So I got the transformation wrong before: the radial distance of a point from the hub is R * (π/2 - latitude).

Anyway point A (latitude = -34.5°, longitude = 138.5°) -- taking the radius of the Earth to be 6400 km -- has FE polar coordinates (r = 13907 km, θ = 138.5°), or FE cartesian coordinates (x = -10416 km, y = 9214.9 km).

Point B (latitude = -34.5°, longitude = 151°) has FE polar coordinates (r = 13907 km, θ = 151°) or FE cartesian coordinates (x = -12163 km, y = 6742.1 km).

So the FE displacement between points A and B is given by (Δx = 1747.6 km, Δy = 2472.8 km). The FE distance along this displacement is sqrt( ΔxΔx + ΔyΔy ) = 3028.0 km.

This is a pretty significant difference from Easter_Bunny's measurement of 2700 km. Note that his measurement is an *upper bound* on the actual distance, since the road he took may have been longer -- but not shorter -- than the shortest path.

Getting to the point again, you can conclude:

1) The cities are not really at the latitudes/longitudes that cartographers would have us believe.

has polar

2) Easter_Bunny's measurement is wrong.

3) The Earth is not flat.

Which do you conclude?