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47-398: An observer standing on Earth's equator visualizes the celestial equator as a semicircle passing through the zenith , the point directly overhead. As the observer moves north (or south), the celestial equator tilts towards the opposite horizon . The celestial equator is defined to be infinitely distant (since it is on the celestial sphere); thus, the ends of the semicircle always intersect

94-525: A plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space . When working exclusively in two-dimensional Euclidean space , the definite article is used, so the Euclidean plane refers to the whole space. Several notions of a plane may be defined. The Euclidean plane follows Euclidean geometry , and in particular

141-546: A sphere flattened 0.336% along its axis. This makes the Equator 0.16% longer than a meridian (a great circle passing through the two poles). The IUGG standard meridian is, to the nearest millimetre, 40,007.862917 kilometres (24,859.733480 mi), one arc-minute of which is 1,852.216 metres (6,076.82 ft), explaining the SI standardization of the nautical mile as 1,852 metres (6,076 ft), more than 3 metres (9.8 ft) less than

188-496: A 12-hour day and 12-hour night. The name is derived from medieval Latin word aequator , in the phrase circulus aequator diei et noctis , meaning 'circle equalizing day and night', from the Latin word aequare 'make equal'. The latitude of the Earth's equator is, by definition, 0° (zero degrees ) of arc. The equator is one of the five notable circles of latitude on Earth;

235-441: A plane OL which intersects the hemisphere in half of a great circle . The hemisphere is bounded by a plane through O and parallel to σ. No ordinary line of σ corresponds to this plane; instead a line at infinity is appended to σ . As any line in this extension of σ corresponds to a plane through O , and since any pair of such planes intersects in a line through O , one can conclude that any pair of lines in

282-418: A plane as a 2-dimensional real manifold , a topological plane which is provided with a differential structure . Again in this case, there is no notion of distance, but there is now a concept of smoothness of maps, for example a differentiable or smooth path (depending on the type of differential structure applied). The isomorphisms in this case are bijections with the chosen degree of differentiability. In

329-403: A single point, but there are some pairs of lines (namely, parallel lines) that do not intersect. A projective plane can be thought of as an ordinary plane equipped with additional "points at infinity" where parallel lines intersect. Thus any two distinct lines in a projective plane intersect at exactly one point. Renaissance artists, in developing the techniques of drawing in perspective , laid

376-408: A two-dimensional or planar space. In mathematics , a Euclidean plane is a Euclidean space of dimension two , denoted E 2 {\displaystyle {\textbf {E}}^{2}} or E 2 {\displaystyle \mathbb {E} ^{2}} . It is a geometric space in which two real numbers are required to determine the position of each point . It

423-539: Is a circle of latitude that divides a spheroid , such as Earth , into the Northern and Southern hemispheres . On Earth, the Equator is an imaginary line located at 0 degrees latitude , about 40,075 km (24,901 mi) in circumference, halfway between the North and South poles. The term can also be used for any other celestial body that is roughly spherical. In spatial (3D) geometry , as applied in astronomy ,

470-580: Is an affine space , which includes in particular the concept of parallel lines . It has also metrical properties induced by a distance , which allows to define circles , and angle measurement . A Euclidean plane with a chosen Cartesian coordinate system is called a Cartesian plane . In Euclidean geometry , a plane is a flat two- dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space R 3 {\displaystyle \mathbb {R} ^{3}} . A prototypical example

517-421: Is defined as one arc-minute of the Equator, so it has different values depending on which radius is assumed. For example, by WSG-84, the distance is 1,855.3248 metres (6,087.024 ft), while by IAU-2000, it is 1,855.3257 metres (6,087.027 ft). This is a difference of less than one millimetre (0.039 in) over the total distance (approximately 1.86 kilometres or 1.16 miles). Earth is commonly modeled as

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564-489: Is not the only geometry that the plane may have. The plane may be given a spherical geometry by using the stereographic projection . This can be thought of as placing a sphere tangent to the plane (just like a ball on the floor), removing the top point, and projecting the sphere onto the plane from this point. This is one of the projections that may be used in making a flat map of part of the Earth's surface. The resulting geometry has constant positive curvature. Alternatively,

611-429: Is one of a room's walls, infinitely extended and assumed infinitesimal thin. The elliptic plane is the real projective plane provided with a metric . Kepler and Desargues used the gnomonic projection to relate a plane σ to points on a hemisphere tangent to it. With O the center of the hemisphere, a point P in σ determines a line OP intersecting the hemisphere, and any line L ⊂ σ determines

658-429: Is tilted towards or away from the sun, resulting in either summer or winter in both hemispheres. This also results in a corresponding movement of the equator away from the subsolar point, which is then situated over or near the relevant tropic circle . Nevertheless, temperatures are high year-round due to the Earth's axial tilt of 23.5° not being enough to create a low minimum midday declination to sufficiently weaken

705-554: The Apollo Moon landings . The precise location of the Equator is not truly fixed; the true equatorial plane is perpendicular to the Earth's rotation axis , which drifts about 9 metres (30 ft) during a year. Geological samples show that the Equator significantly changed positions between 48 and 12 million years ago, as sediment deposited by ocean thermal currents at the Equator shifted. The deposits by thermal currents are determined by

752-511: The celestial equator . In the cycle of Earth's seasons , the equatorial plane runs through the Sun twice a year : on the equinoxes in March and September . To a person on Earth, the Sun appears to travel along the equator (or along the celestial equator) at these times. Locations on the equator experience the shortest sunrises and sunsets because the Sun's daily path is nearly perpendicular to

799-461: The complex projective plane , and finite, such as the Fano plane . In addition to its familiar geometric structure, with isomorphisms that are isometries with respect to the usual inner product, the plane may be viewed at various other levels of abstraction . Each level of abstraction corresponds to a specific category . At one extreme, all geometrical and metric concepts may be dropped to leave

846-532: The geographical mile . The sea-level surface of Earth (the geoid ) is irregular, so the actual length of the Equator is not so easy to determine. Aviation Week and Space Technology on 9 October 1961 reported that measurements using the Transit IV-A satellite had shown the equatorial diameter from longitude 11° West to 169° East to be 1,000 feet (305 m) greater than its diameter ninety degrees away. Download coordinates as: The Equator passes through

893-424: The horizon for most of the year. The length of daylight (sunrise to sunset) is almost constant throughout the year; it is about 14 minutes longer than nighttime due to atmospheric refraction and the fact that sunrise begins (or sunset ends) as the upper limb, not the center, of the Sun's disk contacts the horizon. Earth bulges slightly at the Equator; its average diameter is 12,742 km (7,918 mi), but

940-467: The parallel postulate . A projective plane may be constructed by adding "points at infinity" where two otherwise parallel lines would intersect, so that every pair of lines intersects in exactly one point. The elliptic plane may be further defined by adding a metric to the real projective plane. One may also conceive of a hyperbolic plane , which obeys hyperbolic geometry and has a negative curvature . Abstractly, one may forget all structure except

987-457: The topological plane, which may be thought of as an idealized homotopically trivial infinite rubber sheet, which retains a notion of proximity, but has no distances. The topological plane has a concept of a linear path, but no concept of a straight line. The topological plane, or its equivalent the open disc, is the basic topological neighborhood used to construct surfaces (or 2-manifolds) classified in low-dimensional topology . Isomorphisms of

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1034-444: The Equator (on Earth), noontime sunlight appears almost directly overhead (no more than about 23° from the zenith ) every day, year-round. Consequently, the Equator has a rather stable daytime temperature throughout the year. On the equinoxes (approximately March 20 and September 23) the subsolar point crosses Earth's equator at a shallow angle, sunlight shines perpendicular to Earth's axis of rotation, and all latitudes have nearly

1081-549: The Equator. However, its island of Annobón is 155 km (96 mi) south of the Equator, and the rest of the country lies to the north. France , Norway ( Bouvet Island ), and the United Kingdom are the other three Northern Hemisphere -based countries which have territories in the Southern Hemisphere . Seasons result from the tilt of Earth's axis away from a line perpendicular to the plane of its revolution around

1128-514: The IUGG at its Canberra, Australia meeting of 1979 has an equatorial radius of 6,378.137 km (3,963.191 mi). The WGS 84 (World Geodetic System 1984) which is a standard for use in cartography, geodesy, and satellite navigation including GPS , also has an equatorial radius of 6,378.137 km (3,963.191 mi). For both GRS 80 and WGS 84, this results in a length for the Equator of 40,075.0167 km (24,901.4609 mi). The geographical mile

1175-671: The International Astronomical Union (IAU) use an equatorial radius of 6,378.1366 km (3,963.1903 mi) (codified as the IAU 2009 value). This equatorial radius is also in the 2003 and 2010 IERS Conventions. It is also the equatorial radius used for the IERS 2003 ellipsoid. If it were really circular, the length of the equator would then be exactly 2π times the radius, namely 40,075.0142 km (24,901.4594 mi). The GRS 80 (Geodetic Reference System 1980) as approved and adopted by

1222-513: The Sun's rays even during the solstices. High year-round temperatures extend to about 25° north or south of the equator, although the moderate seasonal temperature difference is defined by the opposing solstices (as it is at higher latitudes) near the poleward limits of this range. Near the equator, there is little temperature change throughout the year, though there may be dramatic differences in rainfall and humidity. The terms summer, autumn, winter and spring do not generally apply. Lowlands around

1269-540: The Sun. Throughout the year, the Northern and Southern hemispheres are alternately turned either toward or away from the Sun, depending on Earth's position in its orbit. The hemisphere turned toward the Sun receives more sunlight and is in summer, while the other hemisphere receives less sun and is in winter (see solstice ). At the equinoxes , Earth's axis is perpendicular to the Sun rather than tilted toward or away, meaning that day and night are both about 12 hours long across

1316-473: The afternoon and 23 °C (73 °F) around sunrise. Rainfall is very high away from cold ocean current upwelling zones, from 2,500 to 3,500 mm (100 to 140 in) per year. There are about 200 rainy days per year and average annual sunshine hours are around 2,000. Despite high year-round sea level temperatures, some higher altitudes such as the Andes and Mount Kilimanjaro have glaciers. The highest point on

1363-601: The axis of Earth, which determines solar coverage of Earth's surface . Changes in Earth's axis can also be observed in the geographical layout of volcanic island chains, which are created by shifting hot spots under Earth's crust as the axis and crust move. This is consistent with the Indian tectonic plate colliding with the Eurasian tectonic plate , which is causing the Himalayan uplift. The International Association of Geodesy (IAG) and

1410-510: The complex numbers) complex manifold , sometimes called the complex line . However, this viewpoint contrasts sharply with the case of the plane as a 2-dimensional real manifold. The isomorphisms are all conformal bijections of the complex plane, but the only possibilities are maps that correspond to the composition of a multiplication by a complex number and a translation. In addition, the Euclidean geometry (which has zero curvature everywhere)

1457-636: The diameter at the equator is about 43 km (27 mi) greater than at the poles. Sites near the Equator, such as the Guiana Space Centre in Kourou , French Guiana , are good locations for spaceports as they have the fastest rotational speed of any latitude, 460 m (1,509 ft)/sec. The added velocity reduces the fuel needed to launch spacecraft eastward (in the direction of Earth's rotation) to orbit, while simultaneously avoiding costly maneuvers to flatten inclination during missions such as

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1504-621: The equator generally have a tropical rainforest climate , also known as an equatorial climate, though cold ocean currents cause some regions to have tropical monsoon climates with a dry season in the middle of the year, and the Somali Current generated by the Asian monsoon due to continental heating via the high Tibetan Plateau causes Greater Somalia to have an arid climate despite its equatorial location. Average annual temperatures in equatorial lowlands are around 31 °C (88 °F) during

1551-468: The equator is at the elevation of 4,690 metres (15,387 ft), at 0°0′0″N 77°59′31″W  /  0.00000°N 77.99194°W  / 0.00000; -77.99194  ( highest point on the equator ) , found on the southern slopes of Volcán Cayambe [summit 5,790 metres (18,996 ft)] in Ecuador . This is slightly above the snow line and is the only place on the equator where snow lies on

1598-431: The equator of a rotating spheroid (such as a planet ) is the parallel (circle of latitude) at which latitude is defined to be 0°. It is an imaginary line on the spheroid, equidistant from its poles , dividing it into northern and southern hemispheres. In other words, it is the intersection of the spheroid with the plane perpendicular to its axis of rotation and midway between its geographical poles . On and near

1645-401: The extension intersect: the point of intersection lies where the plane intersection meets σ or the line at infinity. Thus the axiom of projective geometry, requiring all pairs of lines in a plane to intersect, is confirmed. In mathematics , a projective plane is a geometric structure that extends the concept of a plane . In the ordinary Euclidean plane, two lines typically intersect at

1692-740: The ground. At the equator, the snow line is around 1,000 metres (3,300 ft) lower than on Mount Everest and as much as 2,000 metres (6,600 ft) lower than the highest snow line in the world, near the Tropic of Capricorn on Llullaillaco . There is a widespread maritime tradition of holding ceremonies to mark a sailor's first crossing of the equator. In the past, these ceremonies have been notorious for their brutality, especially in naval practice. Milder line-crossing ceremonies, typically featuring King Neptune , are also held for passengers' entertainment on some civilian ocean liners and cruise ships. Plane (mathematics) In mathematics ,

1739-419: The groundwork for this mathematical topic. The archetypical example is the real projective plane , also known as the extended Euclidean plane. This example, in slightly different guises, is important in algebraic geometry , topology and projective geometry where it may be denoted variously by PG(2, R) , RP , or P 2 (R), among other notations. There are many other projective planes, both infinite, such as

1786-432: The horizon due east and due west, regardless of the observer's position on Earth. At the poles , the celestial equator coincides with the astronomical horizon. At all latitudes , the celestial equator is a uniform arc or circle because the observer is only finitely far from the plane of the celestial equator, but infinitely far from the celestial equator itself. Astronomical objects near the celestial equator appear above

1833-519: The horizon from most places on earth, but they culminate (reach the meridian) highest near the equator. The celestial equator currently passes through these constellations : These are the most globally visible constellations. Over thousands of years, the orientation of Earth's equator and thus the constellations the celestial equator passes through will change due to axial precession . Celestial bodies other than Earth also have similarly defined celestial equators. Equator The equator

1880-611: The land of eleven sovereign states . Indonesia is the country straddling the greatest length of the equatorial line across both land and sea. Starting at the Prime Meridian and heading eastwards, the Equator passes through: The Equator also passes through the territorial seas of three countries: Maldives (south of Gaafu Dhaalu Atoll ), Kiribati (south of Buariki Island ), and the United States (south of Baker Island ). Despite its name, no part of Equatorial Guinea lies on

1927-431: The opposite direction of abstraction, we may apply a compatible field structure to the geometric plane, giving rise to the complex plane and the major area of complex analysis . The complex field has only two isomorphisms that leave the real line fixed, the identity and conjugation . In the same way as in the real case, the plane may also be viewed as the simplest, one-dimensional (in terms of complex dimension , over

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1974-519: The other four are the two polar circles (the Arctic Circle and the Antarctic Circle ) and the two tropical circles (the Tropic of Cancer and the Tropic of Capricorn ). The equator is the only line of latitude which is also a great circle —meaning, one whose plane passes through the center of the globe. The plane of Earth's equator, when projected outwards to the celestial sphere , defines

2021-410: The plane can also be given a metric which gives it constant negative curvature giving the hyperbolic plane . The latter possibility finds an application in the theory of special relativity in the simplified case where there are two spatial dimensions and one time dimension. (The hyperbolic plane is a timelike hypersurface in three-dimensional Minkowski space .) The one-point compactification of

2068-468: The plane is homeomorphic to a sphere (see stereographic projection ); the open disk is homeomorphic to a sphere with the "north pole" missing; adding that point completes the (compact) sphere. The result of this compactification is a manifold referred to as the Riemann sphere or the complex projective line . The projection from the Euclidean plane to a sphere without a point is a diffeomorphism and even

2115-494: The topological plane are all continuous bijections . The topological plane is the natural context for the branch of graph theory that deals with planar graphs , and results such as the four color theorem . The plane may also be viewed as an affine space , whose isomorphisms are combinations of translations and non-singular linear maps. From this viewpoint there are no distances, but collinearity and ratios of distances on any line are preserved. Differential geometry views

2162-478: The topology, producing the topological plane, which is homeomorphic to an open disk . Viewing the plane as an affine space produces the affine plane , which lacks a notion of distance but preserves the notion of collinearity . Conversely, in adding more structure, one may view the plane as a 1-dimensional complex manifold , called the complex line . Many fundamental tasks in mathematics, geometry , trigonometry , graph theory , and graphing are performed in

2209-445: The whole of Earth. Near the equator, this means the variation in the strength of solar radiation is different relative to the time of year than it is at higher latitudes: maximum solar radiation is received during the equinoxes, when a place at the equator is under the subsolar point at high noon, and the intermediate seasons of spring and autumn occur at higher latitudes; and the minimum occurs during both solstices, when either pole

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