What is the circumference of the Earth?
History of geodesy
Aryabhatiya also estimates the circumference of Earth, with an error of less than 1%. He gave the circumference of the earth as 4 967 yojanas and its diameter as 1 5811/24 yojanas. Since 1 yojana = 5 miles this gives the circumference as 24 835 miles, which is an excellent approximation to the currently accepted value of 24 902 miles. Aryabhata gives the radii of the orbits of the planets in terms of the Earth-Sun distance as essentially their periods of rotation around the Sun. He also gave the correct explanation of lunar and solar eclipses and that the Moon shines by reflecting sunlight.
Earth's circumference
Longditude lines, also known as meridian lines, follow the polar circumference, and are all exactly the same length.
Flat Earth
"Christian Topography" (547) by the Alexandrian monk Cosmas Indicopleustes, who had travelled as far as Sri Lanka and the source of the Blue Nile, is now widely considered the most valuable geographical document of the early medieval age, although it received relatively little attention from contemporaries. In it, the author repeatedly expounds the doctrine that the universe consists of only two places, the Earth below the firmament and heaven above it. Carefully drawing on arguments from scripture, he describes the Earth as a rectangle, 400 days' journey long by 200 wide, surrounded by four oceans and enclosed by four massive walls which support the firmament. The spherical Earth theory is contemptuously dismissed as "pagan".
Spherical Earth
The works of the classical Indian astronomer and mathematician, Aryabhatta (476–550 AD), deal with the sphericity of the Earth and the motion of the planets. The final two parts of his Sanskrit magnum opus, the "Aryabhatiya", which were named the "Kalakriya" ("reckoning of time") and the "Gol" ("sphere"), state that the Earth is spherical and that its circumference is 4,967 yojanas. In modern units this is , close to the current equatorial value of .
Minute and second of arc
A minute of arc, arcminute (arcmin), arc minute, or minute arc is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn – it is for this reason that the Earth's circumference is almost exactly 21,600 nautical miles. A minute of arc is of a radian.
Astronomical unit
Earth's orbit around the Sun is an ellipse. The semi-major axis of this elliptic orbit is defined to be half of the straight line segment that joins the perihelion and aphelion. The centre of the Sun lies on this straight line segment, but not at its midpoint. Because ellipses are well-understood shapes, measuring the points of its extremes defined the exact shape mathematically, and made possible calculations for the entire orbit as well as predictions based on observation. In addition, it mapped out exactly the largest straight-line distance that Earth traverses over the course of a year, defining times and places for observing the largest parallax (apparent shifts of position) in nearby stars. Knowing Earth's shift and a star's shift enabled the star's distance to be calculated. But all measurements are subject to some degree of error or uncertainty, and the uncertainties in the length of the astronomical unit only increased uncertainties in the stellar distances. Improvements in precision have always been a key to improving astronomical understanding. Throughout the twentieth century, measurements became increasingly precise and sophisticated, and ever more dependent on accurate observation of the effects described by Einstein's theory of relativity and upon the mathematical tools it used.
Earth's circumference
Earth's circumference lines are the foundation of the coordinate system of latitude and longitude, introduced in the mid-second century BC by Hipparchus.
Earth radius
The Earth's equatorial radius , or semi-major axis, is the distance from its center to the equator and equals . The equatorial radius is often used to compare Earth with other planets.
Earth radius
Regardless of the model, any radius falls between the polar minimum of about 6,357 km and the equatorial maximum of about 6,378 km (3,950 to 3,963 mi). Hence, the Earth deviates from a perfect sphere by only a third of a percent, which supports the spherical model in many contexts and justifies the term "radius of the Earth". While specific values differ, the concepts in this article generalize to any major planet.
Sub-orbital spaceflight
We can calculate the minimum delta-v and the corresponding maximum altitude for a given range, "d", assuming a spherical earth of circumference 40 000 km and neglecting the earth's rotation and atmosphere. Let θ be half the angle that the projectile is to go around the earth, so in degrees it is 45°×"d"/10 000 km. The minimum-delta-v trajectory corresponds to an ellipse with one focus at the centre of the earth and the other at the point halfway between the launch point and the destination point (somewhere inside the earth). (This is the orbit that minimizes the semi-major axis, which is equal to the sum of the distances from a point on the orbit to the two foci. Minimizing the semi-major axis minimizes the specific orbital energy and thus the delta-v, which is the speed of launch.) Geometrical arguments lead then to the following (with "R" being the radius of the earth, about 6370 km):
Great-circle distance
The shape of the Earth closely resembles a flattened sphere (a spheroid) with equatorial radius formula_17 of 6378.137 km; distance formula_18 from the center of the spheroid to each pole is 6356.752 km. When calculating the length of a short north-south line at the equator, the circle that best approximates that line has a radius of formula_19 (which equals the meridian's semi-latus rectum), or 6335.439 km, while the spheroid at the poles is best approximated by a sphere of radius formula_20, or 6399.594 km, a 1% difference. So long as a spherical Earth is assumed, any single formula for distance on the Earth is only guaranteed correct within 0.5% (though better accuracy is possible if the formula is only intended to apply to a limited area). Using the mean earth radius, formula_21 (for the WGS84 ellipsoid) means that in the limit of small flattening, the mean square relative error in the estimates for distance is minimized.
Earth's circumference
1,700 years after Eratosthenes's death, while Christopher Columbus studied what Eratosthenes had written about the size of the Earth, he chose to believe, based on a map by Toscanelli, that the Earth's circumference was one-third smaller. Had Columbus set sail knowing that Eratosthenes's larger circumference value was more accurate, he would have known that the place that he made landfall was not Asia, but rather the New World.
Earth's circumference
Latitude lines, known as circles of latitude are parallel to each other; the equatorial circumference is the largest circle of latitude, and the Earth’s longest circumference distance. Other circles of latitude have smaller circumference; for example, the 60th parallel north or south is approximately half as long as the Equator.
History of geodesy
From these observations, measurements, and/or "known" facts, Eratosthenes concluded that since the angular deviation of the sun from the vertical direction at Alexandria was also the angle of the subtended arc (see illustration), the linear distance between Alexandria and Syene was 1/50 of the circumference of the Earth which thus must be 50×5000 = 250,000 stadia or probably 25,000 geographical miles. The circumference of the Earth is 24,902 mi (40,075.16 km). Over the poles it is more precisely 40,008 km or 24,860 mi. The actual unit of measure used by Eratosthenes was the stadion. No one knows for sure what his stadion equals in modern units, possibly it was the Hellenic 185 m stadion.
Spherical Earth
Around 830 AD, Caliph al-Ma'mun commissioned a group of Muslim astronomers and geographers to measure the distance from Tadmur (Palmyra) to Raqqa in modern Syria. They found the cities to be separated by one degree of latitude and the meridian arc distance between them to be 66 miles and thus calculated the Earth's circumference to be 24,000 miles.
Willebrord Snellius
In 1615 Snellius, after the work of Eratosthenes in Ptolemaic Egypt in the 3rd century BC, probably was the first to try to do a large-scale experiment to measure the circumference of the earth using triangulation. He was helped in his measurements by two of his students, the Austrian barons Erasmus and Casparus Sterrenberg. In several cities he also received support of friends among the city leaders ("regenten"). In his work "The terrae Ambitus vera quantitate" (1617) under the author's name ("The Dutch Eratosthenes") Snellius describes the methods he used. He came up with an estimate of 28,500 Rhineland rods – in modern units 107.37 km for one degree of latitude. 360 times 107.37 then gives a circumference of the Earth of 38,653 km. The actual circumference is 40,075 kilometers, so Snellius underestimated the circumference of the earth by 3.5%.
Earth radius
The distance from the Earth's center to a point on the spheroid surface at geodetic latitude is:
Eartha
Eartha is the world's largest rotating and revolving globe, located within the headquarters of the DeLorme mapping corporation in Yarmouth, Maine. The globe weighs approximately 5,600 pounds (2,500 kg), and has a diameter of over 41 feet (12.5 m).
Voyages of Christopher Columbus
Columbus believed the incorrect calculations of Marinus of Tyre, putting the landmass at 225 degrees, leaving only 135 degrees of water. Moreover, Columbus believed that one degree represented a shorter distance on the Earth's surface than was actually the case – he read maps as if the distances were calculated in Italian miles (about 1,480 meters). Accepting the length of a degree to be 56⅔ miles, from the writings of Alfraganus, he therefore calculated the circumference of the Earth as at most, and the distance from the Canary Islands to Japan as 3,000 Italian miles (). Columbus did not realize Alfraganus used the much longer Arabic mile (about 1,830 m).
Nautical mile
In 1617 the Dutch scientist Willebrord Snell assessed the circumference of the Earth at 24,630 Roman miles (24,024 statute miles). Around that time British mathematician Edmund Gunter improved navigational tools including a new quadrant to determine latitude at sea. He reasoned that the lines of latitude could be used as the basis for a unit of measurement for distance and proposed the nautical mile as one minute or one-sixtieth () of one degree of latitude. As one degree is of a circle, one minute of arc is of a circle (or, in radians, ). These sexagesimal (base 60) units originated in Babylonian astronomy. Gunter used Snell's circumference to define a nautical mile as 6,080 feet, the length of one minute of arc at 48 degrees latitude. Since the earth is not a perfect sphere but is an oblate spheroid with slightly flattened poles, a minute of latitude is not constant, but about at the poles and at the Equator, with a mean value of . France and other countries measured the minute of arc at 45 degrees latitude, making the nautical mile .
Eartha
Eartha was originally designed to be in diameter. In 1999, surveyors hired by the "Guinness Book of World Records" measured the globe at ; while this is noted on the DeLorme web site (as of 2007-09-05), they also list the globe as in diameter. David DeLorme, CEO of the DeLorme mapping company, is credited with the design. The previous record holder is the Globe of Peace located in Apecchio, Pesaro, Italy.
Spherical Earth
Using the knowledge that the Sun is very far away, the ancient Greek geographer Eratosthenes performed an experiment using the differences in the observed angle of the Sun from two different locations to calculate the circumference of the Earth. Though modern telecommunications and timekeeping were not available, he was able to make sure the measurements happened at the same time by having them taken when the Sun was highest in the sky (local noon) at both locations. Using slightly inaccurate assumptions about the locations of two cities, he came to a result within 15% of the correct value.
Regio Patalis
Syene had been used by Eratosthenes of Cyrene in c.220 BC as a point of reference to measure the circumference of the Earth (by observing the angle of a shadow cast at Alexandria on the day of the summer solstice—eighty-three degrees—and deducting that from the ninety-degree right angle of the sun over Syene on the same day, from that deducing the acute angle—seven degrees—at the apex of the segment of the Earth’s circumference represented by the known distance from Syene to Alexandria—504 stadia—and then multiplying that distance by the value of that angle and dividing it by the 360 degrees of the whole circumference of the Earth: 252,000 stadia, or 39,690 km, an error of less than one per cent.
Great-circle distance
The Earth is nearly spherical (see Earth radius), so great-circle distance formulas give the distance between points on the surface of the Earth correct to within about 0.5%. (See .)
Posidonius
Posidonius calculated the Earth's circumference by reference to the position of the star Canopus. As explained by Cleomedes, Posidonius observed Canopus on but never above the horizon at Rhodes, while at Alexandria he saw it ascend as far as 7½ degrees above the horizon (the meridian arc between the latitude of the two locales is actually 5 degrees 14 minutes). Since he thought Rhodes was 5,000 stadia due north of Alexandria, and the difference in the star's elevation indicated the distance between the two locales was 1/48 of the circle, he multiplied 5,000 by 48 to arrive at a figure of 240,000 stadia for the circumference of the earth.
Earth's circumference
In 1791, the French Academy of Sciences selected the circumference definition over the alternative pendular definition because the force of gravity varies slightly over the surface of the Earth, which affects the period of a pendulum. To establish a universally accepted foundation for the definition of the metre, more accurate measurements of this meridian were needed. The French Academy of Sciences commissioned an expedition led by Jean Baptiste Joseph Delambre and Pierre Méchain, lasting from 1792 to 1799, which attempted to accurately measure the distance between a belfry in Dunkerque and Montjuïc castle in Barcelona to estimate the length of the meridian arc through Dunkerque. This portion of the meridian, assumed to be the same length as the Paris meridian, was to serve as the basis for the length of the half meridian connecting the North Pole with the Equator. The problem with this approach is that the exact shape of the Earth is not a simple mathematical shape, such as a sphere or oblate spheroid, at the level of precision required for defining a standard of length. The irregular and particular shape of the Earth smoothed to sea level is represented by a mathematical model called a geoid, which literally means "Earth-shaped". Despite these issues, in 1793 France adopted this definition of the metre as its official unit of length based on provisional results from this expedition. However, it was later determined that the first prototype metre bar was short by about 200 micrometres because of miscalculation of the flattening of the Earth, making the prototype about 0.02% shorter than the original proposed definition of the metre. Regardless, this length became the French standard and was progressively adopted by other countries in Europe.
Decimal degrees
The radius of the semi-major axis of the Earth at the equator is 6,378,137.0 meters resulting in a circumference of 40,075,161.2 meters. The equator is divided into 360 degrees of longitude, so each degree at the equator represents 111,319.9 meters or approximately 111.32 km. As one moves away from the equator towards a pole, however, one degree of longitude is multiplied by the cosine of the latitude, decreasing the distance, approaching zero at the pole. The number of decimal places required for a particular precision at the equator is:
Arc length
In the following lines, formula_69 represents the radius of a circle, formula_70 is its diameter, formula_71 is its circumference, formula_72 is the length of an arc of the circle, and formula_58 is the angle which the arc subtends at the centre of the circle. The distances formula_74 and formula_72 are expressed in the same units.Two units of length, the nautical mile and the metre (or kilometre), were originally defined so the lengths of arcs of great circles on the Earth's surface would be simply numerically related to the angles they subtend at its centre. The simple equation formula_91 applies in the following circumstances:
Axial precession
The Earth is not a perfect sphere but an oblate spheroid, with an equatorial diameter about 43 kilometers larger than its polar diameter. Because of the Earth's axial tilt, during most of the year the half of this bulge that is closest to the Sun is off-center, either to the north or to the south, and the far half is off-center on the opposite side. The gravitational pull on the closer half is stronger, since gravity decreases with the square of distance, so this creates a small torque on the Earth as the Sun pulls harder on one side of the Earth than the other. The axis of this torque is roughly perpendicular to the axis of the Earth's rotation so the axis of rotation precesses. If the Earth was a perfect sphere, there would be no precession.
Orbital effects on climate
where "a" is the ellipse's semi-major axis (half of the longest diameter of the ellipse) and "b" is the ellipse's semi-minor axis (half of the shortest diameter of the ellipse). Thus, for example, if summer and winter are on the part of the orbital ellipse that is furthest away from the sun, then Earth will have the least yearly solar radiation received during those two seasons, and the most yearly solar irradiation received during spring and autumn. With this difference in solar irradiation received, climate should noticeably change throughout the year, each year. Currently, Earth's eccentricity is approximately 0.0167, which is closer to the circular side of the eccentricity range Earth cycles through. Earth's eccentricity has always varied over time, and varies within the range of 0.005 to 0.0607 in one eccentricity cycle with a time period of about 100,000 years. There is another eccentricity cycle with a period of approximately 413,000 years, however, it's primarily only noticed as small variations within the 100,000 year eccentricity cycle. When this climate effect is considered with Earth's obliquity, they merge to offset the magnitude fraction of solar irradiation received in a given hemisphere, thus wonderfully adding to the complexity of the Earth climate system.
Figure of the Earth
Since the Earth is flattened at the poles and bulges at the Equator, geodesy represents the figure of the Earth as an oblate spheroid. The oblate spheroid, or oblate ellipsoid, is an ellipsoid of revolution obtained by rotating an ellipse about its shorter axis. It is the regular geometric shape that most nearly approximates the shape of the Earth. A spheroid describing the figure of the Earth or other celestial body is called a reference ellipsoid. The reference ellipsoid for Earth is called an Earth ellipsoid.
Earth bulge
The mean radius of the earth is about . (See Earth radius) Using the same units for both the altitude of the station and the radius of the earth,
History of geography
The size of the Earth was an important question to the Ancient Greeks. Eratosthenes attempted to calculate its circumference by measuring the angle of the sun at two different locations. While his numbers were problematic, most of the errors cancelled themselves out and he got quite an accurate figure. Since the distance from the Atlantic to India was roughly known, this raised the important question of what was in the vast region east of Asia and to the west of Europe. Crates of Mallus proposed that there were in fact four inhabitable land masses, two in each hemisphere. In Rome a large globe was created depicting this world. That some of the figures Eratosthenes had used in his calculation were considerably in error became known, and Posidonius set out to get a more accurate measurement. This number actually was considerably smaller than the real one, but it became accepted that the eastern part of Asia was not a huge distance from Europe.
Voyages of Christopher Columbus
A spherical Earth had been the general opinion of Ancient Greek science, and this view continued through the Middle Ages (for example, Bede mentions it in "The Reckoning of Time"). In fact Eratosthenes had measured the diameter of the Earth with good precision in the 2nd century BC. Where Columbus did differ from the generally accepted view of his time was in his incorrect arguments that assumed a significantly smaller diameter for the Earth, claiming that Asia could be easily reached by sailing west across the Atlantic. Most scholars accepted Ptolemy's correct assessment that the terrestrial landmass (for Europeans of the time, comprising Eurasia and Africa) occupied 180 degrees of the terrestrial sphere, and dismissed Columbus's claim that the Earth was much smaller, and that Asia was only a few thousand nautical miles to the west of Europe. Columbus's error was attributed to his insufficient experience in navigation at sea.
History of geodesy
Since the spherical shape was the most widely supported during the Greek Era, efforts to determine its size followed. Aristotle reported that mathematicians had calculated the circumference of the Earth (which is slightly over 40,000 km) to be 400,000 stadia (between 62,800 and 74,000 km or 46,250 and 39,250 mi) while Archimedes stated an upper bound of 3,000,000 stadia (483,000 km or 300,000 mi) using the Hellenic stadion which scholars generally take to be 185 meters or of a geographical mile.
Equator
The International Association of Geodesy (IAG) and the International Astronomical Union (IAU) have chosen to use an equatorial radius of 6,378.1366 kilometres (3,963.1903 mi) (codified as the IAU 2009 value). This equatorial radius is also in the 2003 and 2010 IERS Conventions. It is also the equatorial radius used for the IERS 2003 ellipsoid. If it were really circular, the length of the Equator would then be exactly 2π times the radius, namely 40,075.0142 kilometres (24,901.4594 mi). The GRS 80 (Geodetic Reference System 1980) as approved and adopted by the IUGG at its Canberra, Australia meeting of 1979 has an equatorial radius of 6,378.137 kilometres (3,963.191 mi). The WGS 84 (World Geodetic System 1984) which is a standard for use in cartography, geodesy, and satellite navigation including GPS, also has an equatorial radius of 6,378.137 kilometres (3,963.191 mi). For both GRS 80 and WGS 84, this results in a length for the Equator of 40,075.0167 km (24,901.4609 mi).
Geophysics
The Earth is roughly spherical, but it bulges towards the Equator, so it is roughly in the shape of an ellipsoid (see Earth ellipsoid). This bulge is due to its rotation and is nearly consistent with an Earth in hydrostatic equilibrium. The detailed shape of the Earth, however, is also affected by the distribution of continents and ocean basins, and to some extent by the dynamics of the plates.
List of unusual units of measurement
The definitions of both the nautical mile and the kilometre were originally derived from the Earth's circumference as measured through the poles. The nautical mile was defined as a minute of arc of latitude measured along any meridian. A circle has 360 degrees, and each degree is 60 minutes, so the nautical mile was defined as of the Earth's circumference, or about 1,852.22 metres. However, by international agreement, it is now defined to be exactly .
Earth's magnetic field
The Earth and most of the planets in the Solar System, as well as the Sun and other stars, all generate magnetic fields through the motion of electrically conducting fluids. The Earth's field originates in its core. This is a region of iron alloys extending to about 3400 km (the radius of the Earth is 6370 km). It is divided into a solid inner core, with a radius of 1220 km, and a liquid outer core. The motion of the liquid in the outer core is driven by heat flow from the inner core, which is about , to the core-mantle boundary, which is about . The heat is generated by potential energy released by heavier materials sinking toward the core (planetary differentiation, the iron catastrophe) as well as decay of radioactive elements in the interior. The pattern of flow is organized by the rotation of the Earth and the presence of the solid inner core.
Figure of the Earth
The concept of a spherical Earth dates back to around the 6th century BC, but remained a matter of philosophical speculation until the 3rd century BC. The first scientific estimation of the radius of the Earth was given by Eratosthenes about 240 BC, with estimates of the accuracy of Eratosthenes’s measurement ranging from 2% to 15%.
History of the metre
Jean Richer and Giovanni Domenico Cassini measured the parallax of Mars between Paris and Cayenne in French Guiana when Mars was at its closest to Earth in 1672. They arrived at a figure for the solar parallax of 91/2 inches, equivalent to an Earth–Sun distance of about 22000 Earth radii. They were also the first astronomers to have access to an accurate and reliable value for the radius of Earth, which had been measured by their colleague Jean Picard in 1669 as 3269 thousand "toises". Isaac Newton used this measurement for establishing his law of universal gravitation. Picard's geodetic observations had been confined to the determination of the magnitude of the earth considered as a sphere, but the discovery made by Jean Richer turned the attention of mathematicians to its deviation from a spherical form. The determination of the figure of the earth became a problem of the highest importance in astronomy, inasmuch as the diameter of the earth was the unit to which all celestial distances had to be referred.
Earth mass
While the mass of the Earth is implied by stating the Earth's radius and density, it was not usual to state the absolute mass explicitly 
prior to the introduction of scientific notation using powers of 10 in the later 19th century, 
because the absolute numbers would have been too awkward. Ritchie (1850) gives the mass of the Earth's atmosphere as "11,456,688,186,392,473,000 lbs." ( = , modern value is ) and states that "compared with the weight of the globe this mighty sum dwindles to insignificance".
Circle of latitude
Circles of latitude are often called parallels because they are parallel to each other; that is, any two circles are always the same distance apart. A location's position along a circle of latitude is given by its longitude. Circles of latitude are unlike circles of longitude, which are all great circles with the centre of Earth in the middle, as the circles of latitude get smaller as the distance from the Equator increases. Their length can be calculated by a common sine or cosine function. The 60th parallel north or south is half as long as the Equator (disregarding Earth's minor flattening by 0.3%). A circle of latitude is perpendicular to all meridians.
Expansion of the universe
For example, consider the measurement of distance between two places on the surface of the Earth. This is a simple, familiar example of spherical geometry. Because the surface of the Earth is two-dimensional, points on the surface of the Earth can be specified by two coordinates — for example, the latitude and longitude. Specification of a metric requires that one first specify the coordinates used. In our simple example of the surface of the Earth, we could choose any kind of coordinate system we wish, for example latitude and longitude, or X-Y-Z Cartesian coordinates. Once we have chosen a specific coordinate system, the numerical values of the coordinates of any two points are uniquely determined, and based upon the properties of the space being discussed, the appropriate metric is mathematically established too. On the curved surface of the Earth, we can see this effect in long-haul airline flights where the distance between two points is measured based upon a great circle, rather than the straight line one might plot on a two-dimensional map of the Earth's surface. In general, such shortest-distance paths are called "geodesics". In Euclidean geometry, the geodesic is a straight line, while in non-Euclidean geometry such as on the Earth's surface, this is not the case. Indeed, even the shortest-distance great circle path is always longer than the Euclidean straight line path which passes through the interior of the Earth. The difference between the straight line path and the shortest-distance great circle path is due to the curvature of the Earth's surface. While there is always an effect due to this curvature, at short distances the effect is small enough to be unnoticeable.
History of the metre
Instead of the seconds pendulum method, the commission – whose members included Lagrange, Laplace, Monge and Condorcet – decided that the new measure should be equal to one ten-millionth of the distance from the North Pole to the Equator (the quadrant of the Earth's circumference), measured along the meridian passing through Paris. Apart from the obvious consideration of safe access for French surveyors, the Paris meridian was also a sound choice for scientific reasons: a portion of the quadrant from Dunkirk to Barcelona (about 1000 km, or one-tenth of the total) could be surveyed with start- and end-points at sea level, and that portion was roughly in the middle of the quadrant, where the effects of the Earth's oblateness were expected to be the largest. The Spanish-French geodetic mission had confirmed that the acceleration of a body near the surface of the Earth is due to the combined effects of gravity and centrifugal acceleration. Indeed we know now that the resulting acceleration towards the ground is about 0.5% greater at the poles than at the Equator. It follows that the polar diameter of the Earth is smaller than its equatorial diameter. The Academy of Sciences planned to infer the flattening of the Earth from the length's differences between meridional portions corresponding to one degree of latitude. Jean-Baptiste Biot and François Arago published in 1821 their observations completing those of Delambre and Mechain. It was an account of the length's variation of the degrees of latitude along the Paris meridian as well as the account of the variation of the seconds pendulum's length along the same meridian. The seconds pendulum's length is a mean to measure "g", the local acceleration due to local gravity and centrifugal acceleration, which varies depending on one's position on Earth (see Earth's gravity).
Ahmad ibn Muhammad ibn Kathir al-Farghani
In the 15th century, Christopher Columbus used al-Farghani's estimate for the Earth's circumference as the basis for his voyages to America. However, Columbus mistook al-Farghani's 7091-foot Arabic mile to be a 4856-foot Roman mile, causing him to underestimate the Earth's circumference, believing he could take a shortcut to Asia.
Spherical Earth
A circumnavigation alone does not prove that the Earth is spherical. It could be cylindric or irregularly globular or one of many other shapes. Still, combined with trigonometric evidence of the form used by Eratosthenes 1,700 years prior, the Magellan expedition removed any reasonable doubt in educated circles in Europe. The Transglobe Expedition (1979–1982) was the first expedition to make a circumpolar circumnavigation, traveling the world "vertically" traversing both of the poles of rotation using only surface transport.
Structure of the Earth
The average density of Earth is
. Because the average density of surface material is only around , we must conclude that denser materials exist within Earth's core.
This result has been known since the Schiehallion experiment, performed in the 1770s.
Charles Hutton in his 1778 report concluded that the mean density of the Earth must be about formula_1 that of surface rock, concluding that the interior of the Earth must be metallic. Hutton estimated this metallic portion to occupy some 65% of the diameter of the Earth.
Hutton's estimate on the mean density of the Earth was still about 20% too low, at 
Henry Cavendish in his torsion balance experiment of 1798 found a value of , within 1% of the modern value.
Seismic measurements show that the core is divided into two parts, a "solid" inner core with a radius of ≈1,220 km and a liquid outer core extending beyond it to a radius of ≈3,400 km. The densities are between 9,900 and 12,200 kg/m in the outer core and 12,600–13,000 kg/m in the inner core.
Earth radius
The Earth's polar radius , or semi-minor axis, is the distance from its center to the North and South Poles, and equals .
Haversine formula
Either formula is only an approximation when applied to the Earth, which is not a perfect sphere: the "Earth radius" varies from 6356.752 km at the poles to 6378.137 km at the equator. More importantly, the radius of curvature of a north-south line on the earth's surface is 1% greater at the poles (≈6399.594 km) than at the equator (≈6335.439 km)—so the haversine formula and law of cosines cannot be guaranteed correct to better than 0.5%. More accurate methods that consider the Earth's ellipticity are given by Vincenty's formulae and the other formulas in the geographical distance article.
Christopher Columbus
From d'Ailly's "Imago Mundi" Columbus learned of Alfraganus's estimate that a degree of latitude (or a degree of longitude along the equator) spanned 56 miles, but did not realize that this was expressed in the Arabic mile rather than the shorter Roman mile with which he was familiar (1,480 m). He therefore estimated the circumference of the Earth to be about 30,200 km, whereas the correct value is .
Figure of the Earth
The Earth is only approximately spherical, so no single value serves as its natural radius. Distances from points on the surface to the center range from 6,353 km to 6,384 km (3,947 – 3,968 mi). Several different ways of modeling the Earth as a sphere each yield a mean radius of . Regardless of the model, any radius falls between the polar minimum of about 6,357 km and the equatorial maximum of about 6,378 km (3,950 – 3,963 mi). The difference correspond to the polar radius being approximately 0.3% shorter than the equator radius.
Seconds pendulum
In 1790, one year before the metre was ultimately based on a quadrant of the Earth, Talleyrand proposed that the metre be the length of the seconds pendulum at a latitude of 45°. This option, with one-third of this length defining the "foot", was also considered by Thomas Jefferson and others for redefining the yard in the United States shortly after gaining independence from the British Crown.
Instead of the seconds pendulum method, the commission of the French Academy of Sciences – whose members included Lagrange, Laplace, Monge and Condorcet – decided that the new measure should be equal to one ten-millionth of the distance from the North Pole to the Equator (the quadrant of the Earth's circumference), measured along the meridian passing through Paris. Apart from the obvious consideration of safe access for French surveyors, the Paris meridian was also a sound choice for scientific reasons: a portion of the quadrant from Dunkirk to Barcelona (about 1000 km, or one-tenth of the total) could be surveyed with start- and end-points at sea level, and that portion was roughly in the middle of the quadrant, where the effects of the Earth's oblateness were expected to be the largest. The Spanish-French geodetic mission combined with an earlier mesurement of the Paris meridian arc and the Lapland geodetic mission had confirmed that the Earth was an oblate spheroid. Moreover observations were made with a pendulum to determine the local acceleration due to local gravity and centrifugal acceleration; and these observations coincided with the geodetic results in proving that the Earth is flattened at the poles. The acceleration of a body near the surface of the Earth, which is measured with the seconds pendulum, is due to the combined effects of local gravity and centrifugal acceleration. The gravity diminishes with the distance from the center of the Earth while the centrifugal force augments with the distance from the axis of the Earth's rotation, it follows that the resulting acceleration towards the ground is 0.5% greater at the poles than at the Equator and that the polar diameter of the Earth is smaller than its equatorial diameter.
List of unusual units of measurement
The circumference of a great circle of the Earth (about ) is often compared to large distances. For example, one might say that a large number of objects laid end-to-end at the equator "would circle the Earth four and a half times". According to WGS-84, the circumference of a circle through the poles (twice the length of a meridian) is and the length of the equator is . Despite the fact that the difference (0.17%) between the two is insignificant at the low precision that these quantities are typically given to, it is nevertheless often specified as being at the equator.
Observable universe
According to calculations, the current "comoving distance"—proper distance, which takes into account that the universe has expanded since the light was emitted—to particles from which the cosmic microwave background radiation (CMBR) was emitted, which represent the radius of the visible universe, is about 14.0 billion parsecs (about 45.7 billion light-years), while the comoving distance to the edge of the observable universe is about 14.3 billion parsecs (about 46.6 billion light-years), about 2% larger. The radius of the observable universe is therefore estimated to be about 46.5 billion light-years and its diameter about 28.5 gigaparsecs (93 billion light-years, ). The total mass of ordinary matter in the universe can be calculated using the critical density and the diameter of the observable universe to be about 1.5 × 10 kg. In November 2018, astronomers reported that the extragalactic background light (EBL) amounted to 4 × 10 photons.
Earth radius
This "radius of curvature in the prime vertical" which is perpendicular (normal or orthogonal) to at geodetic latitude is:
This radius is also called the transverse radius of curvature. At the equator, .
Earth mass
Before the direct measurement of the gravitational constant, estimates of the Earth mass were limited to estimating Earth's mean density from observation of the crust and estimates on Earth's volume. Estimates on the volume of the earth in the 17th century were based on a circumference estimate of to the degree of latitude, corresponding to a radius of 5,500 km (86% of the Earth's actual radius of about 6,371 km), resulting in an estimated volume of about one third smaller than the correct value.
Earth's circumference
It has been described as "the single most important measurement" of the Earth, assuming the Earth to be a sphere (the Earth is an technically an ellipsoid, albeit with just 0.3% flattening).
Yaʿqūb ibn Ṭāriq
The "Tarkīb al‐aflāk" dealt with cosmography, that is, the placement and sizes of the heavenly bodies. Its estimates of the sizes and distances of the heavenly bodies were tabulated in al-Bīrūnī's work on India; according to him, Yaʿqūb ibn Ṭāriq gave the radius of the Earth as 1,050 "farsakhs", the diameter of the Moon and Mercury as 5,000 farsakhs (4.8 Earth radii), and the diameter of the other heavenly bodies (Venus, the Sun, Mars, Jupiter, and Saturn) as 20,000 "farsakhs" (19.0 Earth radii.)
Absolute rotation
Isaac Newton explained this in his "Principia Mathematica" (1687) in which he outlined his theory and calculations on the shape of the Earth. Newton theorized correctly that the Earth was not precisely a sphere but had an oblate ellipsoidal shape, slightly flattened at the poles due to the centrifugal force of its rotation. Since the surface of the Earth is closer to its center at the poles than at the equator, gravity is stronger there. Using geometric calculations, he gave a concrete argument as to the hypothetical ellipsoid shape of the Earth.
A modern measurement of the Earth's oblateness leads to an equatorial radius of 6378.14 km and a polar radius of 6356.77 km, about 0.1% less oblate than Newton's estimate. A theoretical determination of the precise extent of oblateness in response to a centrifugal force requires an understanding of the make-up of the planet, not only today but during its formation.
Error analysis for the Global Positioning System
Earth has a radius of 6,357 km (at the poles) making "R" = 6,357,000 m and the satellites have an altitude of 20,184 km making their orbit radius "R" = 26,541,000 m. Substituting these in the above equation, with "M" = , "G" = , and "c" = (all in SI units), gives:
This represents the fraction by which the satellites' clocks move faster than Earth's. It is then multiplied by the number of nanoseconds in a day:
History of geodesy
Around AD 830 Caliph al-Ma'mun commissioned a group of astronomers led by Al-Khwarizmi to measure the distance from Tadmur (Palmyra) to Raqqa, in modern Syria. They found the cities to be separated by one degree of latitude and the distance between them to be 66 miles and thus calculated the Earth's circumference to be 24,000 miles. Another estimate given was 56 Arabic miles per degree, which corresponds to 111.8 km per degree and a circumference of 40,248 km, very close to the currently modern values of 111.3 km per degree and 40,068 km circumference, respectively.
Spherical Earth
Using other evidence to hypothesize a spherical shape, the medieval Iranian scholar Al-Biruni used this phenomenon to calculate the Earth's circumference to within of the correct value.
Christopher Columbus
As far back as the 3rd century BC, Eratosthenes had correctly computed the circumference of the Earth by using simple geometry and studying the shadows cast by objects at two remote locations. In the 1st century BC, Posidonius confirmed Eratosthenes's results by comparing stellar observations at two separate locations. These measurements were widely known among scholars, but confusion about the old-fashioned units of distance in which they were expressed led to some debate about the size of the Earth.
Mercator projection
Although the surface of Earth is best modelled by an oblate ellipsoid of revolution, for small scale maps the ellipsoid is approximated by a sphere of radius "a". Many different methods exist for calculating "a". The simplest include (a) the equatorial radius of the ellipsoid, (b) the arithmetic or geometric mean of the semi-axes of the ellipsoid, (c) the radius of the sphere having the same volume as the ellipsoid. The range of all possible choices is about 35 km, but for small scale (large region) applications the variation may be ignored, and mean values of 6,371 km and 40,030 km may be taken for the radius and circumference respectively. These are the values used for numerical examples in later sections. Only high-accuracy cartography on large scale maps requires an ellipsoidal model.
Arabic mile
Around 830 AD, Caliph Al-Ma'mun commissioned a group of Muslim astronomers and Muslim geographers to measure the distance from Tadmur (Palmyra) to Raqqa, in modern Syria. They found the cities to be separated by one degree of latitude and the meridian arc distance between them to be 66 miles and thus calculated the Earth's circumference to be 24,000 miles.
Proper time
At the equator, the radius of the Earth is "r" = 6,378,137 meters. In addition, the rotation of the Earth needs to be taken into account. This imparts on an observer an angular velocity of formula_35 of 2"π" divided by the sidereal period of the Earth's rotation, 86162.4 seconds. So formula_36. The proper time equation then produces
History of Mars observation
In the 5th century CE, the Indian astronomical text "Surya Siddhanta" estimated the angular size of Mars as 2 arc-minutes (1/30 of a degree) and its distance to Earth as 10,433,000 km (1,296,600 yojana, where one yojana is equivalent to eight km in the "Surya Siddhanta"). From this the diameter of Mars is deduced to be 6,070 km (754.4 yojana), which has an error within 11% of the currently accepted value of 6,788 km. However, this estimate was based upon an inaccurate guess of the planet's angular size. The result may have been influenced by the work of Ptolemy, who listed a value of 1.57 arc-minutes. Both estimates are significantly larger than the value later obtained by telescope.
In 1543, Nicolaus Copernicus published a heliocentric model in his work "De revolutionibus orbium coelestium". This approach placed the Earth in an orbit around the Sun between the circular orbits of Venus and Mars. His model successfully explained why the planets Mars, Jupiter and Saturn were on the opposite side of the sky from the Sun whenever they were in the middle of their retrograde motions. Copernicus was able to sort the planets into their correct heliocentric order based solely on the period of their orbits about the Sun. His theory gradually gained acceptance among European astronomers, particularly after the publication of the "Prutenic Tables" by the German astronomer Erasmus Reinhold in 1551, which were computed using the Copernican model.
Reissner–Nordström metric
In practice, the ratio "r"/"r" is often extremely small. For example, the Schwarzschild radius of the Earth is roughly 9 mm (3/8 inch), whereas a satellite in a geosynchronous orbit has a radius "r" that is roughly four billion times larger, at 42,164 km (26,200 miles). Even at the surface of the Earth, the corrections to Newtonian gravity are only one part in a billion. The ratio only becomes large close to black holes and other ultra-dense objects such as neutron stars.
Earth's rotation
The most celebrated test of Earth's rotation is the Foucault pendulum first built by physicist Léon Foucault in 1851, which consisted of a lead-filled brass sphere suspended from the top of the Panthéon in Paris. Because of the Earth's rotation under the swinging pendulum, the pendulum's plane of oscillation appears to rotate at a rate depending on latitude. At the latitude of Paris the predicted and observed shift was about clockwise per hour. Foucault pendulums now swing in museums around the world.
Nicholas Nicastro
Nicastro published his first book-length work of non-fiction in 2008. "Circumference: Eratosthenes and the Ancient Quest to Measure the Globe" tells the story of the first man to accurately measure the size of the Earth. In a review, the "Bryn Mawr Classical Review" observed some scholarly inaccuracies, but noted overall "Given the paucity of material in English on Eratosthenes, anything is a welcome addition, but this book is "much" better than nothing. In its pages, historians of science will learn much about the ancient world, and historians of the ancient world will learn much about science." "Circumference" was subsequently cited as an "exemplar" text for 9th and 10th graders as part of the nationwide Common Core standards for English Language Arts.
Universal Transverse Mercator coordinate system
The WGS 84 spatial reference system describes Earth as an oblate spheroid along north-south axis with an equatorial radius of formula_1 km and an inverse flattening of formula_2. Let's take a point of latitude formula_3 and of longitude formula_4 and compute its UTM coordinates as well as point scale factor formula_5 and meridian convergence formula_6 using a reference meridian of longitude formula_7. By convention, in the northern hemisphere formula_8 km and in the southern hemisphere formula_9 km. By convention also formula_10 and formula_11 km.
Kepler's laws of planetary motion
The eccentricity of the orbit of the Earth makes the time from the March equinox to the September equinox, around 186 days, unequal to the time from the September equinox to the March equinox, around 179 days. A diameter would cut the orbit into equal parts, but the plane through the Sun parallel to the equator of the Earth cuts the orbit into two parts with areas in a 186 to 179 ratio, so the eccentricity of the orbit of the Earth is approximately
Air mass (astronomy)
Using a scale height of 8435 m, Earth’s mean radius of 6371 km,
and including the correction for refraction,
Equator
Earth bulges slightly at the Equator; the "average" diameter of Earth is , but the diameter at the Equator is about greater than at the poles.
Spherical Earth
On a perfectly spherical Earth, flat terrain or ocean, when viewed from the surface, blocks exactly half the sky - a hemisphere of 180°. Moving away from the surface of the Earth means that the ground blocks less and less of the sky. For example, when viewed from the Moon, the Earth blocks only a small portion of the sky, because it is so distant. This phenomenon of geometry means that when viewed from a high mountain, flat ground or ocean blocks less than 180° of the sky. The rate of change in the angle blocked by the sky as altitude increases is different for a disc than a sphere, and values observed show that the Earth is locally convex. (The angles blocked would also be different for a mountain close to the edge of a flat Earth compared to a mountain in the middle of a flat Earth, and this is not observed.) In theory, measurements of this type from all around the Earth would confirm that it is a complete sphere (as opposed to some other shape with convex areas) though actually taking all those measurements would be very expensive.
Earth
The Hill sphere, or the sphere of gravitational influence, of the Earth is about in radius. This is the maximum distance at which the Earth's gravitational influence is stronger than the more distant Sun and planets. Objects must orbit the Earth within this radius, or they can become unbound by the gravitational perturbation of the Sun.
Earth radius
Additionally, the radius can be estimated from the curvature of the Earth at a point. Like a torus, the curvature at a point will be greatest (tightest) in one direction (north–south on Earth) and smallest (flattest) perpendicularly (east–west). The corresponding radius of curvature depends on the location and direction of measurement from that point. A consequence is that a distance to the true horizon at the equator is slightly shorter in the north/south direction than in the east-west direction.
History of geodesy
A parallel later ancient measurement of the size of the Earth was made by another Greek scholar, Posidonius. He noted that the star Canopus was hidden from view in most parts of Greece but that it just grazed the horizon at Rhodes. Posidonius is supposed to have measured the angular elevation of Canopus at Alexandria and determined that the angle was 1/48 of circle. He used a distance from Alexandria to Rhodes, 5000 stadia, and so he computed the Earth's circumference in stadia as 48 times 5000 = 240,000. Some scholars see these results as luckily semi-accurate due to cancellation of errors. But since the Canopus observations are both mistaken by over a degree, the "experiment" may be not much more than a recycling of Eratosthenes's numbers, while altering 1/50 to the correct 1/48 of a circle. Later, either he or a follower appears to have altered the base distance to agree with Eratosthenes's Alexandria-to-Rhodes figure of 3750 stadia since Posidonius's final circumference was 180,000 stadia, which equals 48×3750 stadia. The 180,000 stadia circumference of Posidonius is suspiciously close to that which results from another method of measuring the earth, by timing ocean sunsets from different heights, a method which is inaccurate due to horizontal atmospheric refraction.
Cosmic distance ladder
Direct distance measurements are based upon the astronomical unit (AU), which is the distance between the Earth and the Sun.
Kepler's laws provide precise ratios of the sizes of the orbits of objects orbiting the Sun, but provides no measurement of the overall scale of the orbit system. Radar is used to measure the distance between the orbits of the Earth and of a second body. From that measurement and the ratio of the two orbit sizes, the size of Earth's orbit is calculated. The Earth's orbit is known with an absolute precision of a few meters and a relative precision of a few .
Spherical Earth
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.
Pascual Jordan
In 1966, Jordan published his 182-page work "Die Expansion der Erde. Folgerungen aus der Diracschen Gravitationshypothese" (The expansion of the Earth. Conclusions from the Dirac gravitation hypothesis) in which he developed his theory that, according to Paul Dirac's hypothesis of a steady weakening of gravitation throughout the history of the universe, the Earth may have swollen to its current size, from an initial ball of a diameter of only about . This theory could explain why the ductile lower sima layer of the Earth's crust is of a comparatively uniform thickness, while the brittle upper sial layer of the Earth's crust had broken apart into the main continental plates. The continents having to adapt to the ever flatter surface of the growing ball, the mountain ranges on the Earth's surface would, in the course of that, have come into being as constricted folds. Despite the energy Jordan invested in the expanding Earth theory, his geological work was never taken seriously by either physicists or geologists.
Close to Critical
Revolving on an orbit about the star Altair, Tenebra is an example of one of Hal Clement's "hellworlds". 27 times the mass of Earth, Tenebra is three times Earth's diameter (38,226 kilometers; 23,746 miles) and has three times Earth's gravity at its surface (29.43 meters per second per second; 96.6 feet per second per second), which gives Tenebra an escape velocity of 33.558 kilometers per second (nearly 21 miles per second). Clement also describes the planet as rotating on its axis in a little less than four Earth days.
Ali ibn Isa al-Asturlabi
ʿAlī ibn ʿĪsā al-Asṭurlābī () was an Arab astronomer and geographer of the 9th century. He wrote a treatise on the astrolabe and was an opponent of astrology. During the reign of al-Ma'mun, and together with Khālid ibn ʿAbd al‐Malik al‐Marwarrūdhī, he participated in an expedition to the Plain of Sinjar to measure the length of a degree, or the circumference of the Earth. He measured the Earth's circumference, getting a result of 40,248 km (or, according to other sources, 41,436 km).
Extreme points of Earth
As distinct from all the abovementioned geodesic lines, which may appear straight but are actually arcs of great circles projected on the spheroidal surface of the earth and, accordingly, are not truly straight but rather curving lines, authentically straight lines can be projected through the interior of the earth between most any two points on the surface of the earth (some extreme topographical situations being the rare exceptions). And if the aforementioned (under “fastest point on earth”) maximum radial line projected from the summit of Cayambe in Ecuador to the axial center of the earth is extended to the diametrically opposite point on the surface of the earth (aka the so-called antipodes of the said Cayambe summit, which are located actually on the island of Sumatra as it happens) then the resulting diametrical line would be the longest truly straight line that could be produced anywhere on earth. As the variable circumference of the earth approaches 25,000 miles, such a maximum “diametrical” or “antipodal” line would be on the order of 8,000 miles long.
Globe of Peace
The Globe of Peace (Mappamondo della Pace in Italian) is a large globe located in Apecchio, Pesaro, Italy. It was the Guinness Book of World Records record holder for the world's largest rotating globe until 1999, when it was succeeded by Eartha. It was built over a period of six years by Orfeo Bartolucci with the stated goal of diffusing a message of peace and liberty to all people. It measures 10 metres in diameter and is reported to weigh 170 quintals, or 17,000 kilograms. Reportedly 250 quintals of putty, 30 cubic metres of wood, and a ton (unclear whether English or Metric) of nails were used in its construction. The globe is located outdoors and has a fibreglass skin. It can hold approximately 600 people and internally contains descriptive tables listing every country of the world and their flag.
Earth radius
Another mean radius is the "rectifying radius", giving a sphere with circumference equal to the perimeter of the ellipse described by any polar cross section of the ellipsoid. This requires an elliptic integral to find, given the polar and equatorial radii:
Mount Meru
One yojana can be taken to mean about 11.5 km (9 miles) though its magnitude seems to differ over time periods, e.g. the Earth's circumference is 3,200 yojanas according to Vārāhamihira and slightly less so in the Āryabhatiya, but is said to be 5,026.5 yojanas in the Suryasiddhānta. The Matsya Purana and the Bhāgvata Purāna along with some other Hindu texts consistently give the height of 84,000 yojanas to Mount Meru which translates into 672,000 miles or 1,082,000 kilometers.
Travel in Classical antiquity
Later Greek scientists determined that the Earth was round, although there was some debate as to the veracity of this claim. During the conquests by Alexander the Great, Hellenistic knowledge of the world was expanded, resulting in an improved map of the world by Eratosthenes. He also calculated the circumference of the Earth, and published two treatises about geography, titled "Geographica" and "On the Measurement of the Earth". Contemporaries of Eratosthenes questioned the validity of his methods, although his calculation of the Earth's circumference was quite accurate.
List of asteroid close approaches to Earth in 2019
For reference, the radius of Earth is approximately or 0.0166 lunar distances.Geosynchronous satellites have an orbit with semi-major axis length of or 0.110 lunar distances. The only known asteroid to have passed this distance from Earth was the 1-2 meter 
While most asteroids on this list are confirmed, well-observed unconfirmed objects with a 50% or greater chance of passing within 1 LD of the Earth are included as well.
History of geography
The Vishnudharmottara Purana (compiled between 300-350 AD) contains six chapters on physical and human geography. The locational attributes of peoples and places, and various seasons are the topics of these chapters. Varahamihira's Brihat-Samhita gave a thorough treatment of planetary movements, rainfall, clouds and the formation of water. The mathematician-astronomer Aryabhata gave a precise estimate of the earth's circumference in his treatise Āryabhaṭīya. Aryabhata accurately calculated the Earth's circumference as 24,835 miles, which was only 0.2% smaller than the actual value of 24,902 miles.
Oerth
According to the paper by Gary Holian in "Oerth Journal", Oerth's circumference is about 42,024 km, and its radius measures 6,714 km, about 1% more than that of Earth. There is no flattening of the planet sphere due to rotation, and divine power is again hinted at.
Mathematical coincidence
The polar diameter of the Earth is equal to half a billion inches, to within 0.1%.
Earth radius
In particular, the Earth's "radius of curvature in the (north–south) meridian" at is:
This is the radius that Eratosthenes measured.
Earth ellipsoid
It is an ellipsoid of revolution whose minor axis (shorter diameter), which connects the geographical North Pole and South Pole, is approximately aligned with the Earth's axis of rotation. The ellipsoid is defined by the equatorial axis "a" and the polar axis "b"; their difference is about 21 km, or 0.335%. Additional parameters are the mass function "J2", the correspondent gravity formula, and the rotation period (usually 86164 seconds).
Flat Earth
Early Christian beliefs mention a number of ideas about the shape of the Earth. Athenagoras, an eastern Christian writing around the year 175 CE said, "The world, being made spherical, is confined within the circles of heaven." Methodius (c. 290 AD), an eastern Christian writing against "the theory of the Chaldeans and the Egyptians" who asserted that the Earth was spherical said, "Let us first lay bare ... the theory of the Chaldeans and the Egyptians. They say that the circumference of the universe is likened to the turnings of a well-rounded globe, the Earth being a central point. They say that since its outline is spherical, ... the Earth should be the center of the universe, around which the heaven is whirling." Lactantius, a western Christian writer and advisor to the first Christian Roman Emperor, Constantine, and writing sometime between 304–313 CE, ridiculed the notion of Antipodes and the philosophers who fancied that "the universe is round like a ball. They also thought that heaven revolves in accordance with the motion of the heavenly bodies. ... For that reason, they constructed brass globes, as though after the figure of the universe. ... I am at a loss as to what to say concerning those who, once they have erred, continue in their folly, defending one vain thing by another vain thing." Arnobius, another eastern Christian writing sometime around 305 CE, said, "In the first place, indeed, the world itself is neither right nor left. It has neither upper nor lower regions, nor front nor back. For whatever is round and bounded on every side by the circumference of a solid sphere, has no beginning or end ..."
Spherical Earth
Knowing the difference in angle between two points on the Earth's surface and the surface distance between them allows a calculation of the Earth's size. Using observations at Rhodes (in Greece) and Alexandria (in Egypt) and the distance between them, the Ancient Greek philosopher Posidonius actually did use this technique to calculate the circumference of the planet to within perhaps 4% of the correct value (though modern equivalents of his units of measure are not precisely known).
Structure of the Earth
The mass of Earth is about .
Posidonius
Strabo noted that the distance between Rhodes and Alexandria is 3,750 stadia, and reported Posidonius's estimate of the Earth's circumference to be 180,000 stadia or . Pliny the Elder mentions Posidonius among his sources and without naming him reported his method for estimating the Earth's circumference. He noted, however, that Hipparchus had added some 26,000 stadia to Eratosthenes's estimate. The smaller value offered by Strabo and the different lengths of Greek and Roman stadia have created a persistent confusion around Posidonius's result. Ptolemy used Posidonius's lower value of 180,000 stades (about 33% too low) for the earth's circumference in his "Geography". This was the number used by Christopher Columbus in order to underestimate the distance to India as 70,000 stades.
Eartha
The globe was built with a scale of 1:1,000,000, on which one inch represents , one millimeter represents one kilometer. As with most globes, it's mounted at a 23.5 degree angle, the same axial tilt as the Earth itself; thus the equator is diagonal to the floor. It uses a cantilever mount with two motors, and simulates one day's revolution and rotation every 18 minutes, though it is possible for the motors to fully rotate the globe in as little as one minute.
List of Earth-crossing minor planets
An asteroid with an Earth-crossing orbit is not necessarily in danger of colliding with Earth. The orbit of an Earth-crossing asteroid may not even intersect with that of Earth. This apparent contradiction arises because many asteroids have highly inclined orbits, so although they may have a perihelion less than that of Earth, their paths can never cross. An asteroid for which there is some possibility of a collision with Earth at a future date and which is above a certain size is classified as a potentially hazardous asteroid (PHA). Specifically, an asteroid is a PHA if its Earth minimum orbital intersection distance (MOID) is <0.05 AU and its absolute magnitude is 22 or brighter. The concept of PHA is intended to replace the now abandoned strict definition of ECA (Earth-crossing asteroid) which existed for a few years. Determining if an asteroid was an ECA required calculation of its orbits millennia into the future, including planetary gravitational perturbations, to assess whether a collision with Earth was possible and this has proved to be impractical.