Arthur Carlson <[EMAIL PROTECTED]> writes: > I've been playing in my garden, ... > > *** Does anybody know a relatively simple method for finding the > latitude from observations of the sun over the course of several hours > without recourse to tables and calculations? ***
Thanks to all for the suggestions. I admit that the problem sounds somewhat contrived, but it seems to me to be in the spirit of dialing in the age of quartz watches. David Higgon's answer came closest to what I was looking for. It is nearly as transparent as the shortest shadow method of finding North. I may point out that one can find North and the current declination if one observes the length of the shadow, rather than just timing the direction. In the present case, I actually want to mark the local noon at the solstices and the equinox as well as verify my latitude, so I prefer to use no other shadow-caster than the corner of the roof. Furthermore, I don't have easy access to all the ground North of the corner (Walls and such get in the way.), which rules out some possibilities. The recent posts on astrolabes led me to devise a method involving stereographic projections. The idea is to take three shadow positions (in the minimalist spirit of a mathematician) and project them stereographicly (using a separate diagram, also constructed with pegs and strings). I can then construct the circle through the new points, find the closest and farthest points to my origin, and convert these back to either points on the ground or angles in my diagram. The key is that it is easy to construct a circle from three points, but hard to construct a hyperbola from 5. Furthermore, I know how to utilize the knowledge of the position and height of the gnomon in this scheme (which is why three point are enough). Alberto Nicelli described how to construct a hyperbola given the foci, but the inverse problem is harder. Anyway, I find the geometry of the method interesting. If I get a chance this weekend I'll see if it works in the field. I suspect the biggest errors will come from the fact that the ground is not exactly flat and level. Art Carlson [EMAIL PROTECTED]
