Extreme Points of a Great Circle - (Part 3, Great Circles)

The Northernmost and Southernmost Points of a Great Circle

If you travel from Amsterdam (P1 in Figure 1) to San Francisco (P2) or the other way around, then you first go towards the north for a while, and then towards the south for a while. All great circles except for the equator have a northernmost point (PN) and a southernmost point (PS). You can calculate them as follows.

Fig. 1: Northernmost and Southernmost Point on a Great Circle

Certain Direction from a Point - (Part 2, Great Circles)

Suppose you want to know where you go if you start from a particular town in a particular direction and keep going straight (along a great circle). You can calculate the coordinates of points along the route as follows:

Fig. 2. Mercator and Hondius

Definition of a Great Circle - (Part 1, Great Circles)

[Since great circle calculations are so important on all spheres (like Earth, planets, polar coordinates, etc.) I have to add here such a text. This follows mostly /1/]

Fig. 7. Arthur H. Robinson 1979

["Arthur H. Robinson (January 5, 1915 – October 10, 2004) was an American geographer and cartographer, who was professor in the Geography Department at the University of Wisconsin–Madison from 1947 until he retired in 1980. He was a prolific writer and influential philosopher on cartography.

One of Robinson's most notable accomplishments is the Robinson projection. In 1961, Rand McNally asked Robinson to choose a projection for use as a world map that, among other criteria, was uninterrupted,[9] had limited distortion, and was pleasing to the eye of general viewers.[10] Robinson could not find a projection that satisfied the criteria, so Rand McNally commissioned him to design one.

Robinson proceeded through an iterative process to create a pseudo-cylindrical projection that intends to strike a compromise between distortions in areas and in distances, in order to attain a more natural visualization. The projection has been widely used since its introduction. In 1988, National Geographic adopted it for their world maps but replaced it in 1998 with the Winkel tripel projection."]