Spherical Earth

The concept of a spherical Earth was espoused by Pythagoras apparently on aesthetic grounds, as he also held all other celestial bodies to be spherical. It replaced earlier beliefs in a flat Earth: In early Mesopotamian thought the world was portrayed as a flat disk floating in the ocean, and this forms the premise for early Greek maps like those of Anaximander and Hecataeus. Other speculations as to the shape of Earth include a seven-layered ziggurat or cosmic mountain, alluded to in the Avesta and ancient Persian writings (see seven climes). In fact, the Earth is reasonably well-approximated by an oblate spheroid.^{[citation needed]}

the earth is squareical

Geodesy

Geodesy, also called geodetics, is the scientific discipline that deals with the measurement and representation of the Earth, its gravitational field and geodynamic phenomena (polar motion, earth tides, and crustal motion) in three-dimensional time-varying space.

Geodesy is primarily concerned with positioning and the gravity field and geometrical aspects of their temporal variations, although it can also include the study of Earth's magnetic field. Especially in the German speaking world, geodesy is divided in geomensuration ("Erdmessung" or "höhere Geodäsie"), which is concerned with measuring the earth on a global scale, and surveying ("Ingenieurgeodäsie"), which is concerned with measuring parts of the surface.

Earth's shape can be thought of in at least two ways;

as the shape of the geoid, the mean sea level of the world ocean; or
as the shape of Earth's land surface as it rises above and falls below the sea.

As the science of geodesy measured Earth more accurately, the shape of the geoid was first found not to be a perfect sphere but to approximate an oblate spheroid, a specific type of ellipsoid. More recent measurements have measured the geoid to unprecedented accuracy, revealing mass concentrations beneath Earth's surface.

Spherical models

There are several reasonable ways to approximate Earth's shape as a sphere. Each preserves a different feature of the true Earth in order to compute the radius of the spherical model. All examples in this section assume the WGS 84 datum, with an equatorial radius "a" of 6,378.137 km and a polar radius "b" of 6,356.752 km.

Preserve the equatorial circumference. This is simplest, being a sphere with circumference identical to the equatorial circumference of the real Earth. Since the circumference is the same, so is the radius, at 6,378.137 km.
Preserve the lengths of meridians. This requires an elliptic integral to find, given the polar and equatorial radii: ${\frac {2a}{\pi }}\int _{0}^{\frac {\pi }{2}}{\sqrt {\cos ^{2}\phi +{\frac {b^{2}}{a^{2}}}\sin ^{2}\phi }}\,d\phi$ . A sphere preserving the lengths of meridians has a rectifying radius of 6,367.449 km. This can be approximated using the elliptical quadratic mean: ${\sqrt {\frac {a^{2}+b^{2}}{2}}}\,\!$ , about 6,367.454 km.
Preserve the average circumference. As there are different ways to define an ellipsoid's average circumference (radius vs. arcradius/radius of curvature; elliptically fixed vs. ellipsoidally "fluid"; different integration intervals for quadrant-based geodetic circumferences), there is no definitive, "absolute average circumference". The ellipsoidal quadratic mean is one simple model: ${\sqrt {\frac {3a^{2}+b^{2}}{4}}}\,\!$ , giving a spherical radius of 6,372.798 km.
Preserve the surface area of the real Earth. This gives the authalic radius: ${\sqrt {\frac {a^{2}+{\frac {ab^{2}}{\sqrt {a^{2}-b^{2}}}}\ln {({\frac {a+{\sqrt {a^{2}-b^{2}}}}{b}})}}{2}}}\,\!$ , or 6,371.007 km.
Preserve the volume of the real Earth. This volumetric radius is computed as: ${\sqrt[{3}]{a^{2}b}}$ , or 6371.001 km.

Note that the authalic and volumetric spheres have radii that differ by less than 7 meters, yet both preserve important properties. Hence both are common and occasionally an average of the two is used.

External links

Geodesy

Spherical models

See also

External links