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1 - I am trying to figure out the longitude at which a geodetic great circle reaches its apex. (I have a point and the azimuth at that point identifying the circle) I have found a good resource that shows how to find the maximum latitude itself (and the azimuth at that latitude) but I cannot figure out how to find the longitude at that point.

2 - Also related how can we find the longitudes at which a geodetic great circle intersects a given parallel?

EDIT: The provided link shows sections from the book The 3-D Global Spatial Data Model Foundation of the Spatial Data Infrastructure Earl F . Burkholder

EDIT2: If it is of any help i have access to forward/inverse geodesy functions. I can find a point and the azimuth at that point given a point-bearing-distance. I can find the distance-bearing between any given 2 points.

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Why should there be a (unique) longitude? Even modelling the earth as a prolate spheroid, the longest "great circle" would be invariant under rotation around the earth's axis of rotation. –  hardmath Jan 2 '13 at 16:58
    
edited for clarity. I already have a point and azimuth so it is a unique great circle hence i can use the Clairaut’s Constant mentioned in the link –  hkn Jan 2 '13 at 17:01
    
Can you explain what is meant by the azimuth of a great circle at a point? I am unfamiliar with geodesy terminology. –  Rahul Jan 2 '13 at 17:14
    
link Azimuth is the angle from true north measured clockwise. See figure 6.10 in the link –  hkn Jan 2 '13 at 17:17
    
The article that you linked to is a confused mish-mash of half-truths and misremembered facts, if you ask me. Does your given point lie on the equator? If so, it's easy. If not, we need more data from you. –  TonyK Jan 2 '13 at 17:22
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