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 widespread belief 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 an oblate spheroid.

Early development

Pythagoras

Pythagoras (b. 570 BC) found harmony in the universe and sought to explain it. He reasoned that Earth and the other planets must be spheres, since the most harmonious geometric form was a circle.

Plato

Plato (427 BC - 347 BC) travelled to southern Italy to study Pythagorean mathematics. When he returned to Athens and established his school, Plato also taught his students that Earth was a sphere. If man could soar high above the clouds, Earth would resemble "a ball made of twelve pieces of leather, variegated, a patchwork of colours."

Aristotle

Aristotle (384 BC - 322 BC) was Plato's prize student and "the mind of the school." Aristotle observed "there are stars seen in Egypt and ^* Cyperus which are not seen in the northerly regions." Since this could only happen on a curved surface, he too believed Earth was a sphere "of no great size, for otherwise the effect of so slight a change of place would not be quickly apparent."

Aristotle provided physical evidence for a spherical Earth:

Ships receding over the horizon disappear hull-first;
Travelers going south see southern constellations rise higher above the horizon; and
The shadow of Earth on the Moon during a lunar eclipse is round.

The concepts of symmetry, equilibrium and cyclic repetition permeated Aristotle's work. In Meteorology he divided the world into five climatic zones: Two temperate areas were separated by a torrid zone near the equator, as well as two cold inhospitable regions, "one near our upper or northern pole and the other near the ... southern pole," both impenetrable and girdled with ice. Although no humans could survive in the frigid zones, inhabitants in the southern temperate regions could exist. He called these theoretical people antipodes, literally "feet opposite".

Eratosthenes

Eratosthenes (276 BC - 194 BC) estimated Earth's circumference around 240 BC. He had heard about a place in Egypt where the Sun was directly overhead at the summer solstice and used geometry to come up with a circumference of 250,000 stades. This estimate astonishes some modern writers, as it is within 2% of the modern value of the equatorial circumference, 40,075 kilometres. The length of a 'stade' is contentious - this value uses the most generous estimate for this length.

Claudius Ptolemy

Claudius Ptolemy (90 - 168 AD) lived in Alexandria, the centre of scholarship in the second century. Around 150, he produced his eight-volumne Geographia.

The first part of the Geographia is a discussion of the data and of the methods he used. Like with the model of the solar system in the Almagest, Ptolemy put all this information into a grand scheme. He assigned coordinates to all the places and geographic features he knew, in a grid that spanned the globe. Latitude was measured from the equator, as it is today, but Ptolemy preferred to express it as the length of the longest day rather than degrees of arc (the length of the midsummer day increases from 12h to 24h as you go from the equator to the polar circle). He put the meridian of 0 longitude at the most western land he knew, the Canary Islands.

Geographia indicated the countries of "Serica" and "Sinae" (China) at the extreme right, beyond the island of "Taprobane" (Sri Lanka, oversized) and the "Aurea Chersonesus" (Southeast Asian peninsula).]]

Ptolemy also devised and provided instructions on how to create maps both of the whole inhabited world (oikoumenè) and of the Roman provinces. In the second part of the Geographia he provided the necessary topographic lists, and captions for the maps. His oikoumenè spanned 180 degrees of longitude from the Canary islands in the Atlantic Ocean to China, and about 81 degrees of latitude from the Arctic to the East Indies and deep into Africa; Ptolemy was well aware that he knew about only a quarter of the globe.

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 a few different types of spherical models in common usage, the most popular being the circumferential extremes:

The equatorial circumference is the simplest, as its radius equals the equatorial radius, "a" (for Earth, 6,378.135 km);
The meridional circumference is the other circumferential extreme, which requires an elliptic integral to find. Using Earth's polar radius ("b") of 6,356.75 km, the actual meridional radius equals about 6,367.446989 km (which can be reasonably approximated, using the elliptical quadratic mean: $\sqrt{\frac{a^2+b^2}{2}}\,\!$ , about 6,367.451 km);
While these circumferential extremes are the most commonly employed, they don't provide the best spherical representation, which would be the average circumference. As there are different ways to interpret an ellipsoid's circumference (radius vs. arcradius/radius of curvature; elliptically fixed vs. ellipsoidally "fluid"; different integration intervals for quadrant-based geodetic circumferences), there is likely no definitive, "absolute average circumference"——even using elliptic integrals——only an approximation that approximates the average of all of the different types of mean circumferences. The ellipsoidal quadratic mean satisfies this requirement: $\sqrt{\frac{3a^2+b^2}{4}}\,\!$ . This would be the spherical "great-circle radius" of an ellipsoid (for Earth, about 6,372.795478 km);
The other popular choice as a spherical designation is the ellipsoid surface area's authalic radius: $\sqrt{\frac{a^2+\frac{ab^2}{\sqrt{a^2-b^2}}\ln{(\frac{a+\sqrt{a^2-b^2}}b)}}{2}}\,\!$ , about 6,371.005 km for Earth.

External links

Sphäre | Cartography | Earth

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