Using a map program that draws GCA vectors, I drew a big X from Lihue in Hawaii to NE Maine and from the NW Alaska coast to the Florida Keys and the lines crossed a few miles west of the Minnesota exclave of the NW Angle (the northernmost US land in the lower 48).
How would the geographic center of the 50 states be calculated, such that a nice obelisk could be placed on actual US dirt? Would even divisions of longitude/latitude extremes be crossed to find a point (or the closest dry point in the US)?
What if all US territories (like Puerto Rico and the Virgin Islands, but not including all military bases like Subic Bay) are included?
You’d have to include Guam, which would put the “center” somewhere in the Pacific Ocean west of Seattle. That’s why most people just consider the center of the contiguous states, which about 2.5 miles from Lebanon, Kansas. And has a marker.
But there is a geographic center in South Dakota. The OP’s method of drawing a big X is not how it’s found. Rather they pretend they can place the entire US on a single point (ignoring any land or ocean between parts of the US) and the point where all that is balanced is the geographic center. So Alaska and Hawaii count, but not Canada or the Pacific Ocean in between.
The geographic center of the US is calculated by the amount of land north and south of a point being equal as well as east and west. The geographic center is officially in the town of Belle Fourche, South Dakota and there’s a little monument there to commemorate it (but I think if memory serves that the monument is only an approximation and the real center is like 10 miles away in a wheat field.
The geographic center including Alaska and Hawaii as being in Belle Fourche, South Dakota is dependent on how you define that problem. They used a cardboard cutout as documented here but they no longer make the claim that is the location.
There are numerous problems and one would have to make explicit decisions on the initial conditions to calculate this for many reasons but one that is fairly amusing.
Alaska poses a technical limitation for States if one merely chooses latitude and longitude as Alaska is the state that is farthest North, West, and East! The Aleutian Islands cross the 180 degree meridian of longitude.
That fact about the Aleutians is irrelevant for this question. We’re measuring distance east and west based on how far they are from the US in general, not on how far they are from a point in England. The easternmost point in the US is in Maine, not in Alaska.
Note that the “balance point”, or centroid, is not necessarily the point where you’ll have equal area north and south of that latitude and east and west of that longitude, and in fact, for most shapes, they’ll be different.
Using raw north/south/east/west numbers (drawing a box and finding its center), the beach near Oretown Oregon is the closest point to the center of the 50 states box, which is some 100 miles out in the Pacific.
The balance on a pin idea kind of bothers me, because it fails to account for the significant difference in mass between the western states and the eastern states – but, if you did that, the center would probably end up in Canada.
Can you provide a cite to *a generally accepted definition of geographic center, and a completely satisfactory method for determining it. *
As the OP asked:
The coordinate singularity posed by the 180th longitude would need to be considered, and a choice would need to be made to use a different coordinate system would eliminate the apparent discontinuity. The choice of this different coordinate system may impact the outcome.
While I realize that it wouldn’t be hard to do this it illustrates the issue with a lack of a generally accepted definition of geographic center.
Note the cite from my last post from the USGS explains that in part due to a lack of this definition no monument has been established by the government.
AS pointed out there are a number of ways to do this. You could do it by enclosing the U.S. (however you define it) in a rectangle and take the center of that. That will depend on which map projection you use.
You could find the smallest circle on the globe that encloses everything and take the point on the earth’s surface directly above that point.
You could find the point C that minimizes the sum over all points of (distance from C) raised to some power. The first and second power are the usual choices.
The last method also works for things like the center of the population. In that case you weight each point not equally, but by the population at that point.
I couldn’t find anything for just the U.S. but I did find that the pole of inaccessibility for North America is near Kyle, South Dakota (1,025 miles) from the nearest coastline. As per wikipedia, Canada has one calculated for itself so maybe the U.S. does too? But I’m not sure that it would change at all from being Kyle. It might shift a little East/West, but I can’t imagine that the mexico and canadian border would have many places further from them.
It doesn’t matter which method is used, that fact about the Aleutians is still irrelevant.
The fact that there’s a discontinuity means that the arbitrary origin in Greenwich, England is the wrong one to use for this problem. That origin point was adopted because it’s a very good idea to have navigators everywhere using the same longitude system. But we’re not navigating here, so feel free to switch to another origin point, if that makes your calculations easier. Which point you use should make no difference in the end result. If it does, you’re doing something wrong.
The angle between the western point of Attu and Quoddy Head, Lubec, ME is about 120.5°. Nothing complicated about that. The middle of that arc (aligned to the equator) is about 127.2°W. The furthest west point on the mainland is Cape Flattery, at 124.7°W, and that is way north of where the N/S median would be.