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You'd have to update the approach plates and their digital version in the FMS's database occasionally, but that has to happen anyway, given that I believe almost all of them still use magnetic north as a reference. (Not sure if modern FMSes can store that data in true north format internally, but at least once the runway gets officially renamed I bet that requires an update.)

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Even switching from magnetic to true is unhelpful close enough to the South pole. All directions are north.

We have to switch to "grid" north to make sense of directions there.

https://en.wikipedia.org/wiki/Universal_polar_stereographic_...

The problem isn't exactly that "all directions are North", right? That is true only when you're smack on the pole; even a meter away from it, things are well-defined again in terms of directions.

Problems start when you're moving around or doing trigonometry, though; following bearings starts getting weird even at otherwise negligible distances, for example, and runway designators on the opposite thresholds might not be exactly 180 degrees "apart".

But it's not like these effects don't exist everywhere on earth at some scale; they get gradually more pronounced the closer you get to the poles, so I'd be surprised if avionics software would get really confused by them.

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