Amazingly close, especially for two places I’d heard of before this thread. But I do wonder about that distance calculator. And not just because of the bug you found.
If the exact antipodal distance is 12438, there should be 18 miles between one of these cities and the antipodal point of the other. One minute of latitude is about 1.2 miles (or one nautical mile) and a minute of longitude is less than that. Considering that there’s 5 minutes of latitude and 2 of longitude of difference between the antipodal points, there should be only 6 to 7 miles between them.
Let’s try this other distance calculator. Plugging in the lat-longs here gives 12422 miles for Hamilton NZ to Cordoba.
Exact antipodal points give 12428 miles. Hmm, off by 10 miles from the other. Could they be using different values for the diameter of the Earth? At any rate, that matches my estimation, so I’m more confident in this other distance calculator.
The Earth bulges at the Equator. The equatorial circumference is 24,902 miles, so antipodal points on the Equator are 12,451 miles apart. The polar circumference is 24,819 miles, so the Poles are 12,410 miles apart. Points at intermediate latitudes are an intermediate distance apart, accordingly to a formula which is way beyond me and probably involves a lot of sines and cosines.
Ergo, for this question, you want antipodal cities as close to the Equator as possible. If anyone has an atlas listing every last hamlet in South America and Indonesia, that will help, because these are the only equatorial, antipodal land masses.
Or maybe not. You can connect any two antipodal points via a great circle route over the polar circumference. I never was very good at oblate spheroidal geometry.
The distance calculator I linked to seems to be based on a constant diameter world, since it gives the same antipodal distance (12428 miles) no matter what latitude you use.
The distance calculator the r_k linked to gives different antipodal distances for different parts of the world. It gives a polar distance as 12430 miles and one at the latitude of Cordoba as 12442 miles. It looks like they attempted to allow for the non-spherical Earth, but don’t seem to have gotten it right.
I reckon we have a winner - and one of 'em is a capital city, no less!
Quito in Ecuador is at 0°14’S 78°30’W.
The village of Setul in Sumatra is at about 0°12’N 101°28’E, as near as I can make out from this map. (The nearest sizable town is Pekanbaru, a little to the north).
Allowing for the size of Quito, I think you could say that they are exactly opposite one another.
Sorry that people spent time following up on my earlier post, but as I think about it more, I was wrong. Antipodal points on the equator are separated by the greatest amount in three-dimensional space–the equatorial diameter of the Earth. But when it comes to surface travel, any two antipodal points can be connected via a Great Circle over the poles. Latitude doesn’t matter.
It would be pretty tricky to take this into account in a distance calculator. If you were connecting two points 170 degrees apart on the Equator, the Great Circle you’d travel between them would be the Equator itself. But as you approach extremely close to “antipodality”–say, 179.9 degrees–you have to take into account that the shortest route may not be the direct Great Circle, because of the equatorial bulge and shorter routes over the Poles. The math involved can’t be easy.
Bottom line, any two antipodal points are equally distant, and can be connected by a route of no more than 12,410 miles–even though a mileage calculator may disagree.
Hmm… so two cities 179.4 degrees apart on the equator would (by my calculations) be the same distance apart as any two antipodal points, 12,410 miles. That would mean that the greatest possible distance between any two points on the globe is that between two points on the equator somewhere between 179.4 and 180 degrees apart. So we’re looking for towns in Indonesia and northern South America which are maybe 179.7 degrees apart.
Where did you get the figure for the polar circumference of 24,819? The usual figure given in various web pages is 24,860.
Ah, I think I know how you got it. You took the polar radius and applied the 2pir formula to it. Sorry, that doesn’t work because the polar cross-section of the Earth is not a circle.
Since that first distance calculator gave a polar antipodal distance of 12,430, it seems to be more correct than I thought.
I took it from the first site that came up in Google and used miles, which happened to be some professor’s college syllabus. I can’t vouch for its accuracy, but hey–if I can’t trust Southern Illinois University at Edwardsville, whom can I trust?
OK, the ever-reliable Funk & Wagnall’s Encyclopedia (I should have looked there first) gives the polar circumference as 24,860 and the equatorial as 24,902.
So the distance calculator in Earl Tucker’s link is spot-on–for calculating Great Circle distances. It takes the equatorial bulge into account.
The problem is, that as you approach extremely close to antipodality, the Great Circle is not the shortest possible route. At antipodality, there are an infinite number of Great Circle choices, one of which runs through the Poles with a distance of 12,430 miles. Close to antipodality, there will be a non-Great Circle route, passing near to one of the Poles, with a distance of not more than 12,430 miles.
