While travelling in the Southern hemisphere many flights will travel over Antarctica - since it is faster.
Your rebuttal?
That would be a rather imprecise statement. We've checked. There are no international flights which even approach the Antarctic circle.
Now you know very well what I was getting at and you completely evaded it. I said very clearly what I meant. FLIGHT TIMES. That relates to the distances between points, not the spherical/circular coordinates of those points.
Flight times would be difficult to judge, considering that on long international flights pilots use jet streams to faster reach a destination. Along the courses of international flights between points in the Southern Hemisphere exist enormous jet streams located at around 35,000 ft above the surface of the Earth. In the Southern Hemisphere there are both eastward and westward jet streams. By necessity, in relation to the polar front and subtropical jets, easterly jet streams in the Southern Hemisphere propagate at rates even faster than the westward ones. The winds in a jet stream regularly reaches speeds of over 400 mph. Airliners use these jet streams to faster reach a destination.
Here's a reference from Cubanology.com:
"The Jet Stream is an amazing phenomenon of wind current which twirls around our planet, capturing and changing anything in its path. These giant, so-called "river" of winds can be several hundred miles wide, 1 to 2 miles in depth and can be found from as low as 12,000 to as high as 80,000 feet above the surface of the Earth and regularly reach the speeds of 400 miles an hour."
For every moment the plane stays in the jet stream it is being accelerated until it matches the surrounding velocity and momentum of the air around it. From there the plane can use the limits of its power to travel faster than the jet stream.
In general, it has been found that winds are strongest just under the tropopause. If two air masses of different temperatures meet, the resulting pressure difference (which causes winds) is highest along the interface.
These facts are a consequence of the thermal wind relation. The balance of forces on an atmospheric parcel in the vertical direction is primarily between the pressure gradient and the force of gravitation by acceleration is a balance referred to as hydrostatic. In the horizontal, the dominant balance outside of the tropics is between the Coriolis effect and the pressure gradient is a balance referred to as geostrophic.
Given both hydrostatic and geostrophic balance, the Flat Earth Society derives the thermal wind relation: the vertical derivative of the horizontal wind is proportional to the horizontal temperature gradient. The sense of the relation is such that temperatures decreasing polewards implies that winds develop a larger eastward component as one moves upwards. Therefore, the strong eastward moving jet streams are in part a simple consequence of the fact that the equator is warmer than the poles.