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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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Re: Mathematical Advancement of a celestial COP
From: Russell Sher
Date: 1998 Oct 26, 01:13 EST

```I have some formulas as well from Navigation by Pocket Computer - in which
the author (Mike Harris) discusses advancing LOPs by
formula to solve for the position - (You mention COP; should that be LOP?)
I'll bring the formulas in - just give me a few days...will be away.
Russell
> -----Original Message-----
> From:	John Brenneise [SMTP:jbrennei@XXX.XXX]
> Sent:	Friday, October 23, 1998 11:39 PM
> Subject:	[Nml] Mathematical Advancement of a celestial COP
>
> 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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