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Re: Position from crossing two circles : was [NAV-L] Reality check
From: Herbert Prinz
Date: 2006 Jun 9, 02:44 -0400
From: Herbert Prinz
Date: 2006 Jun 9, 02:44 -0400
George Huxtable wrote:
>The locus of an observer who was somewhere unknown on that circle becomes,
>after that displacement, not a circle at all. It's distorted, and the
>greatest distortion occurs in directions at 45 degrees (and 135, 225,
>315 degrees) to the direction of travel.
>
>
I don't understand this. Shifting the circles in an east-westerly
direction does not distort them at all. Therefore shifting them
north-south must distort them the most. No?
>I haven't come across the A'Hearn and Rossano paper, but it certainly
>seems worth looking up.
>
I will send you a copy. It may take a few days.
>I've had a look at the descrptions of the
>Dozier and Kotlaric methods, in my 1977 Bowditch, but they don't seem
>to be very relevant to the present discussion. If I am
>misunderstanding, perhaps Herbert will explain.
>
>
>
The relevance is simply that the original question was for direct
solutions for the intersection of two circles on the sphere.
The equation
sin H = sin DEC sin lat + cos DEC cos lat cos (GHA + lon)
where lat and lon are variables and H, DEC, and GHA are constants,
describes a small circle on the sphere. The combination of two of those
constitute the so called combined altitude problem. Dozier and Kotlaric
solve it.
Herbert Prinz
