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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2022 Feb 5, 08:13 -0800
David Pike, you wrote:
"Over the next few days, I’ll be mainly observing the Moon’s horns"
I've been trying to come up with ideas to help you and others 'see the light' on this one, and I'll post about that later today. I don't want to add it to this topic.
Your estimate of the position angle from Hatysa to Mintaka by plain triangles is certainly legitimate at the level of accuracy required here, since the separation is only a few degrees and both objects are near the equator. This problem is identical to estimating a course over a short distance on the globe. The math in any latitude:
1) calculate the latitude difference, dLat, in minutes of arc.
2) calculate the longitude difference, dLon, in minutes of arc.
3) convert both to nautical mile coordinate offsets: y=dLat directly, x=dLon·cos(Lat), where either point's Lat or an average Lat may be used.
3a) if Lat is near the equator, cos(Lat) is nearly 1, so this step becomes trivial.
4) distance = sqrt(x²+y²), course = atan(y/x). Course will have to be adjusted for quadrant (common sense applies).
5) check: if distance<500n.m. and both Lats<80°, the result will be "reasonable".
Please note, David: I am well aware that you personally know these things. I'm spelling it out in detail for other people who may be reading along.
In the attached image, modified from one I prepared years ago to show this "position angle" of the Orion North Angles, I have drawn in three lines with estimated position angles taken directly from the image-editing software that I use. I have included lines at 7.0°, 8.5°, and 10.0° position angle to Mintaka. My goal here is to indicate that a visual observer could not reliably tell a difference in orientation of a degree or two in this process. One whole degree of precision is enough to get the job done. I intentionally included 8.5° to pass right through Hatysa, since you asked about that star. Of course when using the Orion North Arrow, the observer's goal is to look at the whole sword, not a specific star.
Frank Reed
