NavList:

Alex E., you wrote:
"In the archeological museum, a guide says: "This mummy is 4003 years old". A visitor asks: "Interesting! How could this be determined with such accuracy?" The guide replies: "When they hired me here, they told me that it is 4000 years old. This was 3 years ago"."

Ha! That's great. :)

As for the ellipsoidal distance, I agree completely that this is almost entirely trivia, but I find that there are two reasons why it matters...

First, there's the annoying reason. A significant fraction of modern apps implement some variant of ellipsoidal distance. The app designers and developers "brag" about it as a fancy "feature" (even when they don't really understand it themselves), and they create anxiety for users if it's not available. Navigation enthusiasts are often convinced that they can live with nothing less than absolute accuracy --whatever that is. If a software product (app) applies the "moldly old" great circle calculation for distance on the surface of the earth, the accuracy-obsessed users may panic. The panic is not necessary... but we can't really control it (see PS).

There's a secondary more interesting issue here which comes up more directly in the ellipsoidal distance calculations but can also be included as a small correction in almost any system for calculating distances including plane sailings and others. It's usually minor but sometimes worth paying attention to. And that is the geodetic, non-central definition of latitude on the ellipsoid, which is, in fact, the latitude that we use on the Earth (latitude referenced to the "normals" of the WGS84 ellipsoid). The lines of latitude on the globe are closer together in equatorial regions of the globe than they are in the pure spherical coordinates of great circle distances. This is an "impact" of the ellipsoidal form of the earth on our coordinates and distance calculations that does not take us down that rabbit-hole of geodesics on the spheroid. And that can be worth something. 

Frank Reed

PS: All those app developers worrying about ellipsoidal distance... And yet how many of them worry about deflection of the vertical for celestial fixes? ... I do! It's included in my apps, but do others? In many real-world cases it's considerably more important to navigation than ellipsoidal distance on the spheroid...