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53-546: The North Clearwater Mountains is the northernmost and shortest subrange. The subrange is 4,321 square miles (11,191 km) in area. Only two of its peaks — the 7,139-foot (2,176 m) Pot Mountain and the 7,077-foot (2,157 m) Black Mountain — rise above 7,000 feet (2,100 m). The Selway Crags lie between the North and South Clearwaters both in latitude and mean elevation. The Selway Crags encompass 885 square miles (2,292 km) and its two highest peaks are

106-481: 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

159-560: 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

212-619: A row of three stacks of chalk that rise about 30 metres (98 ft) out of the sea off the western extremity of the Isle of Wight in the English Channel, United Kingdom, close to Alum Bay and Scratchell's Bay , and part of Totland , the westernmost civil parish of the Isle of Wight. The Needles Lighthouse stands at the outer, western end of the formation. Built in 1859, it has been automated since 1994. The waters and adjoining seabed form part of

265-491: 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

318-549: 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

371-485: Is a stub . You can help Misplaced Pages by expanding it . Latitude In geography , latitude is a coordinate that specifies the north – south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at the south pole to 90° at the north pole, with 0° at the Equator . Lines of constant latitude , or parallels , run east–west as circles parallel to

424-411: 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

477-484: 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

530-453: 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

583-462: 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

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636-682: Is subject to some speculation. A drawing of The Needles by Dutch landscape artist Lambert Doomer (1624–1700), made in 1646, depicts a rock formation with much stouter shape than that shown in Isaac Taylor's 1759 "one inch" map of Hampshire. The Doomer etching is contained in Atlas Blaeu-Van der Hem (published ca. 1662), which is in the Austrian National Library in Vienna . It is not clear from this drawings what transpired and whether Doomer

689-451: 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

742-421: 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

795-505: 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

848-513: The BBC Two TV programme Seven Natural Wonders (2005) as one of the wonders of Southern England . During Storm Eunice on 18 February 2022, the highest recorded wind gust in England was provisionally recorded at The Needles, at 122 miles per hour (196 km/h). LB&SCR H2 class 4-4-2 no. 423 (later no. B423 and 2423) was named The Needles after this landmark. The Needles lie just to

901-571: 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

954-447: The 8,282-foot (2,524 m) Grave Peak and the 7,424-foot (2,263 m) McConnell Mountain. The South Clearwater Mountains is the southernmost and tallest subrange, with 6 peaks above 8,000 feet (2,400 m). The South Clearwaters encompass 3,292 square miles (8,526 km) and its two highest peaks are the 9,001-foot (2,744 m) Stripe Mountain and the 8,943-foot (2,726 m) Salmon Mountain. This Idaho location article

1007-505: The Battery along the cliff edge, using a road reserved for bus traffic. The Needles Breezer also has stops in Alum Bay , Totland , Colwell Bay , Fort Victoria , Yarmouth , and Freshwater Bay . Breezer buses are the only vehicles allowed on the road from Alum Bay, apart from those owned by National Trust staff or, by prior appointment, vehicles transporting disabled visitors. This is because

1060-447: 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

1113-539: The Island from Culver Cliff in the east to the Needles in the west, and then continues under the sea to the Isle of Purbeck , forming Ballard Cliff (near Swanage ), Lulworth Cove and Durdle Door . At Old Harry Rocks (east of Studland and north of Swanage ) these strata lines moving from horizontal to near vertical can be seen from the sea. The shape of the lost Lot's Wife stone column, recorded as collapsing in 1764,

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1166-540: The Needles Marine Conservation Zone and the Needles along with the shore and heath above are part of the Headon Warren and West High Down Site of Special Scientific Interest . The formation takes its name from a fourth needle-shaped pillar called Lot's wife , which collapsed in a storm in 1764. The remaining rocks are not at all needle-like, but the name has stuck. The Needles were featured on

1219-664: 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

1272-567: 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

1325-425: 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

1378-487: The beach. The Needles were a site of a long-standing artillery battery , from the 1860s to 1954, which was eventually decommissioned. A nearby site on High Down was employed in the testing of rockets for the British ICBM programme. The headland at High Down was used for Black Knight and Black Arrow rocket engine tests from 1956 to 1971. During the peak of activity in the early 1960s some 240 people worked at

1431-572: 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

1484-652: The complex, while the rockets were built in nearby East Cowes . These rockets were later used to launch the Prospero X-3 satellite. The site is now owned by the National Trust , and is open to the public. Concrete installations remain, but the buildings that were less durable have either been demolished or were torn down by the elements. In 1982, Prince Charles officially opened the restored Needles Old Battery facility. Underground rocket testing rooms are currently being restored for exhibition. The first phase of restoration

1537-408: 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

1590-529: The definitions of latitude and longitude. In the first step the physical surface is modeled by 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

1643-402: 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 ) ,

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1696-509: 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

1749-452: The equator. Latitude and longitude are used together as a coordinate pair to specify a location on the surface of the Earth. On its own, 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

1802-438: 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

1855-534: The four coastguard cottages owned by the National Trust . A branch of the National Coastwatch Institution is also based at the Needles, sited near the New Battery and Rocket Testing Site on High Down. The Needles – Landmark Attraction (previously known as The Needles Pleasure Park) situated at the top of the cliff at Alum Bay is a small amusement park. A chairlift operates between the park and

1908-399: 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

1961-451: 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

2014-538: 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

2067-494: 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: The Needles The Needles are

2120-458: 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

2173-503: 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

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2226-466: 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

2279-417: 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

2332-515: 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

2385-525: The single track road's position close to the cliff edge is considered dangerous for multiple car use. The Isle of Wight Coast Path has its westernmost point at the Coastguard Cottages. The Needles' pointed shape is a result of their unusual geology. The strata have been so heavily folded during the Alpine Orogeny that the chalk is near vertical. This chalk outcrop runs through the centre of

2438-429: The southwest of Alum Bay , and are a tourist draw. Scenic boat trips operate from Alum Bay that offer close-up views of the Needles. The rocks and lighthouse have become icons of the Isle of Wight , often photographed by visitors, and are featured on many of the souvenirs sold throughout the island. The main tourist attractions of the headland itself are the two gun batteries, the experimental rocket testing station, and

2491-420: 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 )

2544-403: 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

2597-454: 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

2650-468: 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

2703-407: 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

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2756-502: Was completed in 2004. The batteries are accessible by car, foot, bicycle, and bus. Though there is a paved road up to The Old and The New batteries, access is on foot, from a car park. The battery site becomes dangerous in high winds and is closed to the public in winds above force 8 . In the spring and summer, the Southern Vectis bus company sends open-top buses along a route called The Needles Breezer . This route approaches

2809-485: Was exercising artistic license . Doomer's painting shows three stacks when there should have been four, prior to the collapse of Lot's Wife . Just off the end of The Needles formation is the Shingles, a shifting shoal of pebbles just beneath the waves. The Shingles is approximately three miles in length. Many ships have been wrecked on the Shingles and three notable vessels on The Needles themselves: HMS Assurance in

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