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95-468: There is no single internationally agreed symbol, with several symbols in use. The word mile is from the Latin phrase for a thousand paces: mille passus . Navigation at sea was done by eye until around 1500 when navigational instruments were developed and cartographers began using a coordinate system with parallels of latitude and meridians of longitude . The earliest reference of 60 miles to

190-506: A conversion factor used when expressing planetary properties as multiples or fractions of a constant terrestrial radius; if the choice between equatorial or polar radii is not explicit, the equatorial radius is to be assumed, as recommended by the International Astronomical Union (IAU). Earth's rotation , internal density variations, and external tidal forces cause its shape to deviate systematically from

285-489: A parallel of latitude is given by p = N cos ⁡ ( φ ) {\displaystyle p=N\cos(\varphi )} . The Earth's meridional radius of curvature at the equator equals the meridian's semi-latus rectum : The Earth's prime-vertical radius of curvature at the equator equals the equatorial radius, N e = a . The Earth's polar radius of curvature (either meridional or prime-vertical) is: The principal curvatures are

380-604: A quarter meridian . So ⁠ 10,000,000 m / 90 × 60 ⁠ = 1,851.85 m ≈ 1,852 m became the metric length for a nautical mile. France made it legal for the French Navy in 1906, and many metric countries voted to sanction it for international use at the 1929 International Hydrographic Conference. Both the United States and the United Kingdom used an average arcminute—specifically, a minute of arc of

475-403: A degree (5866 ⁠ 2 / 3 ⁠ feet per arcminute ). In 1633, William Oughtred suggested 349,800 feet to a degree (5830 feet per arcminute). Both Gunter and Oughtred put forward the notion of dividing a degree into 100 parts, but their proposal was generally ignored by navigators. The ratio of 60 miles, or 20 leagues, to a degree of latitude remained fixed while the length of the mile

570-473: A degree is a map by Nicolaus Germanus in a 1482 edition of Ptolemy 's Geography indicating one degree of longitude at the Equator contains " milaria 60 ". An earlier manuscript map by Nicolaus Germanus in a previous edition of Geography states " unul gradul log. et latitud sub equinortiali formet stadia 500 que fanut miliaria 62 ⁠ 1 / 2 ⁠ " ("one degree longitude and latitude under

665-558: A great circle of a sphere having the same surface area as the Clarke 1866 ellipsoid . The authalic (equal area) radius of the Clarke 1866 ellipsoid is 6,370,997.2 metres (20,902,222 ft). The resulting arcminute is 1,853.2480 metres (6,080.210 ft). The United States chose five significant digits for its nautical mile, 6,080.2 feet , whereas the United Kingdom chose four significant digits for its Admiralty mile, 6,080 feet. In 1929

760-409: A maximum ( equatorial radius , denoted a ) of nearly 6,378 km (3,963 mi) to a minimum ( polar radius , denoted b ) of nearly 6,357 km (3,950 mi). A globally-average value is usually considered to be 6,371 kilometres (3,959 mi) with a 0.3% variability (±10 km) for the following reasons. The International Union of Geodesy and Geophysics (IUGG) provides three reference values:

855-455: A more precise value for its polar radius is needed. The geocentric radius is the distance from the Earth's center to a point on the spheroid surface at geodetic latitude φ , given by the formula: where a and b are, respectively, the equatorial radius and the polar radius. The extrema geocentric radii on the ellipsoid coincide with the equatorial and polar radii. They are vertices of

950-584: A number of territories with less than a million inhabitants, most of which are UK or US territories, or have close historical ties with the UK or US: American Samoa, Bahamas, Belize, British Virgin Islands, Cayman Islands, Dominica, Falkland Islands, Grenada, Guam, The N. Mariana Islands, Samoa, St. Lucia, St. Vincent & The Grenadines, St. Helena, St. Kitts & Nevis, the Turks & Caicos Islands, and

1045-448: A perfect sphere. Local topography increases the variance, resulting in a surface of profound complexity. Our descriptions of Earth's surface must be simpler than reality in order to be tractable. Hence, we create models to approximate characteristics of Earth's surface, generally relying on the simplest model that suits the need. Each of the models in common use involve some notion of the geometric radius . Strictly speaking, spheres are

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1140-452: A planet causes it to approximate an oblate ellipsoid /spheroid with a bulge at the equator and flattening at the North and South Poles , so that the equatorial radius a is larger than the polar radius b by approximately aq . The oblateness constant q is given by where ω is the angular frequency , G is the gravitational constant , and M is the mass of the planet. For

1235-582: A separate US survey mile ( ⁠ 6336 / 3937 ⁠ km) continues to see some use, although it was officially phased out in 2022. While most countries replaced the mile with the kilometre when switching to the International System of Units (SI), the international mile continues to be used in some countries, such as the United Kingdom, the United States, and a number of countries with fewer than one million inhabitants, most of which are UK or US territories or have close historical ties with

1330-470: A sphere in many ways. This section describes the common ways. The various radii derived here use the notation and dimensions noted above for the Earth as derived from the WGS-84 ellipsoid; namely, A sphere being a gross approximation of the spheroid, which itself is an approximation of the geoid, units are given here in kilometers rather than the millimeter resolution appropriate for geodesy. In geophysics,

1425-524: A trailing period—as "mi", "M", "ml", and "m". The American National Institute of Standards and Technology now uses and recommends "mi" to avoid confusion with the SI metre (m) and millilitre (ml). However, derived units such as miles per hour or miles per gallon continue to be abbreviated as "mph" and "mpg" rather than "mi/h" and "mi/gal". In the United Kingdom, road signs use "m" as the abbreviation for mile though height and width restrictions also use "m" as

1520-583: Is U+3344 ㍄ SQUARE MAIRU , after マイル mairu . The international mile is precisely equal to 1.609 344  km (or ⁠ 25146 / 15625 ⁠  km as a fraction). It was established as part of the 1959 international yard and pound agreement reached by the United States, the United Kingdom, Canada, Australia, New Zealand, and the Union of South Africa , which resolved small but measurable differences that had arisen from separate physical standards each country had maintained for

1615-538: Is based upon the length of a meridian of latitude . The German geographical mile ( geographische Meile ) was previously 1 ⁄ 15 ° of latitude (7.4127 km). The informal term "metric mile" is used in some countries, in sports such as track and field athletics and speed skating , to denote a distance of 1,500 metres (0.932 miles). The 1500 meters is the premier middle distance running event in Olympic sports . In United States high-school competition,

1710-635: Is defined by the First International Extraordinary Hydrographic Conference in Monaco as exactly 1,852 metres (which is 1.151 miles or 6,076.12 feet). In the United States, the nautical mile was defined in the 19th century as 6,080.2 feet (1,853.24 m), whereas in the United Kingdom, the Admiralty nautical mile was defined as 6,080 feet (1,853.18 m) and was about one minute of latitude in

1805-515: Is from Rome. The Italian mile ( miglio , pl.   miglia ) was traditionally considered a direct continuation of the Roman mile, equal to 1000 paces, although its actual value over time or between regions could vary greatly. It was often used in international contexts from the Middle Ages into the 17th century and is thus also known as the "geographical mile", although

1900-400: Is known as the geographical mile . Using the definition ⁠ 1 / 60 ⁠ of a degree of latitude on Mars , a Martian nautical mile equals to 983 m (1,075 yd). This is potentially useful for celestial navigation on a human mission to the planet , both as a shorthand and a quick way to roughly determine the location. Mile#Roman mile The mile , sometimes

1995-560: Is possible to combine the principal radii of curvature above in a non-directional manner. The Earth's Gaussian radius of curvature at latitude φ is: Where K is the Gaussian curvature , K = κ 1 κ 2 = det B det A {\displaystyle K=\kappa _{1}\,\kappa _{2}={\frac {\det \,B}{\det \,A}}} . The Earth's mean radius of curvature at latitude φ is: The Earth can be modeled as

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2090-398: Is used in radar -related subjects and is equal to 6,000 feet (1.8288 kilometres). The radar mile is a unit of time (in the same way that the light year is a unit of distance), equal to the time required for a radar pulse to travel a distance of two miles (one mile each way). Thus, the radar statute mile is 10.8 μs and the radar nautical mile is 12.4 μs. The geographical mile

2185-666: The Sjællandske miil , for instance, had been 11.13 km. The Germans also used a longer version of the geographical mile . The Breslau mile , used in Breslau , and from 1630 officially in all of Silesia , equal to 11,250 ells , or about 6,700 meters. The mile equaled the distance from the Piaskowa Gate all the way to Psie Pole ( Hundsfeld ). By rolling a circle with a radius of 5 ells through Piaskowa Island , Ostrów Tumski and suburban tracts, passing eight bridges on

2280-461: The Exchequer , which thereafter verified local standards until its abolition in the 19th century. New brass standards are known to have been constructed under Henry VII and Elizabeth I . Arnold's c.  1500 Customs of London recorded a mile shorter than previous ones, coming to 0.947 international miles (5,000 feet) or 1.524 km. The English statute mile

2375-701: The Global Positioning System gained importance, true global models were developed which, while not as accurate for regional work, best approximate the Earth as a whole. The following radii are derived from the World Geodetic System 1984 ( WGS-84 ) reference ellipsoid . It is an idealized surface, and the Earth measurements used to calculate it have an uncertainty of ±2 m in both the equatorial and polar dimensions. Additional discrepancies caused by topographical variation at specific locations can be significant. When identifying

2470-466: The decempeda and dioptra then spread its use. In modern times, Agrippa's Imperial Roman mile was empirically estimated to have been about 1,618 yards (1,479 m; 4,854 ft; 0.919 mi) in length, slightly less than the 1,760 yards (1,609 m; 5,280 ft) of the modern international mile. In Hellenic areas of the Empire, the Roman mile ( ‹See Tfd› Greek : μίλιον , mílion )

2565-409: The geographical mile is now a separate standard unit. The Arabic mile ( الميل , al-mīl ) was not the common Arabic unit of length ; instead, Arabs and Persians traditionally used the longer parasang or "Arabic league ". The Arabic mile was, however, used by medieval geographers and scientists and constituted a kind of precursor to the nautical or geographical mile . It extended

2660-446: The international mile and international foot . In the United States, the term statute mile formally refers to the survey mile, but for most purposes, the difference of less than 1 ⁄ 8 inch (3.2 mm) between the survey mile and the international mile (1609.344 metres exactly) is insignificant—one international mile is 0.999 998 US survey miles—so statute mile can be used for either. But in some cases, such as in

2755-460: The international mile or statute mile to distinguish it from other miles, is a British imperial unit and United States customary unit of length; both are based on the older English unit of length equal to 5,280 English feet , or 1,760 yards . The statute mile was standardised between the Commonwealth of Nations and the United States by an international agreement in 1959 , when it

2850-424: The mean radius ( R 1 ) of three radii measured at two equator points and a pole; the authalic radius , which is the radius of a sphere with the same surface area ( R 2 ); and the volumetric radius , which is the radius of a sphere having the same volume as the ellipsoid ( R 3 ). All three values are about 6,371 kilometres (3,959 mi). Other ways to define and measure the Earth's radius involve either

2945-616: The second fundamental form for a surface (Equation (123) in ): e, f, and g are elements of the shape tensor: n = N | N | {\displaystyle n={\frac {N}{|N|}}} is the unit normal to the surface at r {\displaystyle r} , and because ∂ r ∂ φ {\displaystyle {\frac {\partial r}{\partial \varphi }}} and ∂ r ∂ λ {\displaystyle {\frac {\partial r}{\partial \lambda }}} are tangents to

Nautical mile - Misplaced Pages Continue

3040-543: The " ban mile" ( banska milja ), had been the Austrian mile given above. The Ottoman mile was 1,894.35 m (1.17709 mi), which was equal to 5,000 Ottoman foot. After 1933, the Ottoman mile was replaced with the modern Turkish mile (1,853.181 m). The CJK Compatibility Unicode block contains square-format versions of Japanese names for measurement units as written in katakana script. Among them, there

3135-474: The 10th century, the nominal prototype physical standard of English length was an arm-length iron bar (a yardstick) held by the king at Winchester ; the foot was then one-third of its length. Henry I was said to have made a new standard in 1101 based on his own arm. Following the issuance of Magna Carta in 1215, the barons of Parliament directed John and his son to keep the king 's standard measure ( Mensura Domini Regis ) and weight at

3230-417: The Earth ⁠ 1 / q ⁠ ≈ 289 , which is close to the measured inverse flattening ⁠ 1 / f ⁠ ≈ 298.257 . Additionally, the bulge at the equator shows slow variations. The bulge had been decreasing, but since 1998 the bulge has increased, possibly due to redistribution of ocean mass via currents. The variation in density and crustal thickness causes gravity to vary across

3325-402: The Earth at that point" . It is also common to refer to any mean radius of a spherical model as "the radius of the earth" . When considering the Earth's real surface, on the other hand, it is uncommon to refer to a "radius", since there is generally no practical need. Rather, elevation above or below sea level is useful. Regardless of the model, any of these geocentric radii falls between

3420-557: The Earth. Gravitational attraction from the Moon or Sun can cause the Earth's surface at a given point to vary by tenths of a meter over a nearly 12-hour period (see Earth tide ). Given local and transient influences on surface height, the values defined below are based on a "general purpose" model, refined as globally precisely as possible within 5 m (16 ft) of reference ellipsoid height, and to within 100 m (330 ft) of mean sea level (neglecting geoid height). Additionally,

3515-686: The NAD27, is defined in metres. State Plane Coordinate Systems were then updated, but the National Geodetic Survey left individual states to decide which (if any) definition of the foot they would use. All State Plane Coordinate Systems are defined in metres, and 42 of the 50 states only use the metre-based State Plane Coordinate Systems. However, eight states also have State Plane Coordinate Systems defined in feet, seven of them in US survey feet and one in international feet. State legislation in

3610-460: The Roman computations of the mile as 5,000 feet, 1,000 paces , or 8 longer divisions, which they equated with their " furrow 's length" or furlong . The origins of English units are "extremely vague and uncertain", but seem to have been a combination of the Roman system with native British and Germanic systems both derived from multiples of the barleycorn . Probably by the reign of Edgar in

3705-538: The Roman mile is the milestone . All roads radiated out from the Roman Forum throughout the Empire – 50,000 (Roman) miles of stone-paved roads. At every mile was placed a shaped stone. Originally, these were obelisks made from granite, marble, or whatever local stone was available. On these was carved a Roman numeral , indicating the number of miles from the centre of Rome – the Forum. Hence, one can know how far one

3800-670: The Roman mile to fit an astronomical approximation of 1 arcminute of latitude measured directly north-and-south along a meridian . Although the precise value of the approximation remains disputed, it was somewhere between 1.8 and 2.0 km. The " old English mile " of the medieval and early modern periods varied but seems to have measured about 1.3  international miles (2.1 km). The old English mile varied over time and location within England. The old English mile has also been defined as 79,200 or 79,320 inches (1.25 or 1.2519 statute miles). The English long continued

3895-404: The UK or US. The modern English word mile derives from Middle English myle and Old English mīl , which was cognate with all other Germanic terms for miles . These derived from the nominal ellipsis form of mīlle passus 'mile' or mīlia passuum 'miles', the Roman mile of one thousand paces . The present international mile is usually what is understood by

Nautical mile - Misplaced Pages Continue

3990-506: The US State Plane Coordinate Systems (SPCSs), which can stretch over hundreds of miles, the accumulated difference can be significant, so it is important to note that the reference is to the US survey mile. The United States redefined its yard in 1893, and this resulted in US and Imperial measures of distance having very slightly different lengths. The North American Datum of 1983 (NAD83), which replaced

4085-562: The US Virgin Islands. The mile is even encountered in Canada, though this is predominantly in rail transport and horse racing, as the roadways have been metricated since 1977. Ireland gradually replaced miles with kilometres, including in speed measurements; the process was completed in 2005. The US survey mile is 5,280 US survey feet , or 1,609.347 metres and 0.30480061 metres respectively. Both are very slightly longer than

4180-451: The US is important for determining which conversion factor from the metric datum is to be used for land surveying and real estate transactions, even though the difference (2  ppm ) is hardly significant, given the precision of normal surveying measurements over short distances (usually much less than a mile). Twenty-four states have legislated that surveying measures be based on the US survey foot, eight have legislated that they be based on

4275-413: The US survey foot and US survey mile, as permitted by their 1959 decision, with effect on January 1, 2023. The nautical mile was originally defined as one minute of arc along a meridian of the Earth. Navigators use dividers to step off the distance between two points on the navigational chart, then place the open dividers against the minutes-of-latitude scale at the edge of the chart, and read off

4370-468: The US survey mile. Foreign and historical units translated into English as miles usually employ a qualifier to describe the kind of mile being used but this may be omitted if it is obvious from the context, such as a discussion of the 2nd-century Antonine Itinerary describing its distances in terms of miles rather than Roman miles . The mile has been variously abbreviated in English—with and without

4465-627: The definition of the foot in the Mendenhall Order of 1893, with 1 foot =  ⁠ 1200 / 3937 ⁠ (≈0.304800609601) metres and the definition was retained for data derived from NAD27, but renamed the US survey foot to distinguish it from the international foot. Thus a survey mile =  ⁠ 1200 / 3937 ⁠ × 5280 (≈1609.347218694) metres. An international mile = 1609.344 / ( ⁠ 1200 / 3937 ⁠ × 5280) (=0.999998) survey miles. The exact length of

4560-515: The discrepancy with latitude measurement to less than 2%). The metric system was introduced in the Netherlands in 1816, and the metric mile became a synonym for the kilometre, being exactly 1,000 m. Since 1870, the term mijl was replaced by the equivalent kilometer . Today, the word mijl is no longer used, except as part of certain proverbs and compound terms like mijlenver ("miles away"). The German mile ( Meile )

4655-502: The distance along a great circle was 60 miles per degree. However, these referred to the old English mile of 5000 feet and league of 15,000 feet, relying upon Ptolemy's underestimate of the Earth's circumference . In the early seventeenth century, English geographers started to acknowledge the discrepancy between the angular measurement of a degree of latitude and the linear measurement of miles. In 1624 Edmund Gunter suggested 352,000 feet to

4750-456: The distance in nautical miles. The Earth is not perfectly spherical but an oblate spheroid , so the length of a minute of latitude increases by 1% from the equator to the poles, as seen for example in the WGS84 ellipsoid , with 1,843 metres (6,046 ft) at the equator, 1,862 metres (6,108 ft) at the poles and average 1,852 metres (6,076 ft). Since 1929 the international nautical mile

4845-496: The ellipse and also coincide with minimum and maximum radius of curvature. There are two principal radii of curvature : along the meridional and prime-vertical normal sections . In particular, the Earth's meridional radius of curvature (in the north–south direction) at φ is: where e {\displaystyle e} is the eccentricity of the earth. This is the radius that Eratosthenes measured in his arc measurement . If one point had appeared due east of

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4940-478: The equator forms 500 stadia , which make 62 ⁠ 1 / 2 ⁠ miles"). Whether a correction or convenience, the reason for the change from 62 ⁠ 1 / 2 ⁠ to 60 miles to a degree is not explained. Eventually, the ratio of 60 miles to a degree appeared in English in a 1555 translation of Pietro Martire d'Anghiera 's Decades: "[Ptolemy] assigned likewise to every degree three score miles." By

5035-459: The equator is slightly shorter in the north–south direction than in the east–west direction. In summary, local variations in terrain prevent defining a single "precise" radius. One can only adopt an idealized model. Since the estimate by Eratosthenes , many models have been created. Historically, these models were based on regional topography, giving the best reference ellipsoid for the area under survey. As satellite remote sensing and especially

5130-557: The greater importance of furlongs in the Elizabethan-era England meant that the statute mile was made equivalent to 8 furlongs or 5,280 feet in 1593. This form of the mile then spread across the British Empire , some successor states of which continue to employ the mile. The US Geological Survey now employs the metre for official purposes, but legacy data from its 1927 geodetic datum has meant that

5225-671: The international foot, and eighteen have not specified which conversion factor to use. SPCS 83 legislation refers to state legislation that has been passed or updated using the newer 1983 NAD data. Most states have done so. Two states, Alaska and Missouri , and two jurisdictions, Guam and Puerto Rico , do not specify which foot to use. Two states, Alabama and Hawaii , and four jurisdictions, Washington, DC , US Virgin Islands , American Samoa and Northern Mariana Islands , do not have SPCS 83 legislation. In October 2019, US National Geodetic Survey and National Institute of Standards and Technology announced their joint intent to retire

5320-450: The international nautical mile was defined by the First International Extraordinary Hydrographic Conference in Monaco as exactly 1,852 metres (which is 6,076.12 ft). The United States did not adopt the international nautical mile until 1954. Britain adopted it in 1970, but legal references to the obsolete unit are now converted to 1,853 metres (which is 6,079.40 ft). The metre was originally defined as 1 ⁄ 10,000,000 of

5415-429: The land mile varied slightly among English-speaking countries until the international yard and pound agreement in 1959 established the yard as exactly 0.9144 metres, giving a mile of exactly 1,609.344 metres. The US adopted this international mile for most purposes, but retained the pre-1959 mile for some land-survey data, terming it the U. S. survey mile . In the United States, statute mile normally refers to

5510-623: The late 16th century English geographers and navigators knew that the ratio of distances at sea to degrees was constant along any great circle (such as the equator , or any meridian), assuming that Earth was a sphere. In 1574, William Bourne stated in A Regiment for the Sea the "rule to raise a degree" practised by navigators: "But as I take it, we in England should allowe 60 myles to one degrée: that is, after 3 miles to one of our Englishe leagues, wherefore 20 of oure English leagues shoulde answere to one degrée." Likewise, Robert Hues wrote in 1594 that

5605-412: The latitudes of the south of the UK. Other nations had different definitions of the nautical mile. The nautical mile per hour is known as the knot . Nautical miles and knots are almost universally used for aeronautical and maritime navigation, because of their relationship with degrees and minutes of latitude and the convenience of using the latitude scale on a map for distance measuring. The data mile

5700-554: The length of an ell was not standardised, so that the length of a mile could range between 3,280 m and 4,280 m. In the sixteenth, the Dutch had three different miles: small ( kleine ), medium ( middelbaar/gemeen ), and large ( groote ). The Dutch kleine mile had the historical definition of one hour's walking ( uur gaans ), which was defined as 24 stadia, 3000 paces, or 15,000 Amsterdam or Rhineland feet (respectively 4,250 m or 4,710 m). The common Dutch mile

5795-533: The length of the meridian arc from the North pole to the equator (1% of a centesimal degree of latitude), thus one kilometre of distance corresponds to one centigrad (also known as centesimal arc minute) of latitude. The Earth's circumference is therefore approximately 40,000 km. The equatorial circumference is slightly longer than the polar circumference – the measurement based on this ( ⁠ 40,075.017 km / 360 × 60 ⁠ = 1,855.3 metres)

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5890-517: The length of the rod by 1 ⁄ 11 would have amounted to a significant tax increase. Parliament instead opted to maintain the mile of 8 furlongs (which were derived from the rod) and to increase the number of feet per mile from the old Roman value. The applicable passage of the statute reads: "A Mile shall contain eight Furlongs, every Furlong forty Poles, and every Pole shall contain sixteen Foot and an half." The statute mile therefore contained 5,280 feet or 1,760 yards. The distance

5985-419: The mile was changed as with improved calculations of the circumference of the Earth. In 1617, Willebrord Snellius calculated a degree of the circumference of the Earth at 28,500 Rijnlantsche Roeden (within 3.5% of the actual value), which resulted in a Dutch mile of 1900 rods. By the mid-seventeenth century, map scales assigned 2000 rods to the common Dutch mile, which equalled around 7,535 m (reducing

6080-680: The most accepted equivalencies are 1,976  Imperial  yards (1.123 statute miles or 1.81 km). It was legally abolished three times: first by a 1685 act of the Scottish Parliament , again by the 1707 Treaty of Union with England, and finally by the Weights and Measures Act 1824 . It had continued in use as a customary unit through the 18th century but had become obsolete by its final abolition. The Irish mile ( míle or míle Gaelach ) measured 2,240 yards: approximately 1.27 statute miles or 2.048 kilometres. It

6175-412: The only solids to have radii, but broader uses of the term radius are common in many fields, including those dealing with models of Earth. The following is a partial list of models of Earth's surface, ordered from exact to more approximate: In the case of the geoid and ellipsoids, the fixed distance from any point on the model to the specified center is called "a radius of the Earth" or "the radius of

6270-400: The other, one finds the approximate curvature in the east–west direction. This Earth's prime-vertical radius of curvature , also called the Earth's transverse radius of curvature , is defined perpendicular ( orthogonal ) to M at geodetic latitude φ and is: N can also be interpreted geometrically as the normal distance from the ellipsoid surface to the polar axis. The radius of

6365-399: 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 most contexts and justifies the term "radius of the Earth". While specific values differ, the concepts in this article generalize to any major planet . Rotation of

6460-402: The poles and 1,843 metres at the Equator. France and other metric countries state that in principle a nautical mile is an arcminute of a meridian at a latitude of 45°, but that is a modern justification for a more mundane calculation that was developed a century earlier. By the mid-19th century, France had defined a nautical mile via the original 1791 definition of the metre , one ten-millionth of

6555-456: The position of an observable location, the use of more precise values for WGS-84 radii may not yield a corresponding improvement in accuracy . The value for the equatorial radius is defined to the nearest 0.1 m in WGS-84. The value for the polar radius in this section has been rounded to the nearest 0.1 m, which is expected to be adequate for most uses. Refer to the WGS-84 ellipsoid if

6650-638: The previous standards was 2  ppm , or about 3.2 millimetres ( 1 ⁄ 8  inch) per mile. The US standard was slightly longer and the old Imperial standards had been slightly shorter than the international mile. When the international mile was introduced in English-speaking countries, the basic geodetic datum in America was the North American Datum of 1927 (NAD27). This had been constructed by triangulation based on

6745-401: 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

6840-581: The roots of Equation (125) in: where in the first fundamental form for a surface (Equation (112) in ): E, F, and G are elements of the metric tensor : r = [ r 1 , r 2 , r 3 ] T = [ x , y , z ] T {\displaystyle r=[r^{1},r^{2},r^{3}]^{T}=[x,y,z]^{T}} , w 1 = φ {\displaystyle w^{1}=\varphi } , w 2 = λ , {\displaystyle w^{2}=\lambda ,} in

6935-401: The second fundamental form gives the distance from r + d r {\displaystyle r+dr} to the plane tangent at r {\displaystyle r} . The Earth's azimuthal radius of curvature , along an Earth normal section at an azimuth (measured clockwise from north) α and at latitude φ , is derived from Euler's curvature formula as follows: It

7030-450: The spheroid's radius of curvature or the actual topography . A few definitions yield values outside the range between the polar radius and equatorial radius because they account for localized effects. A nominal Earth radius (denoted R E N {\displaystyle {\mathcal {R}}_{\mathrm {E} }^{\mathrm {N} }} ) is sometimes used as a unit of measurement in astronomy and geophysics ,

7125-512: The surface and in time, so that the mean sea level differs from the ellipsoid. This difference is the geoid height , positive above or outside the ellipsoid, negative below or inside. The geoid height variation is under 110 m (360 ft) on Earth. The geoid height can change abruptly due to earthquakes (such as the Sumatra-Andaman earthquake ) or reduction in ice masses (such as Greenland ). Not all deformations originate within

7220-402: The surface, is normal to the surface at r {\displaystyle r} . With F = f = 0 {\displaystyle F=f=0} for an oblate spheroid, the curvatures are and the principal radii of curvature are The first and second radii of curvature correspond, respectively, to the Earth's meridional and prime-vertical radii of curvature. Geometrically,

7315-413: The survey mile, about 3.219 mm ( 1 ⁄ 8  inch) longer than the international mile (the international mile is exactly 0.0002% less than the US survey mile). While most countries abandoned the mile when switching to the metric system , the international mile continues to be used in some countries, such as Liberia , Myanmar , the United Kingdom and the United States. It is also used in

7410-443: The symbol for the metre, which may be displayed alongside feet and inches. The BBC style holds that "there is no acceptable abbreviation for 'miles ' " and so it should be spelled out when used in describing areas. The Roman mile ( mille passus , lit.  "thousand paces"; abbr.   m.p. ; also milia passuum and mille ) consisted of a thousand paces as measured by every other step—as in

7505-491: The term is sometimes used for a race of 1,600 metres (0.994 miles). The Scandinavian mile ( mil ) remains in common use in Norway and Sweden, where it has meant precisely 10 km since metrication in 1889. It is used in informal situations and in measurements of fuel consumption, which are often given as litres per mil . In formal situations (such as official road signs) only kilometres are given. The Swedish mile

7600-458: The total distance of the left foot hitting the ground 1,000 times. When Roman legionaries were well-fed and harshly driven in good weather, they thus created longer miles. The distance was indirectly standardised by Agrippa 's establishment of a standard Roman foot (Agrippa's own) in 29  BC , and the definition of a pace as 5 feet. An Imperial Roman mile thus denoted 5,000  Roman feet . Surveyors and specialised equipment such as

7695-432: The unqualified term mile . When this distance needs to be distinguished from the nautical mile, the international mile may also be described as a land mile or statute mile. In British English , statute mile may refer to the present international mile or to any other form of English mile since the 1593 Act of Parliament , which set it as a distance of 1,760 yards . Under American law , however, statute mile refers to

7790-608: The way, the standard Breslau mile was determined. The Saxon post mile ( kursächsische Postmeile or Polizeimeile , introduced on occasion of a survey of the Saxon roads in the 1700s, corresponded to 2,000 Dresden rods , equivalent to 9.062 kilometres. The Hungarian mile ( mérföld or magyar mérföld ) varied from 8.3790 km to 8.9374 km before being standardised as 8.3536 km. The Portuguese mile ( milha ) used in Portugal and Brazil

7885-605: The yard. As with the earlier statute mile , it continues to comprise 1,760 yards or 5,280 feet. The old Imperial value of the yard was used in converting measurements to metric values in India in a 1976 Act of the Indian Parliament. However, the current National Topographic Database of the Survey of India is based on the metric WGS-84 datum , which is also used by the Global Positioning System . The difference from

7980-494: Was 2.0873 km prior to metrication. The Russian mile ( миля or русская миля , russkaya milya ) was 7.468 km, divided into 7 versts . The Croatian mile ( hrvatska milja ), first devised by the Jesuit Stjepan Glavač on a 1673 map, is the length of an arc of the equator subtended by ⁠ 1 / 10 ⁠ ° or 11.13 km exactly. The previous Croatian mile, now known as

8075-687: Was 24,000 German feet. The standardised Austrian mile used in southern Germany and the Austrian Empire was 7.586 km; the Prussian mile used in northern Germany was 7.5325 km. Following its standardisation by Ole Rømer in the late 17th century, the Danish mile ( mil ) was precisely equal to the Prussian mile and likewise divided into 24,000 feet. These were sometimes treated as equivalent to 7.5 km. Earlier values had varied:

8170-410: Was 32 stadia, 4,000 paces, or 20,000 feet (5,660 m or 6,280 m). The large mile was defined as 5000 paces. The common Dutch mile was preferred by mariners, equating with 15 to one degree of latitude or one degree of longitude on the equator . This was originally based upon Ptolemy 's underestimate of the Earth's circumference. The ratio of 15 Dutch miles to a degree remained fixed while the length of

8265-474: Was established by a Weights and Measures Act of Parliament in 1593 during the reign of Queen Elizabeth I . The act on the Composition of Yards and Perches had shortened the length of the foot and its associated measures, causing the two methods of determining the mile to diverge. Owing to the importance of the surveyor's rod in deeds and surveying undertaken under Henry VIII , decreasing

8360-556: Was formally redefined with respect to SI units as exactly 1,609.344 metres . With qualifiers, mile is also used to describe or translate a wide range of units derived from or roughly equivalent to the Roman mile (roughly 1.48 km ), such as the nautical mile (now 1.852 km exactly), the Italian mile (roughly 1.852 km ), and the Chinese mile (now 500 m exactly). The Romans divided their mile into 5,000 pedēs ("feet") , but

8455-439: Was not uniformly adopted. Robert Morden had multiple scales on his 17th-century maps which included continuing local values: his map of Hampshire , for example, bore two different "miles" with a ratio of 1 : 1.23 and his map of Dorset had three scales with a ratio of 1 : 1.23 : 1.41 . In both cases, the traditional local units remained longer than the statute mile. The English statute mile

8550-400: Was revised with better estimates of the earth’s circumference. In 1637, Robert Norwood proposed a new measurement of 6120 feet for an arcminute of latitude, which was within 44 feet of the currently accepted value for a nautical mile. 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 1,862 metres at

8645-618: Was said to have been codified under Dyfnwal the Bald and Silent and retained unchanged by Hywel the Good . Along with other Welsh units, it was discontinued following the conquest of Wales by Edward I of England in the 13th century. The Scots mile was longer than the English mile, as mentioned by Robert Burns in the first verse of his poem " Tam o' Shanter ". It comprised 8 (Scots) furlongs divided into 320  falls or faws (Scots rods ). It varied from place to place but

8740-416: Was standardised as 36,000 Swedish feet or 10.6884 kilometres (6.6415 miles) in 1649; before that it varied by province from about 6 to 14.485 km. Authalic radius Earth radius (denoted as R 🜨 or R E ) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid (an oblate ellipsoid ), the radius ranges from

8835-443: Was superseded in 1959 by the international mile by international agreement. The Welsh  mile ( milltir or milldir ) was 3 statute miles and 1,470 yards long (6.17 km). It comprised 9,000  paces ( cam ), each of 3  Welsh feet ( troedfedd ) of 9 inches ( modfeddi ). (The Welsh inch is usually reckoned as equivalent to the English inch.) Along with other Welsh units , it

8930-593: Was used beside the native Greek units as equivalent to 8 stadia of 600 Greek feet . The mílion continued to be used as a Byzantine unit and was also used as the name of the zero mile marker for the Byzantine Empire , the Milion , located at the head of the Mese near Hagia Sophia . The Roman mile spread throughout Europe, with its local variations giving rise to the different units. Also arising from

9025-468: Was used in Ireland from the 16th century plantations until the 19th century, with residual use into the 20th century. The units were based on " English measure " but used a linear perch measuring 7 yards (6.4 m) as opposed to the English rod of 5.5 yards (5.0 m). The Dutch mile ( mijl ) has had different definitions throughout history. One of the older definitions was 5,600 ells . But

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