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    Re: A triangle on the equator
    From: Antoine Couëtte
    Date: 2025 Oct 31, 08:21 -0700

    Final shot here.

    I just lately decided to lift the hood of Meridional Parts Tables which I had never used before.

    It has driven me into defining a new Navigation Sphere SPH84 having the same Equator to Pole Meridian Distance than WGS84.

    From such SPH84, it can be observed in page 3 of this "improved" [and final] attachment that, for solving our initial example, using such "Refined" Meridional Parts Tables obtained through the rather simple dx and dy Formulae yields results extremely close from WGS84 without having to go through the very complex Ellipsoid trigonometric Formulae.

    By the same token, I fully agree with your remark here, Dale, since the WGS84 Meridian distance between Equator and Pole has ended up being at 10,001.965 728 km, i.e. exactly the meter short by 0.2 mm you kindly mentioned to me . And:

    Concerning your reply, Lars, to my earlier query " Anybody to comment here on the actual spherical radius to be used ? ",  I might simply add to your own list the SPH84 Sphere defined in the Attachment, with 1' = 1,852.215 855 55 m.

    In all cases, the 1,852 m official definition for the Nautical Mile length remains a valid and quite solid and sturdy one.

    So no need to ever think of changing it, while I had been a bit surprised that except yourself, Lars, noboby came back onto this specific point (maybe, or - even probably - a stupid question on my behalf).

    Nonetheless, this has been a quite instructive subject for me to study in detail and then address - and to adequately cover on NavList  without having actually got lost in sidebar discussions I would say - since I never went into using such Meridional Parts Tables earlier in my life.

    Thanks to you Frank for raising such a topic.

    Antoine

    File:
    251031-Reduced-spacing-between-some-Parallels-on-Ellipsoids-(Final)-.pdf
       
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