Fourmilog: None Dare Call It Reason

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Hint. Sure, the Earth is round, but is it a sphere?

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The location on the Earth's surface most distant from the centre of the Earth is the summit of Chimborazo, an inactive volcano in Ecuador, with an elevation of 6,268.2 metres above mean sea level.

“What!”, you protest, “that's more than 2,500 metres less than the summit of Mount Everest”. Indeed, but recall that the Earth is not a sphere, but rather an oblate spheroid, as its rotation results in an equatorial bulge (of a different kind than the one about which I wrote a whole book). Mount Everest is, to be sure, more than 2.5 kilometres higher above sea level than Chimborazo, but at about 28° N, it is much further from the equatorial bulge. Chimborazo, on the other hand, is only about 1½° south of the equator, and hence almost right on the extremum of the bulge. Sea level, of course, follows the bulge, so elevation above sea level does not indicate distance from the centre of the Earth unless the bulge is taken into account.

Accounting for the bulge, the summit of Chimborazo is 6,384.4 km from the centre of the Earth, while the summit of Mount Everest is 6,382.3 km from the centre. Hence, despite being 2.5 kilometres closer to sea level, Chimborazo's summit is 2.1 km farther from the centre of the Earth.

An interesting puzzle which has many more potential subtleties than this one (which is pretty much a question of geodesy) is “Where on the surface of the Earth is the gravitational acceleration the least?” There are two major effects here: as you approach the equator, the centrifugal force of the Earth's rotation balances the force of gravity and reduces the acceleration, and at higher altitudes, you're farther from the centre of the Earth, which reduces the gravitational force as the inverse square of the distance. A naïve guess would be that these two factors would combine to make the summit of Chimborazo the place to go for the maximum time between dropping your ice axe and having it land on your toe. But we must also consider local gravitational effects: perhaps dense volcanic rock is sufficiently more massive than sedimentary rock at some lower altitude location near the equator that Chimborazo loses out. I suspect the answer to this puzzle is known, but it may not be available to the likes of you and me. Ballistic missile guidance requires precise mapping of the Earth's gravitational field, as inertial navigation systems measure deviation of trajectories from geodesic paths in the ambient gravitational field, and hence hitting a precise point on the Earth's surface requires detailed knowledge of deviations of the local gravitational field from that of an ideal geometric body. For obvious reasons, these data are closely guarded by those who compile them at great expense.