Ellipsoid in the context of Conformal map projection

Longitude (/ˈlɒndʒɪtjuːd/, AU and UK also /ˈlɒŋɡɪ-/) 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.

Because of the Earth's rotation, there is a close connection between longitude and time measurement. Scientifically precise local time varies with longitude: a difference of 15° longitude corresponds to a one-hour difference in local time, due to the differing position in relation to the Sun. Comparing local time to an absolute measure of time allows longitude to be determined. Depending on the era, the absolute time might be obtained from a celestial event visible from both locations, such as a lunar eclipse, or from a time signal transmitted by telegraph or radio. The principle is straightforward, but in practice finding a reliable method of determining longitude took centuries and required the effort of some of the greatest scientific minds.

An elliptical galaxy is a type of galaxy with an approximately ellipsoidal shape and a smooth, nearly featureless image. They are one of the three main classes of galaxy described by Edwin Hubble in his Hubble sequence and 1936 work The Realm of the Nebulae, along with spiral and lenticular galaxies. Elliptical (E) galaxies are, together with lenticular galaxies (S0) with their large-scale disks, and ES galaxies with their intermediate scale disks, a subset of the "early-type" galaxy population.

Most elliptical galaxies are composed of older, low-mass stars, with a sparse interstellar medium, and they tend to be surrounded by large numbers of globular clusters. Star formation activity in elliptical galaxies is typically minimal; they may, however, undergo brief periods of star formation when merging with other galaxies. Elliptical galaxies are believed to make up approximately 10–15% of galaxies in the Virgo Supercluster, and they are not the dominant type of galaxy in the universe overall. They are preferentially found close to the centers of galaxy clusters.

In modern mapping, a topographic map or topographic sheet is a type of map characterized by large-scale detail and quantitative representation of relief features, usually using contour lines (connecting points of equal elevation), but historically using a variety of methods. Traditional definitions require a topographic map to show both natural and artificial features. A topographic survey is typically based upon a systematic observation and published as a map series, made up of two or more map sheets that combine to form the whole map. A topographic map series uses a common specification that includes the range of cartographic symbols employed, as well as a standard geodetic framework that defines the map projection, coordinate system, ellipsoid and geodetic datum. Official topographic maps also adopt a national grid referencing system.

Natural Resources Canada provides this description of topographic maps:

In fluid mechanics, hydrostatic equilibrium, also called hydrostatic balance and hydrostasy, is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. In the planetary physics of Earth, the pressure-gradient force prevents gravity from collapsing the atmosphere of Earth into a thin, dense shell, whereas gravity prevents the pressure-gradient force from diffusing the atmosphere into outer space. In general, it is what causes objects in space to be spherical.

Hydrostatic equilibrium is the distinguishing criterion between dwarf planets and small solar system bodies, and features in astrophysics and planetary geology. Said qualification of equilibrium indicates that the shape of the object is symmetrically rounded, mostly due to rotation, into an ellipsoid, where any irregular surface features are consequent to a relatively thin solid crust. In addition to the Sun, there are a dozen or so equilibrium objects confirmed to exist in the Solar System.

Quaoar (minor-planet designation: 50000 Quaoar) is a ringed dwarf planet in the Kuiper belt, a band of icy planetesimals beyond Neptune. It has a slightly ellipsoidal shape with an average diameter of 1,100 km (680 mi), about half the size of the dwarf planet Pluto. The object was discovered by American astronomers Chad Trujillo and Michael Brown at Palomar Observatory on 4 June 2002. Quaoar has a reddish surface made of crystalline water ice, tholins, and traces of frozen methane.

Quaoar has two thin rings orbiting outside its Roche limit, which defied initial theoretical expectations that rings outside the Roche limit should be unstable. Quaoar has one moon named Weywot and another unnamed moon that has not yet been confirmed. It is believed that Quaoar's elongated shape, gravitational influence of its moons, and extremely cold temperature help keep its rings stable.

A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has circular symmetry.

If the ellipse is rotated about its major axis, the result is a prolate spheroid, elongated like a rugby ball. The American football is similar but has a pointier end than a spheroid could. If the ellipse is rotated about its minor axis, the result is an oblate spheroid, flattened like a lentil or a plain M&M. If the generating ellipse is a circle, the result is a sphere.

Messier 87 (also known as Virgo A or NGC 4486, generally abbreviated to M87) is a supergiant elliptical galaxy in the constellation Virgo that contains several trillion stars. One of the largest and most massive galaxies in the local universe, it has a large population of globular clusters—about 15,000 compared with the 150–200 orbiting the Milky Way—and a jet of energetic plasma that originates at the core and extends at least 1,500 parsecs (4,900 light-years), traveling at a relativistic speed. It is one of the brightest radio sources in the sky and a popular target for both amateur and professional astronomers.

The French astronomer Charles Messier discovered M87 in 1781, and cataloged it as a nebula. M87 is about 16.4 million parsecs (53 million light-years) from Earth and is the second-brightest galaxy within the northern Virgo Cluster, having many satellite galaxies. Unlike a disk-shaped spiral galaxy, M87 has no distinctive dust lanes. Instead, it has an almost featureless, ellipsoidal shape typical of most giant elliptical galaxies, diminishing in luminosity with distance from the center. Forming around one-sixth of its mass, M87's stars have a nearly spherically symmetric distribution. Their population density decreases with increasing distance from the core. It has an active supermassive black hole at its core, which forms the primary component of an active galactic nucleus. The black hole was imaged using data collected in 2017 by the Event Horizon Telescope (EHT), with a final, processed image released on 10 April 2019. In March 2021, the EHT Collaboration presented, for the first time, a polarized-based image of the black hole which may help better reveal the forces giving rise to quasars.

A planetary-mass object (PMO), planemo, or planetary body (sometimes referred to as a world) is, by geophysical definition of celestial objects, any celestial object massive enough to achieve hydrostatic equilibrium and assume an ellipsoid shape, but not enough to sustain core fusion like a star.

The purpose of this term is to classify together a broader range of celestial objects than just "planet", since many objects similar in geophysical terms do not conform to conventional astrodynamic expectations for a planet. Planetary-mass objects can be quite diverse in origin and location, and include planets, dwarf planets, planetary-mass moons and free-floating planets, which may have been ejected from a system (rogue planets) or formed through cloud-collapse rather than accretion (sub-brown dwarfs).

A geodetic datum or geodetic system (also: geodetic reference datum, geodetic reference system, or geodetic reference frame, or terrestrial reference frame) is a global datum reference or reference frame for unambiguously representing the position of locations on Earth by means of either geodetic coordinates (and related vertical coordinates) or geocentric coordinates. Datums are crucial to any technology or technique based on spatial location, including geodesy, navigation, surveying, geographic information systems, remote sensing, and cartography. A horizontal datum is used to measure a horizontal position, across the Earth's surface, in latitude and longitude or another related coordinate system. A vertical datum is used to measure the elevation or depth relative to a standard origin, such as mean sea level (MSL). A three-dimensional datum enables the expression of both horizontal and vertical position components in a unified form. The concept can be generalized for other celestial bodies as in planetary datums.

Since the rise of the global positioning system (GPS), the ellipsoid and datum WGS 84 it uses has supplanted most others in many applications. The WGS 84 is intended for global use, unlike most earlier datums.Before GPS, there was no precise way to measure the position of a location that was far from reference points used in the realization of local datums, such as from the Prime Meridian at the Greenwich Observatory for longitude, from the Equator for latitude, or from the nearest coast for sea level. Astronomical and chronological methods have limited precision and accuracy, especially over long distances. Even GPS requires a predefined framework on which to base its measurements, so WGS 84 essentially functions as a datum, even though it is different in some particulars from a traditional standard horizontal or vertical datum.

A planetary-mass moon is a planetary-mass object that is a natural satellite of another non-stellar celestial object. Because of their mass, these moons are large and ellipsoidal (sometimes spherical) in shape due to hydrostatic equilibrium caused by internal partial melting and differentiation and/or from tidal or radiogenic heating, in some cases forming a subsurface ocean.

Planetary-mass moons are sometimes called satellite planets by some planetary scientists such as Alan Stern, who are more concerned with whether a celestial body has planetary geology (that is, whether it is a planetary body) than its solar or non-solar orbit (planetary dynamics). Thus they consider planetary-mass moons to be a subset of the planets. This conceptualization of planets as three classes of objects (classical planets, dwarf planets and satellite planets) has not been accepted by the International Astronomical Union (the IAU).

In geometry, an inscribed planar shape or solid is one that is enclosed by and "fits snugly" inside another geometric shape or solid. To say that "figure F is inscribed in figure G" means precisely the same thing as "figure G is circumscribed about figure F". A circle or ellipse inscribed in a convex polygon (or a sphere or ellipsoid inscribed in a convex polyhedron) is tangent to every side or face of the outer figure (but see Inscribed sphere for semantic variants). A polygon inscribed in a circle, ellipse, or polygon (or a polyhedron inscribed in a sphere, ellipsoid, or polyhedron) has each vertex on the outer figure; if the outer figure is a polygon or polyhedron, there must be a vertex of the inscribed polygon or polyhedron on each side of the outer figure. An inscribed figure is not necessarily unique in orientation; this can easily be seen, for example, when the given outer figure is a circle, in which case a rotation of an inscribed figure gives another inscribed figure that is congruent to the original one.

Familiar examples of inscribed figures include circles inscribed in triangles or regular polygons, and triangles or regular polygons inscribed in circles. A circle inscribed in any polygon is called its incircle, in which case the polygon is said to be a tangential polygon. A polygon inscribed in a circle is said to be a cyclic polygon, and the circle is said to be its circumscribed circle or circumcircle.

In mathematics, a quadric or quadric surface is a generalization of conic sections (ellipses, parabolas, and hyperbolas). In three-dimensional space, quadrics include ellipsoids, paraboloids, and hyperboloids.

More generally, a quadric hypersurface (of dimension D) embedded in a higher dimensional space (of dimension D + 1) is defined as the zero set of an irreducible polynomial of degree two in D + 1 variables; for example, D=1 is the case of conic sections (plane curves). When the defining polynomial is not absolutely irreducible, the zero set is generally not considered a quadric, although it is often called a degenerate quadric or a reducible quadric.

Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively. Other terms used are ellipticity, or oblateness. The usual notation for flattening is ${\displaystyle f}$ and its definition in terms of the semi-axes ${\displaystyle a}$ and ${\displaystyle b}$ of the resulting ellipse or ellipsoid is

The compression factor is ${\displaystyle b/a}$ in each case; for the ellipse, this is also its aspect ratio.