Final answer:
At the magnetic South Pole, a compass needle will point downward as it aligns with the Earth's magnetic field lines converging at that point.
Along the equator, the compass needle will not change its orientation significantly as it aligns with the Earth's relatively uniform magnetic field in that region.
Step-by-step explanation:
If you are standing on the magnetic South Pole and use a compass, the needle would behave in an unexpected way compared to traditional use in the Northern Hemisphere.
Since the Earth can be thought of as a giant bar magnet with magnetic field lines pointing from north to south, the compass needle's north end would point down toward the ground, trying to align itself with the magnetic field lines that converge at the South Pole.
This is because the 'north' end of a compass is actually magnetically a north pole, which is attracted to the Earth's magnetic south pole — located geographically near the Earth's North Pole.
Furthermore, when flying due west along the equator, as you cross the prime meridian and watch the compass, the orientation of the compass needle will not change significantly in relation to your direction of motion. This is assuming that the Earth's magnetic north pole coincides with the geographic north pole.
Even as you move, the compass will continuously align itself with the Earth's magnetic field, which is generally the same along the equator, maintaining its perpendicular orientation to your westward path.