A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Robert Bernecky
Date: 2018 Apr 2, 06:37 -0700
Now that calculators (in my opinion) are rapidly becoming "old technology" --
I thought it would be good to highlight a formula for sight reduction that calculates the altitude and azimuth of a body, given its declination and local hour angle.
< r, A> = POL( tan dec cos lat - sin lat cos lha, -sin lha)
Hc = acos(r * cos dec)
Zn = A (add 360 if A is negative)
After using this formula for some time, I think it should be more familiar, and possibly more popular, as it has some advantages:
1) Only one complicated formula to memorize/type in
2) The altitude Hc and azimuth Zn are (almost) found in one step
3) No complicated sign rules to remember to find the azimuth
I first became aware of this approach from a post by Robin Stuart. After digging through the archives, I found that people have pieced together the idea, but never made much comment on it:
1) A short "how to use it" write-up, "Polar Reduction"
2) A derivation, based on coordinate transformations (using rotation matrices)
3) Some math background on rotation matrices that explain some of the details (for those who like such stuff).