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54-567: Between 57.3 and 59.5 latitude and 21.5 and 28.1 longitude , Estonia lies on the eastern coast of the Baltic Sea on the level northwestern part of the rising East European Platform . Estonia's continental mainland is bordered to the north by the Gulf of Finland (part of the Baltic Sea) across from Finland , to the east by Lake Peipus and Russia , and to the south by Latvia . Besides

108-484: A geographic coordinate system as defined in the specification of the ISO 19111 standard. Since there are many different reference ellipsoids , the precise latitude of a feature on the surface is not unique: this is stressed in the ISO standard which states that "without the full specification of the coordinate reference system, coordinates (that is latitude and longitude) are ambiguous at best and meaningless at worst". This

162-560: A 300-by-300-pixel sphere, so illustrations usually exaggerate the flattening. The graticule on the ellipsoid is constructed in exactly the same way as on the sphere. The normal at a point on the surface of an ellipsoid does not pass through the centre, except for points on the equator or at the poles, but the definition of latitude remains unchanged as the angle between the normal and the equatorial plane. The terminology for latitude must be made more precise by distinguishing: Geographic latitude must be used with care, as some authors use it as

216-591: A reservoir on the shore of the Gulf of Finland. This was said to have caused severe health problems among area residents. In the coastal town of Paldiski, the removal of waste left by Soviet army nuclear reactors was also a major concern. The combined cost of environmental cleanup at both towns was put at more than EEK3.5 billion. Natural hazards: flooding occurs frequently in the spring in certain areas Environment – current issues: air polluted with sulfur dioxide from oil-shale burning power plants in northeast; however,

270-495: A survey but, with the advent of GPS , it has become natural to use reference ellipsoids (such as WGS84 ) with centre at the centre of mass of the Earth and minor axis aligned to the rotation axis of the Earth. These geocentric ellipsoids are usually within 100 m (330 ft) of the geoid. Since latitude is defined with respect to an ellipsoid, the position of a given point is different on each ellipsoid: one cannot exactly specify

324-555: A synonym for geodetic latitude whilst others use it as an alternative to the astronomical latitude . "Latitude" (unqualified) should normally refer to the geodetic latitude. The importance of specifying the reference datum may be illustrated by a simple example. On the reference ellipsoid for WGS84, the centre of the Eiffel Tower has a geodetic latitude of 48° 51′ 29″ N, or 48.8583° N and longitude of 2° 17′ 40″ E or 2.2944°E. The same coordinates on

378-411: Is also used in the current literature. The parametric latitude is related to the geodetic latitude by: The alternative name arises from the parameterization of the equation of the ellipse describing a meridian section. In terms of Cartesian coordinates p , the distance from the minor axis, and z , the distance above the equatorial plane, the equation of the ellipse is: The Cartesian coordinates of

432-473: Is covered by about 18,000 km (6,950 sq mi) of forest. Arable land amounts to about 9,260 km (3,575 sq mi). Meadows cover about 2,520 km (973 sq mi), and pastureland covers about 1,810 km (699 sq mi). There are more than 1,400 natural and artificial lakes in Estonia. The largest of them, Lake Peipus (3,555 km or 1,373 sq mi), forms much of

486-484: Is determined by the shape of the ellipse which is rotated about its minor (shorter) axis. Two parameters are required. One is invariably the equatorial radius, which is the semi-major axis , a . The other parameter is usually (1) the polar radius or semi-minor axis , b ; or (2) the (first) flattening , f ; or (3) the eccentricity , e . These parameters are not independent: they are related by Many other parameters (see ellipse , ellipsoid ) appear in

540-453: Is determined with the meridian altitude method. More precise measurement of latitude requires an understanding of the gravitational field of the Earth, either to set up theodolites or to determine GPS satellite orbits. The study of the figure of the Earth together with its gravitational field is the science of geodesy . The graticule is formed by the lines of constant latitude and constant longitude, which are constructed with reference to

594-513: Is heaviest in late summer. Estonia's land border with Latvia runs 333 km (207 mi); the Russian border runs 324 km (201 mi). From 1920 to 1945, Estonia's border with Russia, set by the 1920 Tartu Peace Treaty , extended beyond the Narva river in the northeast and beyond the town of Petseri in the southeast. This territory, amounting to some 2,300 km (888 sq mi),

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648-466: Is of great importance in accurate applications, such as a Global Positioning System (GPS), but in common usage, where high accuracy is not required, the reference ellipsoid is not usually stated. In English texts, the latitude angle, defined below, is usually denoted by the Greek lower-case letter phi ( ϕ or φ ). It is measured in degrees , minutes and seconds or decimal degrees , north or south of

702-451: Is the angle between the equatorial plane and the normal to the surface at that point: the normal to the surface of the sphere is along the radial vector. The latitude, as defined in this way for the sphere, is often termed the spherical latitude, to avoid ambiguity with the geodetic latitude and the auxiliary latitudes defined in subsequent sections of this article. Besides the equator, four other parallels are of significance: The plane of

756-421: Is the meridional radius of curvature . The quarter meridian distance from the equator to the pole is For WGS84 this distance is 10 001 .965 729  km . The evaluation of the meridian distance integral is central to many studies in geodesy and map projection. It can be evaluated by expanding the integral by the binomial series and integrating term by term: see Meridian arc for details. The length of

810-456: Is widespread environmental pollution. The worst offender in this regard was the Soviet army. Across military installations covering more than 800 square kilometres (310 sq mi) of Estonian territory, the army dumped hundreds of thousands of tons of jet fuel into the ground, improperly disposed of toxic chemicals, and discarded outdated explosives and weapons in coastal and inland waters. In

864-522: The Philosophiæ Naturalis Principia Mathematica , in which he proved that a rotating self-gravitating fluid body in equilibrium takes the form of an oblate ellipsoid. (This article uses the term ellipsoid in preference to the older term spheroid .) Newton's result was confirmed by geodetic measurements in the 18th century. (See Meridian arc .) An oblate ellipsoid is the three-dimensional surface generated by

918-433: The geoid , a surface which approximates the mean sea level over the oceans and its continuation under the land masses. The second step is to approximate the geoid by a mathematically simpler reference surface. The simplest choice for the reference surface is a sphere , but the geoid is more accurately modeled by an ellipsoid of revolution . The definitions of latitude and longitude on such reference surfaces are detailed in

972-580: The zenith ). On map projections there is no universal rule as to how meridians and parallels should appear. The examples below show the named parallels (as red lines) on the commonly used Mercator projection and the Transverse Mercator projection . On the former the parallels are horizontal and the meridians are vertical, whereas on the latter there is no exact relationship of parallels and meridians with horizontal and vertical: both are complicated curves. \ In 1687 Isaac Newton published

1026-507: The 1990s, during the army's withdrawal from Estonia, extensive damage was done to discarded buildings and equipment. In October 1993, the Estonian Ministry of Environment issued a preliminary report summing up part of the degradation it had surveyed thus far. The report described the worst damage as having been done to Estonia's topsoil and underground water supply by the systematic dumping of jet fuel at six Soviet army air bases. At

1080-475: The Baltic Sea, with 1,520 islands dotting the shore. The two largest islands are Saaremaa (literally, island land), at 2,673 km (1,032 sq mi), and Hiiumaa, at 989 km (382 sq mi). The two islands are favorite Estonian vacation spots. The country's highest point, Suur Munamägi (Egg Mountain), is in the hilly southeast and reaches 318 m (1,043 ft) above sea level. Estonia

1134-450: The Earth's orbit about the Sun is called the ecliptic , and the plane perpendicular to the rotation axis of the Earth is the equatorial plane. The angle between the ecliptic and the equatorial plane is called variously the axial tilt, the obliquity, or the inclination of the ecliptic, and it is conventionally denoted by i . The latitude of the tropical circles is equal to i and the latitude of

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1188-672: The Iron Age inhabitants of the area. Estonia has a temperate climate, with four seasons of near-equal length. Average temperatures range from 16.3  °C (61.3  °F ) on the Baltic islands to 17.1 °C (62.8 °F) inland in July, the warmest month, and from −3.5 °C (25.7 °F) on the Baltic islands to −7.6 °C (18.3 °F) inland in February, the coldest month. Precipitation averages 568 mm (22.4 in) per year and

1242-1336: The Sea , Marine Dumping-London Protocol, Ozone Layer Protection, Ship Pollution, Tropical Timber 2006, Wetlands, Whaling Area: total: 45,228 square kilometres (17,463 sq mi) land: 42,338 square kilometres (16,347 sq mi) water: 2,840 square kilometres (1,100 sq mi) note: includes 1,520 islands in the Baltic Sea Land boundaries: total: 657 km (408 mi) border countries: Latvia 333 km (207 mi), Russia 324 km (201 mi) Coastline: 3,794 km (2,357 mi) Maritime claims: territorial sea: 12  nmi (22.2 km; 13.8 mi) exclusive economic zone : limits as agreed to by Estonia, Finland, Latvia, Sweden, and Russia Elevation extremes: lowest point: Baltic Sea 0 m highest point: Suur Munamägi 318 metres (1,043 ft) Natural resources: oil shale ( kukersite ), peat , rare earth elements , phosphorite , clay, limestone , sand , dolomite , arable land , sea mud Land use (2018 est.): Irrigated land: 40 km (15 sq mi) Total renewable water resources: 12.806 km (3.072 cu mi) (2017 est.) Latitude On its own,

1296-691: The Sun is overhead at some point of the Tropic of Capricorn . The south polar latitudes below the Antarctic Circle are in daylight, whilst the north polar latitudes above the Arctic Circle are in night. The situation is reversed at the June solstice, when the Sun is overhead at the Tropic of Cancer. Only at latitudes in between the two tropics is it possible for the Sun to be directly overhead (at

1350-571: The WGS84 spheroid is The variation of this distance with latitude (on WGS84 ) is shown in the table along with the length of a degree of longitude (east–west distance): A calculator for any latitude is provided by the U.S. Government's National Geospatial-Intelligence Agency (NGA). The following graph illustrates the variation of both a degree of latitude and a degree of longitude with latitude. There are six auxiliary latitudes that have applications to special problems in geodesy, geophysics and

1404-425: The air base near Tapa, site of the worst damage, officials estimated that 6 square kilometres (2.3 sq mi) of land were covered by a layer of fuel; 11 square kilometres (4.2 sq mi) of underground water were said to be contaminated. The water in the surrounding area was undrinkable, and was sometimes set fire by locals to provide heat during the winter. With Danish help, Estonian crews began cleaning up

1458-876: The amounts of pollutants emitted to the air have fallen dramatically and the pollution load of wastewater at purification plants has decreased substantially due to improved technology and environmental monitoring; Estonia has more than 1,400 natural and manmade lakes, the smaller of which in agricultural areas need to be monitored; coastal seawater is polluted in certain locations. Environment – international agreements: party to: Air Pollution, Air Pollution-Heavy Metals, Air Pollution-Nitrogen Oxides, Air Pollution-Persistent Organic Pollutants, Air Pollution-Sulphur 85, Air Pollution-Volatile Organic Compounds, Antarctic Treaty, Biodiversity , Climate Change, Climate Change- Kyoto Protocol , Climate Change- Paris Agreement , Comprehensive Nuclear Test Ban , Desertification , Endangered Species, Environmental Modification, Hazardous Wastes, Law of

1512-425: The angle subtended at the centre by the meridian arc from the equator to the point concerned. If the meridian distance is denoted by m ( ϕ ) then where R denotes the mean radius of the Earth. R is equal to 6,371 km or 3,959 miles. No higher accuracy is appropriate for R since higher-precision results necessitate an ellipsoid model. With this value for R the meridian length of 1 degree of latitude on

1566-457: The border between Estonia and Russia. Located in central Estonia, Võrtsjärv is the second-largest lake (270 km or 104 sq mi). The Narva and Emajõgi are among the most important of the country's many rivers. A small, recent cluster of meteorite craters, the largest of which is called Kaali are found on the Estonian island of Saaremaa . The impact may have been witnessed by

1620-638: The centre of the Earth and perpendicular to the rotation axis intersects the surface at a great circle called the Equator . Planes parallel to the equatorial plane intersect the surface in circles of constant latitude; these are the parallels. The Equator has a latitude of 0°, the North Pole has a latitude of 90° North (written 90° N or +90°), and the South Pole has a latitude of 90° South (written 90° S or −90°). The latitude of an arbitrary point

1674-408: The datum ED50 define a point on the ground which is 140 metres (460 feet) distant from the tower. A web search may produce several different values for the latitude of the tower; the reference ellipsoid is rarely specified. The length of a degree of latitude depends on the figure of the Earth assumed. On the sphere the normal passes through the centre and the latitude ( ϕ ) is therefore equal to

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1728-402: The ellipsoid to that point Q on the surrounding sphere (of radius a ) which is the projection parallel to the Earth's axis of a point P on the ellipsoid at latitude ϕ . It was introduced by Legendre and Bessel who solved problems for geodesics on the ellipsoid by transforming them to an equivalent problem for spherical geodesics by using this smaller latitude. Bessel's notation, u ( ϕ ) ,

1782-517: The equator. For navigational purposes positions are given in degrees and decimal minutes. For instance, The Needles lighthouse is at 50°39.734′ N 001°35.500′ W. This article relates to coordinate systems for the Earth: it may be adapted to cover the Moon, planets and other celestial objects ( planetographic latitude ). For a brief history, see History of latitude . In celestial navigation , latitude

1836-438: The following sections. Lines of constant latitude and longitude together constitute a graticule on the reference surface. The latitude of a point on the actual surface is that of the corresponding point on the reference surface, the correspondence being along the normal to the reference surface, which passes through the point on the physical surface. Latitude and longitude together with some specification of height constitute

1890-399: The geocentric latitude ( θ ) and the geodetic latitude ( ϕ ) is: For points not on the surface of the ellipsoid, the relationship involves additionally the ellipsoidal height h : where N is the prime vertical radius of curvature. The geodetic and geocentric latitudes are equal at the equator and at the poles but at other latitudes they differ by a few minutes of arc. Taking the value of

1944-424: The land, play key economic roles in this generally resource-poor country. Estonia boasts over 1,500 lakes , numerous bogs , and 3,794 kilometers of coastline marked by numerous bays, straits, and inlets. {{{annotations}}} Estonia is a flat country covering 45,339 km (17,505 sq mi), of which internal waters comprise 4.6%. Estonia has a long, shallow coastline (3,794 km or 2,357 mi) along

1998-451: The latitude and longitude of a geographical feature without specifying the ellipsoid used. Many maps maintained by national agencies are based on older ellipsoids, so one must know how the latitude and longitude values are transformed from one ellipsoid to another. GPS handsets include software to carry out datum transformations which link WGS84 to the local reference ellipsoid with its associated grid. The shape of an ellipsoid of revolution

2052-538: The meridian arc between two given latitudes is given by replacing the limits of the integral by the latitudes concerned. The length of a small meridian arc is given by When the latitude difference is 1 degree, corresponding to ⁠ π / 180 ⁠ radians, the arc distance is about The distance in metres (correct to 0.01 metre) between latitudes ϕ {\displaystyle \phi }  − 0.5 degrees and ϕ {\displaystyle \phi }  + 0.5 degrees on

2106-512: The part of the European continent, Estonian territory also includes the larger islands of Saaremaa and Hiiumaa , and over 2,200 other islands and islets in the Baltic Sea, off the western and northern shores of the country's mainland. Average elevation in Estonia reaches 50 m (164 ft). The climate is maritime, wet, with moderate winters and cool summers. Oil shale and limestone deposits, along with forests which cover 47% of

2160-523: The point are parameterized by Cayley suggested the term parametric latitude because of the form of these equations. The parametric latitude is not used in the theory of map projections. Its most important application is in the theory of ellipsoid geodesics, ( Vincenty , Karney ). The rectifying latitude , μ , is the meridian distance scaled so that its value at the poles is equal to 90 degrees or ⁠ π / 2 ⁠ radians: Estonian kroon Too Many Requests If you report this error to

2214-463: The polar circles is its complement (90° - i ). The axis of rotation varies slowly over time and the values given here are those for the current epoch . The time variation is discussed more fully in the article on axial tilt . The figure shows the geometry of a cross-section of the plane perpendicular to the ecliptic and through the centres of the Earth and the Sun at the December solstice when

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2268-509: The reference ellipsoid to the plane or in calculations of geodesics on the ellipsoid. Their numerical values are not of interest. For example, no one would need to calculate the authalic latitude of the Eiffel Tower. The expressions below give the auxiliary latitudes in terms of the geodetic latitude, the semi-major axis, a , and the eccentricity, e . (For inverses see below .) The forms given are, apart from notational variants, those in

2322-473: The rotation axis of the Earth. The primary reference points are the poles where the axis of rotation of the Earth intersects the reference surface. Planes which contain the rotation axis intersect the surface at the meridians ; and the angle between any one meridian plane and that through Greenwich (the Prime Meridian ) defines the longitude: meridians are lines of constant longitude. The plane through

2376-417: The rotation of an ellipse about its shorter axis (minor axis). "Oblate ellipsoid of revolution" is abbreviated to 'ellipsoid' in the remainder of this article. (Ellipsoids which do not have an axis of symmetry are termed triaxial .) Many different reference ellipsoids have been used in the history of geodesy . In pre-satellite days they were devised to give a good fit to the geoid over the limited area of

2430-519: The semi-major axis and the inverse flattening, ⁠ 1 / f ⁠ . For example, the defining values for the WGS84 ellipsoid, used by all GPS devices, are from which are derived The difference between the semi-major and semi-minor axes is about 21 km (13 miles) and as fraction of the semi-major axis it equals the flattening; on a computer monitor the ellipsoid could be sized as 300 by 299 pixels. This would barely be distinguishable from

2484-666: The site, although they estimated the likely cost to be as much as 4 million EEK . The Ministry of Environment assigned a monetary cost of more than 10 billion EEK to the damage to the country's topsoil and water supply. However, the ministry was able to allocate only 5 million EEK in 1993 for cleanup operations. In a 1992 government report to the United Nations Conference on the Environment and Development, Estonia detailed other major environmental concerns. For instance, for several consecutive years Estonia had led

2538-420: The sphere is 111.2 km (69.1 statute miles) (60.0 nautical miles). The length of one minute of latitude is 1.853 km (1.151 statute miles) (1.00 nautical miles), while the length of 1 second of latitude is 30.8 m or 101 feet (see nautical mile ). In Meridian arc and standard texts it is shown that the distance along a meridian from latitude ϕ to the equator is given by ( ϕ in radians) where M ( ϕ )

2592-403: The squared eccentricity as 0.0067 (it depends on the choice of ellipsoid) the maximum difference of ϕ − θ {\displaystyle \phi {-}\theta } may be shown to be about 11.5 minutes of arc at a geodetic latitude of approximately 45° 6′. The parametric latitude or reduced latitude , β , is defined by the radius drawn from the centre of

2646-458: The standard reference for map projections, namely "Map projections: a working manual" by J. P. Snyder. Derivations of these expressions may be found in Adams and online publications by Osborne and Rapp. The geocentric latitude is the angle between the equatorial plane and the radius from the centre to a point of interest. When the point is on the surface of the ellipsoid, the relation between

2700-472: The study of geodesy, geophysics and map projections but they can all be expressed in terms of one or two members of the set a , b , f and e . Both f and e are small and often appear in series expansions in calculations; they are of the order ⁠ 1 / 298 ⁠ and 0.0818 respectively. Values for a number of ellipsoids are given in Figure of the Earth . Reference ellipsoids are usually defined by

2754-406: The term "latitude" normally refers to the geodetic latitude as defined below. Briefly, the geodetic latitude of a point is the angle formed between the vector perpendicular (or normal ) to the ellipsoidal surface from the point, and the plane of the equator . Two levels of abstraction are employed in the definitions of latitude and longitude. In the first step the physical surface is modeled by

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2808-407: The theory of map projections: The definitions given in this section all relate to locations on the reference ellipsoid but the first two auxiliary latitudes, like the geodetic latitude, can be extended to define a three-dimensional geographic coordinate system as discussed below . The remaining latitudes are not used in this way; they are used only as intermediate constructs in map projections of

2862-460: The world in the production of sulfur dioxide per capita. Nearly 75% of Estonia's air pollution was reported to come from two oil shale-based thermal power stations operating near Narva . The mining of oil shale in northeastern Estonia has also left large mounds of limestone tailings dotting the region. Near the town of Sillamäe , site of a former uranium enrichment plant, about 1,200 tons of uranium and about 750 tons of thorium had been dumped into

2916-422: Was transferred to Soviet Russia at the end of World War II . There live 65 different species of mammals in the Estonian forests. There are an estimated 700 brown bears, over 150 wolves, 400 lynxes, 14,000–16,000 beavers, 3,400 wild boars, 10,000–11,000 moose and 120,000–130,000 deer. There are also red deer and other wild animals. One of the most burdensome legacies of the 1944–1991 Soviet occupation of Estonia

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