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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{at}XXX.XXX]
    > Sent:	Friday, October 23, 1998 11:39 PM
    > To:	'navigation{at}XXX.XXX'
    > 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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