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42-529: Elevation is not to be confused with the distance from the center of the Earth. Due to the equatorial bulge , the summits of Mount Everest and Chimborazo have, respectively, the largest elevation and the largest geocentric distance. In aviation, the term elevation or aerodrome elevation is defined by the ICAO as the highest point of the landing area. It is often measured in feet and can be found in approach charts of

84-418: A e − a p a = 5 4 ω 2 a 3 G M = 15 π 4 1 G T 2 ρ {\displaystyle f={\frac {a_{e}-a_{p}}{a}}={\frac {5}{4}}{\frac {\omega ^{2}a^{3}}{GM}}={\frac {15\pi }{4}}{\frac {1}{GT^{2}\rho }}} where A related quantity

126-405: A = c reduces to a sphere. An oblate spheroid with c < a has surface area The oblate spheroid is generated by rotation about the z -axis of an ellipse with semi-major axis a and semi-minor axis c , therefore e may be identified as the eccentricity . (See ellipse .) A prolate spheroid with c > a has surface area The prolate spheroid is generated by rotation about

168-425: A 3D Elevation Program (3DEP) to keep up with growing needs for high quality topographic data. 3DEP is a collection of enhanced elevation data in the form of high quality LiDAR data over the conterminous United States, Hawaii, and the U.S. territories. There are three bare earth DEM layers in 3DEP which are nationally seamless at the resolution of 1/3, 1, and 2 arcseconds. Equatorial bulge An equatorial bulge

210-518: A centripetal force; the decreasing effect is strongest on the Equator. The fact that the Earth's gravitational field slightly deviates from being spherically symmetrical also affects the orbits of satellites through secular orbital precessions. They depend on the orientation of the Earth's symmetry axis in the inertial space, and, in the general case, affect all the Keplerian orbital elements with

252-456: A force. The acceleration that is required to circumnavigate the Earth's axis along the equator at one revolution per sidereal day is 0.0339 m/s . Providing this acceleration decreases the effective gravitational acceleration. At the Equator, the effective gravitational acceleration is 9.7805 m/s . This means that the true gravitational acceleration at the Equator must be 9.8144 m/s (9.7805 + 0.0339 = 9.8144). At

294-404: A massive body in a close orbit. The most extreme example is Jupiter's moon Io , which becomes slightly more or less prolate in its orbit due to a slight eccentricity, causing intense volcanism . The major axis of the prolate spheroid does not run through the satellite's poles in this case, but through the two points on its equator directly facing toward and away from the primary. This combines with

336-470: A spheroid whose radius is 6,378.137 km (3,963.191 mi) at the Equator and 6,356.752 km (3,949.903 mi) at the poles . The word spheroid originally meant "an approximately spherical body", admitting irregularities even beyond the bi- or tri-axial ellipsoidal shape; that is how the term is used in some older papers on geodesy (for example, referring to truncated spherical harmonic expansions of

378-476: Is 21 km (13 mi) closer to Earth's center than if standing at sea level on the Equator. As a result, the highest point on Earth, measured from the center and outwards, is the peak of Mount Chimborazo in Ecuador rather than Mount Everest . But since the ocean also bulges, like Earth and its atmosphere , Chimborazo is not as high above sea level as Everest is. Similarly the lowest point on Earth, measured from

420-429: Is a difference between the equatorial and polar diameters of a planet , due to the centrifugal force exerted by the rotation about the body's axis. A rotating body tends to form an oblate spheroid rather than a sphere . The planet Earth has a rather slight equatorial bulge; its equatorial diameter is about 43 km (27 mi) greater than its polar diameter, with a difference of about 1 ⁄ 298 of

462-811: Is also a shape of archaeological artifacts. The oblate spheroid is the approximate shape of rotating planets and other celestial bodies , including Earth, Saturn , Jupiter , and the quickly spinning star Altair . Saturn is the most oblate planet in the Solar System , with a flattening of 0.09796. See planetary flattening and equatorial bulge for details. Enlightenment scientist Isaac Newton , working from Jean Richer 's pendulum experiments and Christiaan Huygens 's theories for their interpretation, reasoned that Jupiter and Earth are oblate spheroids owing to their centrifugal force . Earth's diverse cartographic and geodetic systems are based on reference ellipsoids , all of which are oblate. The prolate spheroid

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504-411: Is no equilibrium there can be violent convection, and as long as there is violent convection friction can convert kinetic energy to heat, draining rotational kinetic energy from the system. When the equilibrium state has been reached then large scale conversion of kinetic energy to heat ceases. In that sense the equilibrium state is the lowest state of energy that can be reached. The Earth's rotation rate

546-415: Is so strong that at the faster rotation rate the required centripetal force is larger than with the starting rotation rate. Something analogous to this occurs in planet formation. Matter first coalesces into a slowly rotating disk-shaped distribution, and collisions and friction convert kinetic energy to heat, which allows the disk to self-gravitate into a very oblate spheroid. As long as the proto-planet

588-411: Is still slowing down, though gradually, by about two thousandths of a second per rotation every 100 years. Estimates of how fast the Earth was rotating in the past vary, because it is not known exactly how the moon was formed. Estimates of the Earth's rotation 500 million years ago are around 20 modern hours per "day". The Earth's rate of rotation is slowing down mainly because of tidal interactions with

630-542: Is still too oblate to be in equilibrium, the release of gravitational potential energy on contraction keeps driving the increase in rotational kinetic energy. As the contraction proceeds, the rotation rate keeps going up, hence the required force for further contraction keeps going up. There is a point where the increase of rotational kinetic energy on further contraction would be larger than the release of gravitational potential energy. The contraction process can only proceed up to that point, so it halts there. As long as there

672-488: Is the flattening (sometimes called ellipticity or oblateness), which can depend on a variety of factors including the size, angular velocity , density , and elasticity . A way for one to get a feel for the type of equilibrium involved is to imagine someone seated in a spinning swivel chair and holding a weight in each hand; if the individual pulls the weights inward towards them, work is being done and their rotational kinetic energy increases. The increase in rotation rate

714-422: Is the longitude , and − ⁠ π / 2 ⁠ < β < + ⁠ π / 2 ⁠ and −π < λ < +π . Then, the spheroid's Gaussian curvature is and its mean curvature is Both of these curvatures are always positive, so that every point on a spheroid is elliptic. The aspect ratio of an oblate spheroid/ellipse, c  : a , is the ratio of the polar to equatorial lengths, while

756-538: Is the approximate shape of the ball in several sports, such as in the rugby ball . Several moons of the Solar System approximate prolate spheroids in shape, though they are actually triaxial ellipsoids . Examples are Saturn 's satellites Mimas , Enceladus , and Tethys and Uranus ' satellite Miranda . In contrast to being distorted into oblate spheroids via rapid rotation, celestial objects distort slightly into prolate spheroids via tidal forces when they orbit

798-544: Is the body's second dynamic form factor , J 2 : with J 2 = − √ 5 C 20 = 1.082 626 68 × 10 for Earth, where Real flattening is smaller due to mass concentration in the center of celestial bodies. Oblate ellipsoid 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

840-445: Is the main type of map used to depict elevation, often through contour lines . In a Geographic Information System (GIS), digital elevation models (DEM) are commonly used to represent the surface (topography) of a place, through a raster (grid) dataset of elevations. Digital terrain models are another way to represent terrain in GIS. USGS (United States Geologic Survey) is developing

882-421: The flattening (also called oblateness ) f , is the ratio of the equatorial-polar length difference to the equatorial length: The first eccentricity (usually simply eccentricity, as above) is often used instead of flattening. It is defined by: The relations between eccentricity and flattening are: All modern geodetic ellipsoids are defined by the semi-major axis plus either the semi-minor axis (giving

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924-492: The Earth's gravity geopotential model ). The equation of a tri-axial ellipsoid centred at the origin with semi-axes a , b and c aligned along the coordinate axes is The equation of a spheroid with z as the symmetry axis is given by setting a = b : The semi-axis a is the equatorial radius of the spheroid, and c is the distance from centre to pole along the symmetry axis. There are two possible cases: The case of

966-400: The actinide and lanthanide elements are shaped like prolate spheroids. In anatomy, near-spheroid organs such as testis may be measured by their long and short axes . Many submarines have a shape which can be described as prolate spheroid. For a spheroid having uniform density, the moment of inertia is that of an ellipsoid with an additional axis of symmetry. Given a description of

1008-419: The sea level , the imaginary surface used as a reference frame from which to measure altitudes . This surface coincides with the mean water surface level in oceans, and is extrapolated over land by taking into account the local gravitational potential and the centrifugal force. The difference of the radii is thus about 21 km (13 mi). An observer standing at sea level on either pole , therefore,

1050-402: The z -axis of an ellipse with semi-major axis c and semi-minor axis a ; therefore, e may again be identified as the eccentricity . (See ellipse .) These formulas are identical in the sense that the formula for S oblate can be used to calculate the surface area of a prolate spheroid and vice versa. However, e then becomes imaginary and can no longer directly be identified with

1092-530: The "center of the Earth". In the WGS-84 standard Earth ellipsoid , widely used for map-making and the GPS system, Earth's radius is assumed to be 6 378.137  km ( 3 963.191  mi) to the Equator and 6 356.752 3142  km ( 3 949.902 7642  mi) to either pole, meaning a difference of 21.384 6858  km ( 13.287 8277  mi) between the radii or 42.769 3716  km ( 26.575 6554  mi) between

1134-531: The Moon and the Sun. Since the solid parts of the Earth are ductile , the Earth's equatorial bulge has been decreasing in step with the decrease in the rate of rotation. Because of a planet's rotation around its own axis, the gravitational acceleration is less at the equator than at the poles . In the 17th century, following the invention of the pendulum clock , French scientists found that clocks sent to French Guiana , on

1176-460: The aerodrome. It is not to be confused with terms such as the altitude or height. GIS or geographic information system is a computer system that allows for visualizing, manipulating, capturing, and storage of data with associated attributes. GIS offers better understanding of patterns and relationships of the landscape at different scales. Tools inside the GIS allow for manipulation of data for spatial analysis or cartography. A topographical map

1218-432: The aspect ratio), the flattening, or the first eccentricity. While these definitions are mathematically interchangeable, real-world calculations must lose some precision. To avoid confusion, an ellipsoidal definition considers its own values to be exact in the form it gives. The most common shapes for the density distribution of protons and neutrons in an atomic nucleus are spherical , prolate, and oblate spheroidal, where

1260-606: The center and outwards, is the Litke Deep in the Arctic Ocean rather than Challenger Deep in the Pacific Ocean . But since the ocean also flattens, like Earth and its atmosphere, Litke Deep is not as low below sea level as Challenger Deep is. More precisely, Earth's surface is usually approximated by an ideal oblate ellipsoid , for the purposes of defining precisely the latitude and longitude grid for cartography , as well as

1302-406: The combined effects of gravity and rotation , the figure of the Earth (and of all planets ) is not quite a sphere, but instead is slightly flattened in the direction of its axis of rotation. For that reason, in cartography and geodesy the Earth is often approximated by an oblate spheroid, known as the reference ellipsoid , instead of a sphere. The current World Geodetic System model uses

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1344-402: The diameters, and a relative flattening of 1/298.257223563. The ocean surface is much closer to this standard ellipsoid than the solid surface of Earth is. Gravity tends to contract a celestial body into a sphere , the shape for which all the mass is as close to the center of gravity as possible. Rotation causes a distortion from this spherical shape; a common measure of the distortion

1386-415: The eccentricity. Both of these results may be cast into many other forms using standard mathematical identities and relations between parameters of the ellipse. The volume inside a spheroid (of any kind) is If A = 2 a is the equatorial diameter, and C = 2 c is the polar diameter, the volume is Let a spheroid be parameterized as where β is the reduced latitude or parametric latitude , λ

1428-453: 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 . Due to

1470-413: The equatorial diameter. If Earth were scaled down to a globe with an equatorial diameter of 1 metre (3.3 ft), that difference would be only 3 mm (0.12 in). While too small to notice visually, that difference is still more than twice the largest deviations of the actual surface from the ellipsoid, including the tallest mountains and deepest oceanic trenches . Earth's rotation also affects

1512-486: The exception of the semimajor axis . If the reference z axis of the coordinate system adopted is aligned along the Earth's symmetry axis, then only the longitude of the ascending node Ω, the argument of pericenter ω and the mean anomaly M undergo secular precessions. Such perturbations, which were earlier used to map the Earth's gravitational field from space, may play a relevant disturbing role when satellites are used to make tests of general relativity because

1554-400: The fact that the effective gravitational acceleration is less strong at the equator than at the poles. About 70% of the difference is contributed by the fact that objects circumnavigate the Earth's axis, and about 30% is due to the non-spherical shape of the Earth. The diagram illustrates that on all latitudes the effective gravitational acceleration is decreased by the requirement of providing

1596-408: The much smaller relativistic effects are qualitatively indistinguishable from the oblateness-driven disturbances. The flattening f {\displaystyle f} for the equilibrium configuration of a self-gravitating spheroid, composed of uniform density incompressible fluid, rotating steadily about some fixed axis, for a small amount of flattening, is approximated by: f =

1638-461: The northern coast of South America , ran slower than their exact counterparts in Paris. Measurements of the acceleration due to gravity at the equator must also take into account the planet's rotation. Any object that is stationary with respect to the surface of the Earth is actually following a circular trajectory, circumnavigating the Earth's axis. Pulling an object into such a circular trajectory requires

1680-509: The polar axis is assumed to be the spin axis (or direction of the spin angular momentum vector). Deformed nuclear shapes occur as a result of the competition between electromagnetic repulsion between protons, surface tension and quantum shell effects . Spheroids are common in 3D cell cultures . Rotating equilibrium spheroids include the Maclaurin spheroid and the Jacobi ellipsoid . Spheroid

1722-455: The poles, the gravitational acceleration is 9.8322 m/s . The difference of 0.0178 m/s between the gravitational acceleration at the poles and the true gravitational acceleration at the Equator is because objects located on the Equator are about 21 km (13 mi) further away from the center of mass of the Earth than at the poles, which corresponds to a smaller gravitational acceleration. In summary, there are two contributions to

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1764-486: The smaller oblate distortion from the synchronous rotation to cause the body to become triaxial. The term is also used to describe the shape of some nebulae such as the Crab Nebula . Fresnel zones , used to analyze wave propagation and interference in space, are a series of concentric prolate spheroids with principal axes aligned along the direct line-of-sight between a transmitter and a receiver. The atomic nuclei of

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