OP is correct, it would have to be calculated out.
Sandwich trench is a contender.
See the graph ( R for radius. flat line = spherical at that latitude)
See how at 60 its still not many km out of round (Compared to polar radius… at 90)
Well South Sandwich trench is a few km deeper than the Litke trench, but at 60 lattitude the earth radius is only a few km higher due to the equatorial bulge effect.
So its not quite obvious if South Sandwich goes down to closer to the centre of the earth than the Litke deep.
My guess is that McMurdo base at 78 degrees south and sea level has it beat. Using Saint Cad’s formula above and multiplying by the equatorial radius, which he appears to have left out, I get a radius about 2 km longer at that latitude, which would put it about 900 meters closer than the top of the ice cap at the pole.
In which case, standing on the shore of the northernmost island in the world, KaffeKlubben Island (or possibly the unconfirmed rock called 83-42 slightly further north) would be the winner.
What it means is that we are using elevation above or below sea level like it tells us if something is closer to the center of the Earth - but it doesn’t because “sea level” follows the geiod which is not a uniform distance from the center and in fact is centered at the Earth’s center of gravity - not the geometric center.
So let’s say we have two valleys and one is 1km below sea level and the other is 2km below sea level. We are thinking the second feature is 1km closer to the center of the Earth. Oh but wait - the Earth is an ellipsoid so we do some calculations (see the formula I wrote) and we decided that based on the latitudes, Valley 1 starts out 1.3km closer to the center of the Earth than Valley 2 because it is closer to the pole. So that means that Valley 1 is 0.3km closer to the Earth’s center than Valley 2 right?
Wrong? Sea level - the whole basis for measuring elevations is not an ellipsoid and doesn’t match the geometric model of the Earth. Look at the diagram h=H+N hereto see what this all means.
And your other criticism? I’ve seen responses in GQ a fkload more technical than mine and I’ve never see ANYONE ever say “Hey! Llama! GQ isn’t for technical stuff.” This isn’t an oncology forum or a astrophysics forum or a materials engineering forum either so are you going to call out people who make technical posts about those subjects too?
Just throwing it out there: what about the Kola borehole? It’s 12 km below the surface and was drilled quite close to the North Pole (near Murmansk on Russia’s northern coast).
I believe that the OP specified that it had to be accessible, and that you had to return alive. The bottom of the Kola borehole reached a temperature of 180 C, and the pressure of the drilling mud would probably overcome the structural integrity of any vehicle you submerged yourself in. If you weren’t trapped and crushed by the flowing rock first.
Extreme points of the Earth on Wikipedia has a listing for the (natural) closest point to Earth’s center, though it lists it as “probably” being near the geographic North Pole under the arctic ocean. I imagine that a number of members of the US and Russian/Soviet Navies have the distinction of visiting that point, or a point a few tens fo meters above it.
That appears to refer to the Litke Deep mentioned earlier as the best guess. I imagine no members of the US or Russian navies have been anywhere near the bottom of it since you need submarines specially designed for extreme depths to go 5.5 km down.
