Vertex (great circle)

The vertex of a great circle is the point of highest latitude the track reaches, where it runs due east-west and its course is 090 or 270. Each great circle has two vertices, one in each hemisphere, 180 degrees of longitude apart. The vertex fixes the shape of a great-circle route: from it the latitude falls away symmetrically, and its position is found from the initial course and departure latitude by Napier’s rules on the navigational triangle, with cos latitude of vertex equal to sin initial course times cos latitude of departure. When the computed vertex lies beyond a safe latitude, a composite great-circle track caps it at a limiting parallel.