A coordinate singularity occurs when an apparent singularity or discontinuity occurs in one coordinate frame that can be removed by choosing a different frame.
An example is the apparent (longitudinal) singularity at the 90 degree latitude in spherical coordinates. An object moving due north (for example, along the line 0 degrees longitude) on the surface of a sphere will suddenly experience an instantaneous change in longitude at the pole (i.e., jumping from longitude 0 to longitude 180 degrees). In fact, longitude is not uniquely defined at the poles. This discontinuity, however, is only apparent; it is an artifact of the coordinate system chosen, which is singular at the poles. A different coordinate system would eliminate the apparent discontinuity, e.g. by replacing the latitude/longitude representation with an n-vector representation.
Stephen Hawking aptly summed this up, when once asking the question, "What lies north of the North Pole?". [1]
The ecliptic or ecliptic plane is the orbital plane of Earth around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic against the background of stars. The ecliptic is an important reference plane and is the basis of the ecliptic coordinate system.
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 the equator. Latitude and longitude are used together as a coordinate pair to specify a location on the surface of the Earth.
Longitude is a geographic coordinate that specifies the east–west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter lambda (λ). Meridians are imaginary semicircular lines running from pole to pole that connect points with the same longitude. The prime meridian defines 0° longitude; by convention the International Reference Meridian for the Earth passes near the Royal Observatory in Greenwich, south-east London on the island of Great Britain. Positive longitudes are east of the prime meridian, and negative ones are west.
The geographic coordinate system (GCS) is a spherical or geodetic coordinate system for measuring and communicating positions directly on the Earth as latitude and longitude. It is the simplest, oldest and most widely used of the various spatial reference systems that are in use, and forms the basis for most others. Although latitude and longitude form a coordinate tuple like a cartesian coordinate system, the geographic coordinate system is not cartesian because the measurements are angles and are not on a planar surface.
In astronomy, the ecliptic coordinate system is a celestial coordinate system commonly used for representing the apparent positions, orbits, and pole orientations of Solar System objects. Because most planets and many small Solar System bodies have orbits with only slight inclinations to the ecliptic, using it as the fundamental plane is convenient. The system's origin can be the center of either the Sun or Earth, its primary direction is towards the vernal (March) equinox, and it has a right-hand convention. It may be implemented in spherical or rectangular coordinates.
The galactic coordinate system is a celestial coordinate system in spherical coordinates, with the Sun as its center, the primary direction aligned with the approximate center of the Milky Way Galaxy, and the fundamental plane parallel to an approximation of the galactic plane but offset to its north. It uses the right-handed convention, meaning that coordinates are positive toward the north and toward the east in the fundamental plane.
In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity.
A circle of latitude or line of latitude on Earth is an abstract east–west small circle connecting all locations around Earth at a given latitude coordinate line.
Midnight sun is a natural phenomenon that occurs in the summer months in places north of the Arctic Circle or south of the Antarctic Circle, when the Sun remains visible at the local midnight. When midnight sun is seen in the Arctic, the Sun appears to move from left to right. In Antarctica, the equivalent apparent motion is from right to left. This occurs at latitudes from 65°44' to 90° north or south, and does not stop exactly at the Arctic Circle or the Antarctic Circle, due to refraction.
ISO 6709, Standard representation of geographic point location by coordinates, is the international standard for representation of latitude, longitude and altitude for geographic point locations.
The selenographic coordinate system is used to refer to locations on the surface of Earth's moon. Any position on the lunar surface can be referenced by specifying two numerical values, which are comparable to the latitude and longitude of Earth. The longitude gives the position east or west of the Moon's prime meridian, which is the line passing from the lunar north pole through the point on the lunar surface directly facing Earth to the lunar south pole. This can be thought of as the midpoint of the visible Moon as seen from the Earth. The latitude gives the position north or south of the lunar equator. Both of these coordinates are given in degrees.
The European Terrestrial Reference System 1989 (ETRS89) is an ECEF geodetic Cartesian reference frame, in which the Eurasian Plate as a whole is static. The coordinates and maps in Europe based on ETRS89 are not subject to change due to the continental drift.
The World Geographic Reference System (GEOREF) is a geocode, a grid-based method of specifying locations on the surface of the Earth. GEOREF is essentially based on the geographic system of latitude and longitude, but using a simpler and more flexible notation. GEOREF was used primarily in aeronautical charts for air navigation, particularly in military or inter-service applications, but it is rarely seen today. However, GEOREF can be used with any map or chart that has latitude and longitude printed on it.
The n-vector representation is a three-parameter non-singular representation well-suited for replacing geodetic coordinates for horizontal position representation in mathematical calculations and computer algorithms.
Geohash is a public domain geocode system invented in 2008 by Gustavo Niemeyer which encodes a geographic location into a short string of letters and digits. Similar ideas were introduced by G.M. Morton in 1966. It is a hierarchical spatial data structure which subdivides space into buckets of grid shape, which is one of the many applications of what is known as a Z-order curve, and generally space-filling curves.
A position representation is a set of parameters used to express a position relative to a reference. When representing positions relative to the Earth, it is often most convenient to represent vertical position separately, and to use some other parameters to represent horizontal position. There are also several applications where only the horizontal position is of interest, this might e.g. be the case for ships and ground vehicles/cars. It is a type of geographic coordinate system.
In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. Wolfgang Rindler coined the term in the 1950s.
The IERS Reference Meridian (IRM), also called the International Reference Meridian, is the prime meridian maintained by the International Earth Rotation and Reference Systems Service (IERS). It passes about 5.3 arcseconds east of George Biddell Airy's 1851 transit circle which is 102 metres (335 ft) at the latitude of the Royal Observatory, Greenwich. Thus it differs slightly from the historical Greenwich meridian.
A chronometric singularity is a point at which time cannot be measured or described.
A discrete global grid (DGG) is a mosaic that covers the entire Earth's surface. Mathematically it is a space partitioning: it consists of a set of non-empty regions that form a partition of the Earth's surface. In a usual grid-modeling strategy, to simplify position calculations, each region is represented by a point, abstracting the grid as a set of region-points. Each region or region-point in the grid is called a cell.