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    Re: Finding great circle apex?
    From: David Pike
    Date: 2019 Jan 17, 11:13 -0800

    Tony you wrote:

    There was a discussion of GC (great circle) attributes like the maximum latitude reached when following such a route, etc.

    I can't seems to find this in the archive.

    Could you please help me with:

    • GC apex formula
    • position of GC "poles"

    Presumably maximum latitude for a great circle (GC) occurs when the line of the GC lies east/west.  I see that in 2000 I received 100/100 for an MSc module final exercise, which required me to find the initial bearing and final back bearing for the GC from New York to London; the distance; and the longitude for the bearing to be 270/090 in both spherical and ellipsoidal geometry.  I would imagine if I was able to find the longitude for 270/090, it would be easy for you to obtain the latitude. 

    I’ve just pulled my submission from the shelf, and I’m afraid to say that after 20 years the little grey cells must have got a bit fused.  I can’t understand a word of it.  As far as I can see, I divided the basic spherical triangle into two by dropping a line (meridian) down from the pole which landed perpendicular to the GC.  I then had two spherical triangles, each with a 90 degree angle in one corner.  Now having a side and two angles, I used something called Napier’s Rule to do the magic and get the chlong angle at the top.  Knowing a side and three angles of a half triangle, obtaining the co lat should be easy.

    If none of the experts picks this up, I can photograph the pages and email them to you.

    For the ellipsoidal, I appear to have used something called the Andoyer-Lambert method.  Now there’s a name to set a big long string moving. DaveP


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