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    $\begingroup$ The interesting thing about antipodes is that it doesn't matter which direction you start in, the arc from one to the other is always the same distance (assuming a perfect sphere). That means almost by definition that it's the halfway point. $\endgroup$ Commented May 8, 2021 at 2:14
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    $\begingroup$ @MarkRansom: exactly. In navigation this is called great circle navigation. 'Hiking along a meridian' as suggested by the OP is just a special case of that. en.wikipedia.org/wiki/Great_circle. $\endgroup$
    – user22279
    Commented May 8, 2021 at 7:57