# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: dip, dip short, distance off with buildings, etc.**

**From:**Frank Reed CT

**Date:**2006 Jan 13, 02:52 EST

I wrote: > With a sextant we > are measuring the altitude of point B from point A so that means that we > know the angle in the triangle at point A, let's call that gamma. Bill, you asked: "Which triangle? The small oblique or large oblique?" The only triangle I defined. You have point C at the center of the Earth, point A at height h above the Earth's surface, and point B some distance away at height H above the Earth's surface.Those three points make a big triangle ABC. Our GOAL is to find the angle in the triangle at point C (since, if we multiply that by the Earth's radius, we get the distance). Now what do we measure with our sextant or theodolite? Well, we're at point A, and we measure altitudes above the horizontal which is, by definition, the plane perpendicular to side AC of the triangle. Now how is that related to the angle at point A in the big triangle (the angle "CAB")? Clearly that's just 90 degrees plus the measured altitude. So we KNOW the angle CAB. This is equivalent to the measured parameter (or at minimum, it's related to the measured parameter by a simple relationship). So we know the corner angle at point A (the observer), which I named "gamma", and we are seeking the corner angle at point C (the center of the Earth), which I named "phi". But, uh-oh, we're stuck with another angle --the one at point B. Wait... no we're not. Since it's a simple plane triangle, all three angles must add up to 180 degrees. That means that the angle in the big triangle at point B is NECESSARILY equal to 180-(gamma+phi). Ok so far?? If you haven't drawn a picture of this yet, you can't possibly be ok here so please make sure you've got a picture of this. And if you don't want to draw your own picture, see image 488 in the archive (see below). Now we are in a position where we can apply the law of sines (the ordinary plane trig law of sines...) to the big triangle ABC. Set it up as sin("angle at A")/(R+H)=sin("angle at B")/(R+h). And work from there. You'll need to remember that sin(a+b)=sin(a)*cos(b)+cos(a)*sin(b). That's enough triangles for now, I think! I don't know if anyone will get a kick out of it or not, but if you like this kind of math/physics, I've photographed some of my notes. This is RAW material. You can download it at www.HistoricalAtlas.com/lunars/refnotes.zip. It's about 5.7 megabytes. By the way, try to bookmark or record these addresses with the "HistoricalAtlas" part intact. Yes, it currently points to one of my other addresses "clockwk.com" but that's changing soon. -FER 42.0N 87.7W, or 41.4N 72.1W. www.HistoricalAtlas.com/lunars