5

A little over 600 km, based on a list of "large and medium airports with scheduled services". You can use the World Airports Voronoi Diagram to get an idea. Each cell of this diagram is the region that is closer to the airport within it than to any other, and so the point furthest from any airport must be at one of the vertices of this diagram, ...


Only top voted, non community-wiki answers of a minimum length are eligible