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58-559: The rocks of the Elkhorns were formed about 74 to 81 million years ago ( Late Cretaceous time) as a result of the Farallon tectonic plate subducting beneath western North America and allowing magma to rise to the surface. The Elkhorn Mountains Volcanics are extrusive rocks related to the plutonic granites of the Boulder Batholith . Volcanic flows, lahars , and ash falls from sources in

116-481: 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

174-587: A subalpine climate ( Köppen Dfc ). Late Cretaceous The Late Cretaceous (100.5–66 Ma ) is the younger of two epochs into which the Cretaceous Period is divided in the geologic time scale . Rock strata from this epoch form the Upper Cretaceous Series . The Cretaceous is named after creta , the Latin word for the white limestone known as chalk . The chalk of northern France and

232-560: 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

290-458: 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 the definitions of latitude and longitude. In

348-473: A noticeable impact; most notably the abandoned mining town of Elkhorn . Recently with efforts conducted by the BLM , Montana FWP and Helena National Forest , new conservation and wildlife management plans have been put into place including big horn sheep reintroduction and the westslope cutthroat trout restoration program. Management of the 2000+ elk herd in the area and the suppression of noxious weeds

406-443: 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

464-549: 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

522-679: A variety of enantiornithe and ornithurine forms. Early Neornithes such as Vegavis co-existed with forms as bizarre as Yungavolucris and Avisaurus . Though mostly small, marine Hesperornithes became relatively large and flightless, adapted to life in the open sea. Though primarily represented by azhdarchids , other forms like pteranodontids , tapejarids ( Caiuajara and Bakonydraco ), nyctosaurids and uncertain forms ( Piksi , Navajodactylus ) are also present. Historically, it has been assumed that pterosaurs were in decline due to competition with birds, but it appears that neither group overlapped significantly ecologically, nor

580-471: 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 the equator. Latitude and longitude are used together as a coordinate pair to specify

638-402: Is also an ongoing task. Despite the impacts of mining, around 100,000 acres of the Elkhorns were still roadless in 1992; this included 85,000 acres of roadless National Forest land as well as adjacent BLM, state and private lands. Congress designated 175,000 acres of the range as the "Elkhorns Wildlife Management Area," and one of Montana's most productive elk herds inhabits the range. Because

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696-411: 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

754-444: Is associated with a breccia pipe in the volcanics. The mountain range seen today is related to regional structural uplift dating mostly to Oligocene time. A forest fire in 1988 burned 47,000 acres (190 km²) of the mountain range, leaving carpets of seedlings growing into new lodgepole pine forests. The land has been used extensively in the past for gold and silver mining , logging , and open range grazing, leaving

812-484: 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

870-453: 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

928-474: Is it particularly evident that a true systematic decline was ever in place, especially with the discovery of smaller pterosaur species. Several old mammal groups began to disappear, with the last eutriconodonts occurring in the Campanian of North America . In the northern hemisphere, cimolodont , multituberculates , metatherians and eutherians were the dominant mammals, with the former two groups being

986-462: 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

1044-451: 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

1102-421: 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

1160-505: 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

1218-460: The Deccan Traps , both of which have been firmly dated to the time of the extinction event. In theory, these events reduced sunlight and hindered photosynthesis , leading to a massive disruption in Earth's ecology . A much smaller number of researchers believe the extinction was more gradual, resulting from slower changes in sea level or climate . Latitude In geography , latitude

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1276-590: The white cliffs of south-eastern England date from the Cretaceous Period. During the Late Cretaceous, the climate was warmer than present, although throughout the period a cooling trend is evident. The tropics became restricted to equatorial regions and northern latitudes experienced markedly more seasonal climatic conditions. Due to plate tectonics , the Americas were gradually moving westward, causing

1334-571: 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

1392-565: The Atlantic Ocean to expand. The Western Interior Seaway divided North America into eastern and western halves; Appalachia and Laramidia . India maintained a northward course towards Asia. In the Southern Hemisphere, Australia and Antarctica seem to have remained connected and began to drift away from Africa and South America. Europe was an island chain. Populating some of these islands were endemic dwarf dinosaur species. In

1450-813: The Cretaceous Period derived from the German name Kreidezeit , and T is the abbreviation for the Tertiary Period (a historical term for the period of time now covered by the Paleogene and Neogene periods). The event marks the end of the Mesozoic Era and the beginning of the Cenozoic Era. "Tertiary" being no longer recognized as a formal time or rock unit by the International Commission on Stratigraphy ,

1508-447: 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

1566-631: The Elkhorn Mountains reach as far as Choteau, Montana , but the thickest deposits lie within a radius of about 60 miles (97 km) from the Elkhorns. The volcanics probably originally covered an area of about 10,000 square miles (26,000 km). Mineral deposits associated with the Elkhorn Mountains Volcanics include those mined at Elkhorn, Montana , now a ghost town, and gold at the Golden Sunlight Mine near Whitehall , which

1624-512: The Elkhorns are higher in elevation than the nearby section of the Continental Divide , they catch more moisture than do most other ranges east of the Divide. For this reason, the Elkhorns are especially diverse, with 148 documented vertebrate species. Tizer Basin is a SNOTEL weather station situated by Big Tizer Creek near Bullock Hill (Montana) . 7,917 ft (2,413 m), Tizer Basin has

1682-847: The K-T event is now called the Cretaceous—Paleogene (or K-Pg) extinction event by many researchers. Non- avian dinosaur fossils are found only below the Cretaceous–Paleogene boundary and became extinct immediately before or during the event. A very small number of dinosaur fossils have been found above the Cretaceous–Paleogene boundary, but they have been explained as reworked fossils , that is, fossils that have been eroded from their original locations then preserved in later sedimentary layers. Mosasaurs , plesiosaurs , pterosaurs and many species of plants and invertebrates also became extinct. Mammalian and bird clades passed through

1740-643: The Late Cretaceous, the hadrosaurs , ankylosaurs , and ceratopsians experienced success in Asiamerica (Western North America and eastern Asia). Tyrannosaurs dominated the large predator niche in North America. They were also present in Asia, although were usually smaller and more primitive than the North American varieties. Pachycephalosaurs were also present in both North America and Asia. Dromaeosaurids shared

1798-664: 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

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1856-567: 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

1914-425: 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

1972-519: The boundary with few extinctions, and evolutionary radiation from those Maastrichtian clades occurred well past the boundary. Rates of extinction and radiation varied across different clades of organisms. Many scientists hypothesize that the Cretaceous–Paleogene extinctions were caused by catastrophic events such as the massive asteroid impact that caused the Chicxulub crater , in combination with increased volcanic activity , such as that recorded in

2030-572: 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

2088-408: 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

2146-402: 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 ) ,

2204-509: 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

2262-483: 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

2320-438: 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

2378-399: 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

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2436-451: 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

2494-538: 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

2552-636: The most common mammals in North America. In the southern hemisphere there was instead a more complex fauna of dryolestoids , gondwanatheres and other multituberculates and basal eutherians ; monotremes were presumably present, as was the last of the haramiyidans , Avashishta . Mammals, though generally small, ranged into a variety of ecological niches, from carnivores ( Deltatheroida ), to mollusc-eater ( Stagodontidae ), to herbivores (multituberculates, Schowalteria , Zhelestidae and Mesungulatidae ) to highly atypical cursorial forms ( Zalambdalestidae , Brandoniidae ). True placentals evolved only at

2610-531: The numerous teleost fishes, which in turn evolved into new advanced and modern forms ( Neoteleostei ). Ichthyosaurs and pliosaurs , on the other hand, became extinct during the Cenomanian-Turonian anoxic event . Near the end of the Cretaceous Period, flowering plants diversified. In temperate regions, familiar plants like magnolias , sassafras , roses , redwoods , and willows could be found in abundance. The Cretaceous–Paleogene extinction event

2668-458: 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

2726-503: 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

2784-466: 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

2842-417: 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

2900-495: The same geographical distribution, and are well documented in both Mongolia and Western North America. Additionally therizinosaurs (known previously as segnosaurs) appear to have been in North America and Asia. Gondwana held a very different dinosaurian fauna, with most predators being abelisaurids and carcharodontosaurids ; and titanosaurs being among the dominant herbivores. Spinosaurids were also present during this time. Birds became increasingly common, diversifying in

2958-515: 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

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3016-420: 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 )

3074-403: 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

3132-454: 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

3190-468: 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

3248-407: 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

3306-433: The very end of the epoch; the same can be said for true marsupials . Instead, nearly all known eutherian and metatherian fossils belong to other groups. In the seas, mosasaurs suddenly appeared and underwent a spectacular evolutionary radiation. Modern sharks also appeared and penguin-like polycotylid plesiosaurs (3 meters long) and huge long-necked elasmosaurs (13 meters long) also diversified. These predators fed on

3364-537: Was a large-scale mass extinction of animal and plant species in a geologically short period of time, approximately 66  million years ago (Ma). It is widely known as the K–T extinction event and is associated with a geological signature, usually a thin band dated to that time and found in various parts of the world, known as the Cretaceous–Paleogene boundary (K–T boundary). K is the traditional abbreviation for

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