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

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Mathematical Advancement of a celestial COP
From: John Brenneise
Date: 1998 Oct 23, 3:39 PM

```I have some code that takes the place of H.O. 229 or H.O. 249 by
numerically solving the following:

sin(h1) = cos(phi)cos(beta1)cos(theta-alpha1) + sin(phi)sin(beta1)
sin(h2) = cos(phi)cos(beta2)cos(theta-alpha2) + sin(phi)sin(beta2)

where  h1 is the corrected angle of elevation for a circle centered
at latitude beta1, GHA alpha1 and h2 is the corrected angle of
elevation for a circle centered at latitude beta2, GHA alpha2.

The question concerns running fixes.

The COP from the earlier of the two observations must be advanced
along the DR course.  In terms of the center of the circle, I propose
that (beta1,alpha1) must be moved along the loxodrome defined by
the course angle for a distance to be scaled by a factor related to the
difference between the course angle and the azimuth angle to the
celestial object.

So, what I need is a good reference and or insight on Spherical
Trigonometry to test my assumption.

Any ideas?

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