DOWNLOAD-DESKTOP-NOTEBOOK.nb (9.51 MB)
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As noted in the Wikipedia article, you don’t need to pick antipodes. You can drill a straight tunnel between any two arbitrary points and the time needed will be the same. See “Straight path between two arbitrary points”.
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That’s a great point, Ed — yes, the travel time remains the same for any straight tunnel through the Earth, not only the one passing through the center. I focused on the pole-to-pole case for clarity and symmetry in visualization, but the result indeed holds for all chordal paths between two arbitrary points. Thanks for highlighting this elegant aspect of the problem!