Solution to GLOBE TRAVERSAL

the North Pole. AND, a ring near the South Pole, slightly more than 1 mile North of the South Pole, where after you go 1 mile South, you walk in a 1 mile circle totally around the South Pole, then North back to where you started.

This covers most of the answer, but you could also start out a bit closer to the south pole, such that your walk that circles totally around the south pole is only 1/2 mile in length, and you do it twice. This is another ring of answers, and if you do the circle walk 3 times, this is another rings of answers, and so forth.