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In geodesy, a meridian arc measurement is the distance between two points with the same longitude, i.e., a segment of a meridian curve or its length. Two or more such determinations at different locations then specify the shape of the reference ellipsoid which best approximates the shape of the geoid. This process is called the determination of the Figure of the Earth. The earliest determinations of the size of a spherical Earth required a single arc. The latest determinations use astro-geodetic measurements and the methods of satellite geodesy to determine the reference ellipsoids. Those interested in accurate expressions of the meridian arc for the WGS84 ellipsoid should consult the subsection entitled numerical expressions. ==The Earth as a sphere== (詳細はcaliphs in the 9th century, but it was the Alexandrian scientist Eratosthenes who, abut 240 BC, first calculated a realistic value. He knew that on the summer solstice at local noon the sun goes through the zenith in the ancient Egyptian city of Syene (Assuan). He also knew from his own measurements that, at the same moment in his hometown of Alexandria, the zenith distance was 1/50 of a full circle (7.2°). Assuming that Alexandria was due north of Syene, Eratosthenes concluded that the distance between Alexandria and Syene must be 1/50 of Earth's circumference. Using data from caravan travels, he estimated the distance to be 5000 stadia (about 500 nautical miles)—which implies a circumference of 252,000 stadia. Assuming the Attic stadion (185 m) this corresponds to 46,620 km, or 16% too great. However, if Eratosthenes used the Egyptian stadion (157.5 m) his measurement turns out to be 39,690 km, an error of only 1%. Syene is not precisely on the Tropic of Cancer and not directly south of Alexandria. The sun appears as a disk of 0.5°, and an estimate of the overland distance traveling along the Nile or through the desert couldn't be more accurate than about 10%. Eratosthenes' estimation of Earth’s size was accepted for nearly two thousand years. A similar method was used by Posidonius about 150 years later, and slightly better results were calculated in AD 827 by the grade measurement of the Caliph al-Ma'mun. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Meridian arc」の詳細全文を読む スポンサード リンク
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