Deflection Flat-Planet Positioning system

The sky's the limit
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For those entities who inhabit non-infinite flat planets, gaining an accurate "world-view" can be exceedingly difficult.

Because the gravitational flux vectors on such a world are not parallel with the local surface normals, it is common for such denizens to arrive at the misconception that their world is curved - or, even worse, rotating.

Bouguer Deflection Flat-Planet Positioning system (which shall, obviously, be known by a different name since the natives won't know Bouguer from Braille) consists of a tripod with an attached plumb bob. The tripod can be leveled via a transit to the local horizon; the plumb bob will then point to a position somewhere below the tripod. The deflection from center is precisely toward the gravitational center of the world disc, and the magnitude of offset is proportional to the distance from center.

Thus, given an appropriately scaled map (disc-shaped, of course) flipped upside down under the tripod (and, of course, oriented along a known axis, preferably the axis of rotation of the sky) the plumb bob will simply point directly to the user's position on the map. (Well, on the back of the map. Put your finger on the spot and flip it over.)

If you've never been to a flat world, proceed with caution. That guard rail is there for a reason.

lurch, Dec 16 2006

What is getting measured http://en.wikipedia...iki/Bouguer_anomaly
The world is just a mountain in the void [lurch, Dec 16 2006]

Who I'm talking about http://en.wikipedia...wiki/Pierre_Bouguer
Measured gravitational deflections in the Andes. Or, at least, tried. [lurch, Dec 16 2006, last modified Apr 05 2007]


       I like the idea of a Gravity Positioning System, but it depends on the thickness of disc-world as well. Denizens could calibrate levels of drunkardness by comparing their angle of lean, compared to the bob.
Ling, Dec 16 2006

       Yes, you're right about the thickness thing. I hope that it's not too thick, compared with its size. Also what is supporting the planet in the void needs to be taken into consideration. One tremendous turtle we can cope with. However, if it is indeed "elephants all the way down", I fear this won't work.
lurch, Dec 17 2006

       I think too thin and too thick are not so good. It has to be 'just right' - like you say, about a single turtle's worth.
Too thick - turtles all the way down - means the centre of gravity is almost perpendicular to any point on disc world. On the contrary, a very thin disc world has a centre of gravity that is at the centre of the circle. That means the bob will point horizontally from most places. It has to be somewhere in between.

       In the disc world novels, everyone walks upright, so it must be turtles all the way down in that case.
Ling, Dec 17 2006

       Won't work. Your plumb bob is going to point to any position on a circle a given distance from center of the map. You can get your distance from the hub this way, but not your position on that circle.
Galbinus_Caeli, Dec 17 2006

       Sorry, I need to be a bit more clear. The plumb bob will always point the same way at a specific position on the planet (Well, not a planet, since it isn't spherical) but the map could be rotated around the tripod without affecting the position and angle of the Bob, but changing the location it is pointing at.
Galbinus_Caeli, Dec 17 2006

       That is why you must orient your map along a known axis.
methinksnot, Dec 17 2006

       How does one achieve this known axis?
Galbinus_Caeli, Dec 17 2006

       One option would be the axis of rotation of the sky, as indicated by lurch. Other possibilities include the turtle's head-to-tail axis (look over the guard rail- carefully now- to see where the head is) and the line formed by two celestial bodies (given a known time of day).
methinksnot, Dec 17 2006


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