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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Advancing a position circle. was : [NAV-L] Position from crossing two circles
From: Lars Bergman
Date: 2006 Jun 19, 14:04 +0200
From: Lars Bergman
Date: 2006 Jun 19, 14:04 +0200
George wrote, a few days ago: "Consider this simple example, once again. 3 observers, A, B, and C, see a star positioned at dec = 0 degrees, GHA = 0 degrees, at an altitude of 30 degrees. A is at 60N, 0W, B is at 0N, 60W, C is at 45N, 45W. It is obvious that A and B are on that circle, centred at 0N 0W, radius 60 degrees, and a bit of simple spherical trig (or altitude tables) shows that C is also exactly on the circle. Each observer travels due North through a distance of 60 miles. Now A is at 61N, 0W, B is at 1N, 60W, C is at 46N, 45W. Do those 3 new positions lie on a circle? If so, where is its centre and what is its radius? I guarantee that nobody will provide such a centre or radius, because those positions are no longer on a circle. And the discrepancy from a circle is not by an infinitesimal amount, either. but by something over 14 miles, after a shift of only 60 miles." Being well aware that Alex has pointed out that 3 points will be parts of a circle, it is interesting to calculate the centre and radius in George's example: centre 0.378380N 0.625482E radius 60.623519 degs /Lars
