NavList:

Bob Goethe, you wrote:
"Does anybody know of a place on the earth where, measuring the astronomical latitude and longitude as accurately as may be done, the deflection of vertical (DOV) would result in two spots being 100 meters or more apart and still having the exact same astronomical latitude and longitude?"

Wouldn't that be fun?! Fortunately, no such places exist on the Earth. It's a question of the rate of change of the DOV compared to the natural "rolling" of the vertical as we cross the globe. The natural rate is just the usual "minute of arc per nautical mile". To get a double-valued celestial navigation scenario (where separated points could have the same astronomical latitude and longitude), we would need a change in the deflection of the vertical that's faster than that. And there are no such places on the Earth as far as I know. 

We could search among the asteroids for a small world with the shape to make this happen. Contact binaries (two spheres resting against each other) could produce the right double-valued field. Also a "biconcave disk" would work. That's the shape of a human red blood cell --basically a disk but pinched at the center. On an asteroid with that shape, the gravity field would be a bunch of parallel vectors on each side. The local vertical would be the same "star" everywhere. And that implies that celestial navigation altitudes would be the same at all points on each side. It wouldn't work anymore for navigation!

Frank Reed