Earth's circumference in the context of "Minute and second of arc"

Spherical Earth or Earth's curvature refers to the approximation of the figure of the Earth as a sphere. The earliest documented mention of the concept dates from around the 5th century BC, when it appears in the writings of Greek philosophers. In the 3rd century BC, Hellenistic astronomy established the roughly spherical shape of Earth as a physical fact and calculated the Earth's circumference. This knowledge was gradually adopted throughout the Old World during Late Antiquity and the Middle Ages, displacing earlier beliefs in a flat Earth. A practical demonstration of Earth's sphericity was achieved by Ferdinand Magellan and Juan Sebastián Elcano's circumnavigation (1519–1522).

The realization that the figure of the Earth is more accurately described as an ellipsoid dates to the 17th century, as described by Isaac Newton in Principia. In the early 19th century, the flattening of the earth ellipsoid was determined to be of the order of 1/300 (Delambre, Everest). The modern value as determined by the US DoD World Geodetic System since the 1960s is close to 1/298.25. The scientific study of the shape of the Earth is known as geodesy.

Eratosthenes of Cyrene (/ɛrəˈtɒsθəniːz/; Ancient Greek: Ἐρατοσθένης [eratostʰénɛːs]; c. 276 BC – c. 195/194 BC) was an Ancient Greek philosopher, polymath and scholar. He was known as a mathematician, geographer, poet, astronomer, and music theorist. Eratosthenes became the chief librarian at the Library of Alexandria. His work was the precursor to the modern discipline of geography, and he introduced some of its terminology, coining the terms geography and geographer.

He is best remembered as the first known person to calculate the Earth's circumference. He was also the first to calculate Earth's axial tilt, which similarly proved to have remarkable accuracy. He created the first global projection of the world incorporating parallels and meridians based on the available geographic knowledge of his era. Eratosthenes was the founder of scientific chronology; he used Egyptian and Persian records to estimate the dates of the main events of the Trojan War, dating the sack of Troy to 1184 BC. In number theory, he introduced the sieve of Eratosthenes, an efficient method of identifying prime numbers and composite numbers.

The Library of Alexandria in Alexandria, Egypt, was one of the largest and most significant libraries of the ancient world. The library was part of a larger research institution called the Mouseion, which was dedicated to the Muses, the nine goddesses of the arts. The idea of a universal library in Alexandria may have been proposed by Demetrius of Phalerum, an exiled Athenian statesman living in Alexandria, to Ptolemy I Soter, who may have established plans for the library, but the library itself was probably not built until the reign of his son Ptolemy II Philadelphus. The library quickly acquired many papyrus scrolls, owing largely to the Ptolemaic kings' aggressive and well-funded policies for procuring texts. It is unknown precisely how many scrolls were housed at any given time, but estimates range from 40,000 to 400,000 at its height.

Alexandria came to be regarded as the capital of knowledge and learning, in part because of the Great Library. Many important and influential scholars worked at the Library during the third and second centuries BC, including: Zenodotus of Ephesus, who worked towards standardizing the works of Homer; Callimachus, who wrote the Pinakes, sometimes considered the world's first library catalog; Apollonius of Rhodes, who composed the epic poem the Argonautica; Eratosthenes of Cyrene, who calculated the circumference of the earth within a few hundred kilometers of accuracy; Hero of Alexandria, who invented the first recorded steam engine; Aristophanes of Byzantium, who invented the system of Greek diacritics and was the first to divide poetic texts into lines; and Aristarchus of Samothrace, who produced the definitive texts of the Homeric poems as well as extensive commentaries on them. During the reign of Ptolemy III Euergetes, a daughter library was established in the Serapeum, a temple to the Greco-Egyptian god Serapis.

A nautical mile is a unit of length used in air, marine, and space navigation, and for the definition of territorial waters. Historically, it was defined as the meridian arc length corresponding to one minute (⁠1/60⁠ of a degree) of latitude at the equator, so that Earth's polar circumference is very near to 21,600 nautical miles (that is 60 minutes × 360 degrees). Today the international nautical mile is defined as exactly 1,852 metres (about 6,076 ft; 1.151 mi). The derived unit of speed is the knot, one nautical mile per hour.

The nautical mile is not part of the International System of Units (SI), nor is it accepted for use with SI. However, it is still in common use globally in air, marine, and space contexts due to its correspondence with geographic coordinates.

A minute of arc, arcminute (abbreviated as arcmin), arc minute, or minute arc, denoted by the symbol ′, is a unit of angular measurement equal to ⁠1/60⁠ of a degree. Since one degree is ⁠1/360⁠ of a turn, or complete rotation, one arcminute is ⁠1/21600⁠ of a turn. The nautical mile (nmi) was originally defined as the arc length of a minute of latitude on a spherical Earth, so the actual Earth's circumference is very near 21600 nmi. A minute of arc is ⁠π/10800⁠ of a radian.

A second of arc, arcsecond (abbreviated as arcsec), or arc second, denoted by the symbol ″, is a unit of angular measurement equal to ⁠1/60⁠ of a minute of arc, ⁠1/3600⁠ of a degree, ⁠1/1296000⁠ of a turn, and ⁠π/648000⁠ (about ⁠1/206264.8⁠) of a radian.

The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of ⁠1/299792458⁠ of a second, where the second is defined by a hyperfine transition frequency of caesium.

The metre was originally defined in 1791 by the French National Assembly as one ten-millionth of the distance from the equator to the North Pole along a great circle, so the Earth's polar circumference is approximately 40000 km.