Geographical centre

In geography, the centroid of the two-dimensional shape of a region of Earth's surface (projected radially to sea level or onto a geoid surface) is known as its geographic centre or geographical centre or (less commonly) gravitational centre. The study of geographic centers is called centrography. Informally, determining the centroid is often described as finding the point upon which the shape (cut from a uniform plane) would balance. This method is also sometimes described as the "gravitational method". One example of a refined approach using an azimuthal equidistant projection, also potentially incorporating an iterative process, was described by Peter A. Rogerson in 2015. The abstract says "the new method minimizes the sum of squared great circle distances from all points in the region to the center". However, as that property is also true of a centroid (of area), this aspect is effectively just different terminology for determining the centroid. In 2019, New Zealand's GNS Science also used an iterative approach (and a variety of different projections) when determining a centre position for New Zealand's extended continental shelf. However, other methods have also been proposed or used to determine the centres of various countries and regions. These include:

centroid of volume (incorporating elevations into calculations), instead of the more usual centroid of area as described above. centre point of a bounding box completely enclosing the area. While relatively easy to determine, a centre point calculated using this method will generally also vary (relative to the shape of the landmass or region) depending on the orientation of the bounding box to the area under consideration. In this sense it is not a robust method. finding the longitude that divides the region into two equal area parts to the east and west, and then similarly the latitude that divides the region into two equal area parts to the north and south. Like the bounding box approach described above this method would not generally locate precisely the same point if the same shaped region was oriented differently. As noted in a United States Geological Survey document, "There is no generally accepted definition of geographic center, and no completely satisfactory method for determining it." In general, there is room for debate around various details such as whether or not to include islands and similarly, large bodies of water, how best to handle the curvature of the Earth (a more significant factor with larger regions) and closely related to that issue, which map projection to use.

Definition and methods According to the United States Geological Survey there is no generally agreed upon definition of a geographic center and no satisfying method to determine it, while research into it and study of centrography is ongoing. Generally centrography deals with point pattern analysis.

Definition Geometrically defined the central point of all land is the centroid of all land surfaces within the two dimensions of the Geoid surface which approximates the Earth's outer shape. The term centre of minimum distance specifies the concept more precisely as the domain is the sphere surface without boundary and not the three-dimensional body. Explained in a different way, it is the location on the surface of Earth where the sum of distances to all locations on land is the smallest. Assuming an airplane with infinite energy and resources, if one were to fly from one start location to any location on land and back again, and repeat this from the same start location to all possible destinations, the starting location where the total travel distance is the smallest would be the geographical centre of Earth. Its distance definition follows the shortest path on the surface of Earth along the great circle (orthodrome).

Methods The calculation method of the median point in centrography is an often applied one, but a sensitive one. Refinement of the median point can be achieved by increasing the division of the area in quartilides, decilides and centrilides. Another method to determine a center is making use of the center of gravity of an area.

History of centrography Around the world throughout history many real and illusive places were identified as axis mundi or centers of the world. Examples among many throughout history and across the world are Delphi (the "omphalos", the navel of the world), Jerusalem, Cusco, the Great Pyramid of Giza, and Prayagraj (Allahabad, India). The modern study of centrography dates back to 1872, with the publishing of work on the issue by Julius Erasmus Hilgard. By the 1930s it had developed into a broad field of combining cartography and statistical data.

Center of Earth's land

The geographical centre of Earth is the geometric centre of all land surfaces on Earth. Earth's land is unevenly distributed across the surface of Earth, making the calculation of the center a challenge that has been attempted through different geographic approaches, but hasn't produced widely agreed results and satisfying methods. Throughout history many different places have been called centers of the world. Scientific calculations in 1944 identified the median point of Earth's land area to be in Tarnopol (Galicia, Ukraine) at 49°20′00″N 26°20′14″E excluding Antarctic sea ice. If Antarctic sea ice is included, the median point is instead in İzmir (Turkey) at 38°25′00″N 27°25′00″E. If the center of gravity is used, the center is instead at 43°31′00″N 28°20′00″E, near the Black Sea coastal town of Balchik (Bulgaria). Calculations from 2002 have again calculated the center of Earth's land somewhere along the Romanian Black Sea coast, depending on the amount of Antarctic ice taken into account. Additionally the center of the land hemisphere was also calculated, finding a central area spaning two focal areas around Brittany to the Mediterranean sea between the Balearic Islands and Catalonia.

Other claims

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