Географічні координати: відмінності між версіями
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Геодезичні системи координат постійно змінюються. Це пов'язано як з уточненням та доповненням даних геодезичної основи, так і з створенням ''місцевих систем координат'', геодезичною основою яких є множина доступних опорних пунктів, розташованих на обмеженій території. Місцеві системи координат застосовуються при складанні детальних планів місцевості з найменшими спотвореннями дійсних відстаней, кутів та площ.
== Горизонтальні координати ==
=== Широта і довгота ===
{{Location map-line|lat=0|caption=Equator, the 0° parallel of latitude}}
{{Main|Latitude|Longitude}}
The «latitude» (abbreviation: Lat., [[φ]], or phi) of a point on Earth's surface is the angle between the equatorial plane and the straight line that passes through that point and through (or close to) the center of the Earth.<ref group=n>Alternative versions of latitude and longitude include geocentric coordinates, which measure with respect to Earth's center; geodetic coordinates, which model Earth as an [[еліпсоїд]]; and geographic coordinates, which measure with respect to a plumb line at the location for which coordinates are given.</ref> Lines joining points of the same latitude trace circles on the surface of Earth called [[паралель|parallels]], as they are parallel to the Equator and to each other. The [[Північний полюс]] is 90° N; the [[Південний полюс]] is 90° S. The 0° parallel of latitude is designated the [[Екватор]], the [[fundamental plane (spherical coordinates)|fundamental plane]] of all geographic coordinate systems. The Equator divides the globe into [[Північна півкуля|Northern]] and [[Південна півкуля]]s.
{{Location map-line|lon=0|caption=Prime Meridian, the 0° of longitude}}
The «longitude» (abbreviation: Long., [[λ]], or lambda) of a point on Earth's surface is the angle east or west of a reference [[меридіан|meridian]] to another meridian that passes through that point. All meridians are halves of great [[еліпс]]s (often called [[велике коло]]s), which converge at the North and South Poles. The meridian of the [[Велика Британія|British]] [[Гринвіцька королівська обсерваторія|Royal Observatory]] in [[Гринвіч|Greenwich]], in south-east London, England, is the international [[нульовий меридіан]], although some organizations—such as the French [[Institut Géographique National]]—continue to use other meridians for internal purposes. The prime meridian determines the proper [[Східна півкуля|Eastern]] and [[Західна півкуля]]s, although maps often divide these hemispheres further west in order to keep the [[Старий світ]] on a single side. The [[Антиподи|antipodal]] meridian of Greenwich is both 180°W and 180°E. This is not to be conflated with the [[Міжнародна лінія зміни дат]], which diverges from it in several places for political reasons, including between far eastern Russia and the far western [[Алеутські острови]].
The combination of these two components specifies the position of any location on the surface of Earth, without consideration of [[altitude]] or depth. The grid formed by lines of latitude and longitude is known as a «graticule».<ref>{{Cite book|url=https://books.google.co.uk/books?id=jPVxSDzVRP0C&pg=PA224&dq=graticule|title=Glossary of the Mapping Sciences|last=American Society of Civil Engineers|date=1994-01-01|publisher=ASCE Publications|isbn=9780784475706|language=en|page=224}}</ref> The origin/zero point of this system is located in the [[Гвінейська затока]] about {{convert|625|km|sp=us|abbr=on|sigfig=2}} south of [[Tema]], [[Гана]].
==== Length of a degree ====
{{main|Length of a degree of latitude|Length of a degree of longitude}}
{{unreferenced section|date=May 2015}}
On the GRS80 or [[Світова геодезична система]] spheroid at [[рівень моря]] at the Equator, one latitudinal second measures ''30.715 [[метр]]s'', one latitudinal minute is ''1843 metres'' and one latitudinal degree is ''110.6 kilometres''. The circles of longitude, meridians, meet at the geographical poles, with the west-east width of a second naturally decreasing as latitude increases. On the [[Екватор]] at sea level, one longitudinal second measures ''30.92 metres'', a longitudinal minute is ''1855 metres'' and a longitudinal degree is ''111.3 kilometres''. At 30° a longitudinal second is ''26.76 metres'', at Greenwich (51°28′38″N) ''19.22 metres'', and at 60° it is ''15.42 metres''.
On the WGS84 spheroid, the length in meters of a degree of latitude at latitude φ (that is, the distance along a north–south line from latitude (φ − 0.5) degrees to (φ + 0.5) degrees) is about
: <math>111132.92 - 559.82\, \cos 2\varphi + 1.175\, \cos 4\varphi - 0.0023\, \cos 6\varphi</math><ref name=GISS>[http://gis.stackexchange.com/questions/75528/length-of-a-degree-where-do-the-terms-in-this-formula-come-from] Geographic Information Systems — Stackexchange</ref>
Similarly, the length in meters of a degree of longitude can be calculated as
: <math>111412.84\, \cos \varphi - 93.5\, \cos 3\varphi + 0.118\, \cos 5\varphi</math><ref name=GISS/>
(Those coefficients can be improved, but as they stand the distance they give is correct within a centimeter.)
An alternative method to estimate the length of a longitudinal degree at latitude <math>\textstyle{\varphi}\,\!</math> is to assume a spherical Earth (to get the width per minute and second, divide by 60 and 3600, respectively):
: <math> \frac{\pi}{180}M_r\cos \varphi \!</math>
where [[Радіус Землі|Earth's average meridional radius]] <math>\textstyle{M_r}\,\!</math> is {{nowrap|6,367,449 m}}. Since the Earth is not spherical that result can be off by several tenths of a percent; a better approximation of a longitudinal degree at latitude <math>\textstyle{\varphi}\,\!</math> is
: <math>\frac{\pi}{180}a \cos \beta \,\!</math>
where Earth's equatorial radius <math>a</math> equals ''6,378,137 m'' and <math>\textstyle{\tan \beta = \frac{b}{a}\tan\varphi}\,\!</math>; for the GRS80 and WGS84 spheroids, b/a calculates to be 0.99664719. (<math>\textstyle{\beta}\,\!</math> is known as the [[Широта|reduced (or parametric) latitude]]). Aside from rounding, this is the exact distance along a parallel of latitude; getting the distance along the shortest route will be more work, but those two distances are always within 0.6 meter of each other if the two points are one degree of longitude apart.
{| class="wikitable"
|+ Longitudinal length equivalents at selected latitudes
|-
! style="width:100px;" | Latitude
! style="width:150px;" | City
! style="width:100px;" | Degree
! style="width:100px;" | Minute
! style="width:100px;" | Second
! style="width:100px;" | ±0.0001°
|-
| 60°
| [[Санкт-Петербург]]
| style="text-align:center;" | 55.80 km
| style="text-align:center;" | 0.930 km
| style="text-align:center;" | 15.50 m
| style="text-align:center;" | 5.58 m
|-
| 51° 28′ 38″ N
| [[Гринвіч]]
| style="text-align:center;" | 69.47 km
| style="text-align:center;" | 1.158 km
| style="text-align:center;" | 19.30 m
| style="text-align:center;" | 6.95 m
|-
| 45°
| [[Бордо]]
| style="text-align:center;" | 78.85 km
| style="text-align:center;" | 1.31 km
| style="text-align:center;" | 21.90 m
| style="text-align:center;" | 7.89 m
|-
| 30°
| [[Новий Орлеан]]
| style="text-align:center;" | 96.49 km
| style="text-align:center;" | 1.61 km
| style="text-align:center;" | 26.80 m
| style="text-align:center;" | 9.65 m
|-
| 0°
| [[Кіто]]
| style="text-align:center;" | 111.3 km
| style="text-align:center;" | 1.855 km
| style="text-align:center;" | 30.92 m
| style="text-align:center;" | 11.13 m
|}
<!--The Equator is the [[fundamental plane (spherical coordinates)|fundamental plane]] of all geographic coordinate systems. All spherical coordinate systems define such a fundamental plane.-->
=== Map projection ===
{{main|Map projection}}
To establish the position of a geographic location on a [[географічна карта]], a map projection is used to convert geodetic coordinates to plane coordinates on a map; it projects the datum ellipsoidal coordinates and height onto a flat surface of a map. The datum, along with a map projection applied to a grid of reference locations, establishes a ''grid system'' for plotting locations. Common map projections in current use include the [[Система координат UTM|Universal Transverse Mercator]] (UTM), the [[Military Grid Reference System]] (MGRS), the [[United States National Grid]] (USNG), the [[Global Area Reference System]] (GARS) and the [[World Geographic Reference System]] (GEOREF).<ref name=NGA_grids>{{cite web|title=Grids and Reference Systems|url=http://earth-info.nga.mil/GandG/coordsys/grids/referencesys.html|publisher=National Geospatial-Intelligence Agenc|accessdate=4 March 2014}}</ref>
Coordinates on a map are usually in terms [[northing]] N and [[easting]] E offsets relative to a specified origin.
Map projection formulas depend in the geometry of the projection as well as parameters dependent on the particular location at which the map is projected. The set of parameters can vary based on type of project and the conventions chosen for the projection. For the [[transverse Mercator projection]] used in UTM, the parameters associated are the latitude and longitude of the natural origin, the false northing and false easting, and an overall scale factor.<ref name=OGP7_2>{{cite web|title=Geomatics Guidance Note Number 7, part 2 Coordinate Conversions and Transformations including Formulas|url=http://info.ogp.org.uk/geodesy/guides/docs/G7-2.pdf|publisher=International Association of Oil and Gas Producers (OGP)|accessdate=5 March 2014|pages=9–10|deadurl=yes|archiveurl=https://web.archive.org/web/20140306005736/http://info.ogp.org.uk/geodesy/guides/docs/G7-2.pdf|archivedate=6 March 2014|df=dmy-all}}</ref> Given the parameters associated with particular location or grin, the projection formulas for the transverse Mercator are a complex mix of algebraic and trigonometric functions.{{r|OGP7_2|page1=45-54}}
==== UTM and UPS systems ====
{{Main|Universal Transverse Mercator|Universal Polar Stereographic}}
The [[Система координат UTM]] (UTM) and [[Universal Polar Stereographic]] (UPS) coordinate systems both use a metric-based cartesian grid laid out on a [[Map projection#Projections by preservation of a metric property|conformally projected]] surface to locate positions on the surface of the Earth. The UTM system is not a single [[картографічна проекція]] but a series of sixty, each covering 6-degree bands of longitude. The UPS system is used for the polar regions, which are not covered by the UTM system.
==== Stereographic coordinate system ====
{{further|Stereographic projection}}
During medieval times, the stereographic coordinate system was used for navigation purposes.{{Citation needed|date=December 2007}} The stereographic coordinate system was superseded by the latitude-longitude system. Although no longer used in navigation, the stereographic coordinate system is still used in modern times to describe crystallographic orientations in the fields of [[кристалографія]], [[мінералогія]] and materials science.{{Citation needed|date=December 2007}}
== Примітки ==
{{reflist}}
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