Geodesy

Geodesy (/dʒiːˈɒdɪsi/)[1] is the Earth science of accurately measuring and understanding Earth's geometric shape, orientation in space and gravitational field.[2] The field also incorporates studies of how these properties change over time and equivalent measurements for other planets (known as planetary geodesy). Geodynamical phenomena include crustal motion, tides and polar motion, which can be studied by designing global and national control networks, applying space and terrestrial techniques and relying on datums and coordinate systems.

Geodetisch station1855
An old geodetic pillar (1855) at Ostend, Belgium

Definition

The word "geodesy" comes from the Ancient Greek word γεωδαισία geodaisia (literally, "division of Earth").

It is primarily concerned with positioning within the temporally varying gravity field. Geodesy in the German-speaking world is divided into "higher geodesy" ("Erdmessung" or "höhere Geodäsie"), which is concerned with measuring Earth on the global scale, and "practical geodesy" or "engineering geodesy" ("Ingenieurgeodäsie"), which is concerned with measuring specific parts or regions of Earth, and which includes surveying. Such geodetic operations are also applied to other astronomical bodies in the solar system. It is also the science of measuring and understanding Earth's geometric shape, orientation in space, and gravity field.

To a large extent, the shape of Earth is the result of rotation, which causes its equatorial bulge, and the competition of geological processes such as the collision of plates and of volcanism, resisted by Earth's gravity field. This applies to the solid surface, the liquid surface (dynamic sea surface topography) and Earth's atmosphere. For this reason, the study of Earth's gravity field is called physical geodesy.

Geoid and reference ellipsoid

The geoid is essentially the figure of Earth abstracted from its topographical features. It is an idealized equilibrium surface of sea water, the mean sea level surface in the absence of currents and air pressure variations, and continued under the continental masses. The geoid, unlike the reference ellipsoid, is irregular and too complicated to serve as the computational surface on which to solve geometrical problems like point positioning. The geometrical separation between the geoid and the reference ellipsoid is called the geoidal undulation. It varies globally between ±110 m, when referred to the GRS 80 ellipsoid.

A reference ellipsoid, customarily chosen to be the same size (volume) as the geoid, is described by its semi-major axis (equatorial radius) a and flattening f. The quantity f = ab/a, where b is the semi-minor axis (polar radius), is a purely geometrical one. The mechanical ellipticity of Earth (dynamical flattening, symbol J2) can be determined to high precision by observation of satellite orbit perturbations. Its relationship with the geometrical flattening is indirect. The relationship depends on the internal density distribution, or, in simplest terms, the degree of central concentration of mass.

The 1980 Geodetic Reference System (GRS 80) posited a 6,378,137 m semi-major axis and a 1:298.257 flattening. This system was adopted at the XVII General Assembly of the International Union of Geodesy and Geophysics (IUGG). It is essentially the basis for geodetic positioning by the Global Positioning System (GPS) and is thus also in widespread use outside the geodetic community. The numerous systems that countries have used to create maps and charts are becoming obsolete as countries increasingly move to global, geocentric reference systems using the GRS 80 reference ellipsoid.

The geoid is "realizable", meaning it can be consistently located on Earth by suitable simple measurements from physical objects like a tide gauge. The geoid can, therefore, be considered a real surface. The reference ellipsoid, however, has many possible instantiations and is not readily realizable, therefore it is an abstract surface. The third primary surface of geodetic interest—the topographic surface of Earth—is a realizable surface.

Coordinate systems in space

The locations of points in three-dimensional space are most conveniently described by three cartesian or rectangular coordinates, X, Y and Z. Since the advent of satellite positioning, such coordinate systems are typically geocentric: the Z-axis is aligned with Earth's (conventional or instantaneous) rotation axis.

Prior to the era of satellite geodesy, the coordinate systems associated with a geodetic datum attempted to be geocentric, but their origins differed from the geocenter by hundreds of meters, due to regional deviations in the direction of the plumbline (vertical). These regional geodetic data, such as ED 50 (European Datum 1950) or NAD 27 (North American Datum 1927) have ellipsoids associated with them that are regional "best fits" to the geoids within their areas of validity, minimizing the deflections of the vertical over these areas.

It is only because GPS satellites orbit about the geocenter, that this point becomes naturally the origin of a coordinate system defined by satellite geodetic means, as the satellite positions in space are themselves computed in such a system.

Geocentric coordinate systems used in geodesy can be divided naturally into two classes:

  1. Inertial reference systems, where the coordinate axes retain their orientation relative to the fixed stars, or equivalently, to the rotation axes of ideal gyroscopes; the X-axis points to the vernal equinox
  2. Co-rotating, also ECEF ("Earth Centred, Earth Fixed"), where the axes are attached to the solid body of Earth. The X-axis lies within the Greenwich observatory's meridian plane.

The coordinate transformation between these two systems is described to good approximation by (apparent) sidereal time, which takes into account variations in Earth's axial rotation (length-of-day variations). A more accurate description also takes polar motion into account, a phenomenon closely monitored by geodesists.

Coordinate systems in the plane

Litography archive of the Bayerisches Vermessungsamt
A Munich archive with lithography plates of maps of Bavaria

In surveying and mapping, important fields of application of geodesy, two general types of coordinate systems are used in the plane:

  1. Plano-polar, in which points in a plane are defined by a distance s from a specified point along a ray having a specified direction α with respect to a base line or axis;
  2. Rectangular, points are defined by distances from two perpendicular axes called x and y. It is geodetic practice—contrary to the mathematical convention—to let the x-axis point to the north and the y-axis to the east.

Rectangular coordinates in the plane can be used intuitively with respect to one's current location, in which case the x-axis will point to the local north. More formally, such coordinates can be obtained from three-dimensional coordinates using the artifice of a map projection. It is not possible to map the curved surface of Earth onto a flat map surface without deformation. The compromise most often chosen—called a conformal projection—preserves angles and length ratios, so that small circles are mapped as small circles and small squares as squares.

An example of such a projection is UTM (Universal Transverse Mercator). Within the map plane, we have rectangular coordinates x and y. In this case, the north direction used for reference is the map north, not the local north. The difference between the two is called meridian convergence.

It is easy enough to "translate" between polar and rectangular coordinates in the plane: let, as above, direction and distance be α and s respectively, then we have

The reverse transformation is given by:

Heights

In geodesy, point or terrain heights are "above sea level", an irregular, physically defined surface. Heights come in the following variants:

  1. Orthometric heights
  2. Normal heights
  3. Geopotential heights

Each has its advantages and disadvantages. Both orthometric and normal heights are heights in metres above sea level, whereas geopotential numbers are measures of potential energy (unit: m2 s−2) and not metric. Orthometric and normal heights differ in the precise way in which mean sea level is conceptually continued under the continental masses. The reference surface for orthometric heights is the geoid, an equipotential surface approximating mean sea level.

None of these heights is in any way related to geodetic or ellipsoidial heights, which express the height of a point above the reference ellipsoid. Satellite positioning receivers typically provide ellipsoidal heights, unless they are fitted with special conversion software based on a model of the geoid.

Geodetic data

Because geodetic point coordinates (and heights) are always obtained in a system that has been constructed itself using real observations, geodesists introduce the concept of a "geodetic datum": a physical realization of a coordinate system used for describing point locations. The realization is the result of choosing conventional coordinate values for one or more datum points.

In the case of height data, it suffices to choose one datum point: the reference benchmark, typically a tide gauge at the shore. Thus we have vertical data like the NAP (Normaal Amsterdams Peil), the North American Vertical Datum 1988 (NAVD 88), the Kronstadt datum, the Trieste datum, and so on.

In case of plane or spatial coordinates, we typically need several datum points. A regional, ellipsoidal datum like ED 50 can be fixed by prescribing the undulation of the geoid and the deflection of the vertical in one datum point, in this case the Helmert Tower in Potsdam. However, an overdetermined ensemble of datum points can also be used.

Changing the coordinates of a point set referring to one datum, so to make them refer to another datum, is called a datum transformation. In the case of vertical data, this consists of simply adding a constant shift to all height values. In the case of plane or spatial coordinates, datum transformation takes the form of a similarity or Helmert transformation, consisting of a rotation and scaling operation in addition to a simple translation. In the plane, a Helmert transformation has four parameters; in space, seven.

A note on terminology

In the abstract, a coordinate system as used in mathematics and geodesy is called a "coordinate system" in ISO terminology, whereas the International Earth Rotation and Reference Systems Service (IERS) uses the term "reference system". When these coordinates are realized by choosing datum points and fixing a geodetic datum, ISO says "coordinate reference system", while IERS says "reference frame". The ISO term for a datum transformation again is a "coordinate transformation".[3]

Point positioning

Geodetic Control Mark
Geodetic Control Mark (example of a deep benchmark)

Point positioning is the determination of the coordinates of a point on land, at sea, or in space with respect to a coordinate system. Point position is solved by computation from measurements linking the known positions of terrestrial or extraterrestrial points with the unknown terrestrial position. This may involve transformations between or among astronomical and terrestrial coordinate systems. The known points used for point positioning can be triangulation points of a higher-order network or GPS satellites.

Traditionally, a hierarchy of networks has been built to allow point positioning within a country. Highest in the hierarchy were triangulation networks. These were densified into networks of traverses (polygons), into which local mapping surveying measurements, usually with measuring tape, corner prism, and the familiar red and white poles, are tied.

Nowadays all but special measurements (e.g., underground or high-precision engineering measurements) are performed with GPS. The higher-order networks are measured with static GPS, using differential measurement to determine vectors between terrestrial points. These vectors are then adjusted in traditional network fashion. A global polyhedron of permanently operating GPS stations under the auspices of the IERS is used to define a single global, geocentric reference frame which serves as the "zero order" global reference to which national measurements are attached.

For surveying mappings, frequently Real Time Kinematic GPS is employed, tying in the unknown points with known terrestrial points close by in real time.

One purpose of point positioning is the provision of known points for mapping measurements, also known as (horizontal and vertical) control. In every country, thousands of such known points exist and are normally documented by national mapping agencies. Surveyors involved in real estate and insurance will use these to tie their local measurements.

Geodetic problems

In geometric geodesy, two standard problems exist—the first (direct or forward) and the second (inverse or reverse).

First (direct or forward) geodetic problem
Given a point (in terms of its coordinates) and the direction (azimuth) and distance from that point to a second point, determine (the coordinates of) that second point.
Second (inverse or reverse) geodetic problem
Given two points, determine the azimuth and length of the line (straight line, arc or geodesic) that connects them.

In plane geometry (valid for small areas on Earth's surface), the solutions to both problems reduce to simple trigonometry. On a sphere, however, the solution is significantly more complex, because in the inverse problem the azimuths will differ between the two end points of the connecting great circle, arc.

On the ellipsoid of revolution, geodesics may be written in terms of elliptic integrals, which are usually evaluated in terms of a series expansion—see, for example, Vincenty's formulae. In the general case, the solution is called the geodesic for the surface considered. The differential equations for the geodesic can be solved numerically.

Observational concepts

Here we define some basic observational concepts, like angles and coordinates, defined in geodesy (and astronomy as well), mostly from the viewpoint of the local observer.

  • Plumbline or vertical: the direction of local gravity, or the line that results by following it.
  • Zenith: the point on the celestial sphere where the direction of the gravity vector in a point, extended upwards, intersects it. It is more correct to call it a direction rather than a point.
  • Nadir: the opposite point—or rather, direction—where the direction of gravity extended downward intersects the (obscured) celestial sphere.
  • Celestial horizon: a plane perpendicular to a point's gravity vector.
  • Azimuth: the direction angle within the plane of the horizon, typically counted clockwise from the north (in geodesy and astronomy) or the south (in France).
  • Elevation: the angular height of an object above the horizon, Alternatively zenith distance, being equal to 90 degrees minus elevation.
  • Local topocentric coordinates: azimuth (direction angle within the plane of the horizon), elevation angle (or zenith angle), distance.
  • North celestial pole: the extension of Earth's (precessing and nutating) instantaneous spin axis extended northward to intersect the celestial sphere. (Similarly for the south celestial pole.)
  • Celestial equator: the (instantaneous) intersection of Earth's equatorial plane with the celestial sphere.
  • Meridian plane: any plane perpendicular to the celestial equator and containing the celestial poles.
  • Local meridian: the plane containing the direction to the zenith and the direction to the celestial pole.

Measurements

A NASA project manager talks about his work for the Space Geodesy Project, including an overview of its four fundamental techniques: GPS, VLBI, SLR, and DORIS.

The level is used for determining height differences and height reference systems, commonly referred to mean sea level. The traditional spirit level produces these practically most useful heights above sea level directly; the more economical use of GPS instruments for height determination requires precise knowledge of the figure of the geoid, as GPS only gives heights above the GRS80 reference ellipsoid. As geoid knowledge accumulates, one may expect the use of GPS heighting to spread.

The theodolite is used to measure horizontal and vertical angles to target points. These angles are referred to the local vertical. The tacheometer additionally determines, electronically or electro-optically, the distance to target, and is highly automated to even robotic in its operations. The method of free station position is widely used.

For local detail surveys, tacheometers are commonly employed although the old-fashioned rectangular technique using angle prism and steel tape is still an inexpensive alternative. Real-time kinematic (RTK) GPS techniques are used as well. Data collected are tagged and recorded digitally for entry into a Geographic Information System (GIS) database.

Geodetic GPS receivers produce directly three-dimensional coordinates in a geocentric coordinate frame. Such a frame is, e.g., WGS84, or the frames that are regularly produced and published by the International Earth Rotation and Reference Systems Service (IERS).

GPS receivers have almost completely replaced terrestrial instruments for large-scale base network surveys. For planet-wide geodetic surveys, previously impossible, we can still mention satellite laser ranging (SLR) and lunar laser ranging (LLR) and very-long-baseline interferometry (VLBI) techniques. All these techniques also serve to monitor irregularities in Earth's rotation as well as plate tectonic motions.

Gravity is measured using gravimeters, of which there are two kinds. First, "absolute gravimeters" are based on measuring the acceleration of free fall (e.g., of a reflecting prism in a vacuum tube). They are used to establish the vertical geospatial control and can be used in the field. Second, "relative gravimeters" are spring-based and are more common. They are used in gravity surveys over large areas for establishing the figure of the geoid over these areas. The most accurate relative gravimeters are called "superconducting" gravimeters, which are sensitive to one-thousandth of one-billionth of Earth-surface gravity. Twenty-some superconducting gravimeters are used worldwide for studying Earth's tides, rotation, interior, and ocean and atmospheric loading, as well as for verifying the Newtonian constant of gravitation.

In the future, gravity and altitude, will be measured by relativistic time dilation measured by strontium optical clocks.

Units and measures on the ellipsoid

Geographical latitude and longitude are stated in the units degree, minute of arc, and second of arc. They are angles, not metric measures, and describe the direction of the local normal to the reference ellipsoid of revolution. This is approximately the same as the direction of the plumbline, i.e., local gravity, which is also the normal to the geoid surface. For this reason, astronomical position determination – measuring the direction of the plumbline by astronomical means – works fairly well provided an ellipsoidal model of the figure of Earth is used.

One geographical mile, defined as one minute of arc on the equator, equals 1,855.32571922 m. One nautical mile is one minute of astronomical latitude. The radius of curvature of the ellipsoid varies with latitude, being the longest at the pole and the shortest at the equator as is the nautical mile.

A metre was originally defined as the 10-millionth part of the length from equator to North Pole along the meridian through Paris (the target was not quite reached in actual implementation, so that is off by 200 ppm in the current definitions). This means that one kilometre is roughly equal to (1/40,000) * 360 * 60 meridional minutes of arc, which equals 0.54 nautical mile, though this is not exact because the two units are defined on different bases (the international nautical mile is defined as exactly 1,852 m, corresponding to a rounding of 1,000/0.54 m to four digits).

Temporal change

In geodesy, temporal change can be studied by a variety of techniques. Points on Earth's surface change their location due to a variety of mechanisms:

  • Continental plate motion, plate tectonics
  • Episodic motion of tectonic origin, especially close to fault lines
  • Periodic effects due to tides
  • Postglacial land uplift due to isostatic adjustment
  • Mass variations due to hydrological changes
  • Anthropogenic movements such as reservoir construction or petroleum or water extraction

The science of studying deformations and motions of Earth's crust and its solidity as a whole is called geodynamics. Often, study of Earth's irregular rotation is also included in its definition.

Techniques for studying geodynamic phenomena on the global scale include:

Notable geodesists

Mathematical geodesists before 1900

20th century geodesists

Unlisted

See also

Fundamentals
Governmental agencies
International organizations
Other

References

  1. ^ "geodesy | Definition of geodesy in English by Lexico Dictionaries". Lexico Dictionaries | English. Retrieved 2019-08-15.
  2. ^ "What Is Geodesy". National Ocean Service. Retrieved 8 February 2018.
  3. ^ (ISO 19111: Spatial referencing by coordinates).
  4. ^ "DEFENSE MAPPING AGENCY TECHNICAL REPORT 80-003". Ngs.noaa.gov. Retrieved 8 December 2018.
  5. ^ "Guy Bomford tribute". Bomford.net. Retrieved 8 December 2018.

Further reading

  • F. R. Helmert, Mathematical and Physical Theories of Higher Geodesy, Part 1, ACIC (St. Louis, 1964). This is an English translation of Die mathematischen und physikalischen Theorieen der höheren Geodäsie, Vol 1 (Teubner, Leipzig, 1880).
  • F. R. Helmert, Mathematical and Physical Theories of Higher Geodesy, Part 2, ACIC (St. Louis, 1964). This is an English translation of Die mathematischen und physikalischen Theorieen der höheren Geodäsie, Vol 2 (Teubner, Leipzig, 1884).
  • B. Hofmann-Wellenhof and H. Moritz, Physical Geodesy, Springer-Verlag Wien, 2005. (This text is an updated edition of the 1967 classic by W.A. Heiskanen and H. Moritz).
  • W. Kaula, Theory of Satellite Geodesy : Applications of Satellites to Geodesy, Dover Publications, 2000. (This text is a reprint of the 1966 classic).
  • Vaníček P. and E.J. Krakiwsky, Geodesy: the Concepts, pp. 714, Elsevier, 1986.
  • Torge, W (2001), Geodesy (3rd edition), published by de Gruyter, ISBN 3-11-017072-8.
  • Thomas H. Meyer, Daniel R. Roman, and David B. Zilkoski. "What does height really mean?" (This is a series of four articles published in Surveying and Land Information Science, SaLIS.)

External links

Geodesy at Wikibooks Media related to Geodesy at Wikimedia Commons

Elevation

The elevation of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface (see Geodetic datum § Vertical datum).

The term elevation is mainly used when referring to points on the Earth's surface, while altitude or geopotential height is used for points above the surface, such as an aircraft in flight or a spacecraft in orbit, and depth is used for points below the surface.

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.

Equator

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 the 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 Earth, the equator is about 40,075 km (24,901 mi) long, of which 78.8% lies across water and 21.3% over land. Indonesia is the country straddling the greatest length of the equatorial line across both land and sea.

Faculty of Geodesy, University of Zagreb

The Faculty of Geodesy at the University of Zagreb (Croatian: Geodetski fakultet Sveučilišta u Zagrebu) is the only Croatian institution providing high education in Geomatics engineering and the largest faculty in this domain in southeastern Europe.

Figure of the Earth

Figure of the Earth is a term of art in geodesy that refers to the size and shape used to model Earth. The size and shape it refers to depend on context, including the precision needed for the model. The sphere is an approximation of the figure of the Earth that is satisfactory for many purposes. Several models with greater accuracy have been developed so that coordinate systems can serve the precise needs of navigation, surveying, cadastre, land use, and various other concerns.

Geodetic datum

A geodetic datum or geodetic system (also: geodetic reference datum or geodetic reference system) is a coordinate system, and a set of reference points, used to locate places on the Earth (or similar objects). An approximate definition of sea level is the datum WGS 84, an ellipsoid, whereas a more accurate definition is Earth Gravitational Model 2008 (EGM2008), using at least 2,159 spherical harmonics. Other datums are defined for other areas or at other times; ED50 was defined in 1950 over Europe and differs from WGS 84 by a few hundred meters depending on where in Europe you look.

Mars has no oceans and so no sea level, but at least two martian datums have been used to locate places there.

Datums are used in geodesy, navigation, and surveying by cartographers and satellite navigation systems to translate positions indicated on maps (paper or digital) to their real position on Earth. Each starts with an ellipsoid (stretched sphere), and then defines latitude, longitude and altitude coordinates. One or more locations on the Earth's surface are chosen as anchor "base-points".

The difference in co-ordinates between datums is commonly referred to as datum shift. The datum shift between two particular datums can vary from one place to another within one country or region, and can be anything from zero to hundreds of meters (or several kilometers for some remote islands). The North Pole, South Pole and Equator will be in different positions on different datums, so True North will be slightly different. Different datums use different interpolations for the precise shape and size of the Earth (reference ellipsoids).

Because the Earth is an imperfect ellipsoid, localised datums can give a more accurate representation of the area of coverage than WGS 84. OSGB36, for example, is a better approximation to the geoid covering the British Isles than the global WGS 84 ellipsoid. However, as the benefits of a global system outweigh the greater accuracy, the global WGS 84 datum is becoming increasingly adopted.Horizontal datums are used for describing a point on the Earth's surface, in latitude and longitude or another coordinate system. Vertical datums measure elevations or depths.

Geographic coordinate system

A geographic coordinate system is a coordinate system that enables every location on Earth to be specified by a set of numbers, letters or symbols. The coordinates are often chosen such that one of the numbers represents a vertical position and two or three of the numbers represent a horizontal position; alternatively, a geographic position may be expressed in a combined three-dimensional Cartesian vector.

A common choice of coordinates is latitude, longitude and elevation.

To specify a location on a plane requires a map projection.

Geographical pole

A geographical pole is either of the two points on a rotating body (planet, dwarf planet, natural satellite, sphere...etc.) where its axis of rotation intersects its surface. As with Earth's North and South Poles, they are usually called that body's "north pole" and "south pole", one lying 90 degrees in one direction from the body's equator and the other lying 90 degrees in the opposite direction from the equator.

Every planet has geographical poles. If, like the Earth, a body generates a magnetic field, it will also possess magnetic poles.Perturbations in a body's rotation mean that geographical poles wander slightly on its surface. The Earth's North and South Poles, for example, move by a few metres over periods of a few years. As cartography requires exact and unchanging coordinates, the averaged locations of geographical poles are taken as fixed cartographic poles and become the points where the body's great circles of longitude intersect.

Geoid

The geoid () is the shape that the ocean surface would take under the influence of the gravity and rotation of Earth alone, if other influences such as winds and tides were absent. This surface is extended through the continents (such as with very narrow hypothetical canals). According to Gauss, who first described it, it is the "mathematical figure of the Earth", a smooth but irregular surface whose shape results from the uneven distribution of mass within and on the surface of Earth. It can be known only through extensive gravitational measurements and calculations. Despite being an important concept for almost 200 years in the history of geodesy and geophysics, it has been defined to high precision only since advances in satellite geodesy in the late 20th century.

All points on a geoid surface have the same effective potential (the sum of gravitational potential energy and centrifugal potential energy). The force of gravity acts everywhere perpendicular to the geoid, meaning that plumb lines point perpendicular and water levels parallel to the geoid if only gravity and rotational acceleration were at work. The surface of the geoid is higher than the reference ellipsoid wherever there is a positive gravity anomaly (mass excess) and lower than the reference ellipsoid wherever there is a negative gravity anomaly (mass deficit).

International Union of Geodesy and Geophysics

The International Union of Geodesy and Geophysics (IUGG; French: Union géodésique et géophysique internationale, UGGI) is an international non-governmental organisation dedicated to the scientific study of the Earth and its space environment using geophysical and geodetic techniques.

The IUGG was established in Brussels, Belgium in 1919. Some areas within its scope are environmental preservation, reduction of the effects of natural hazards, and mineral resources.

Irish grid reference system

The Irish grid reference system is a system of geographic grid references used for paper mapping in Ireland (both Northern Ireland and the Republic of Ireland). The Irish grid partially overlaps the British grid, and uses a similar co-ordinate system but with a meridian more suited to its westerly location.

Latitude

In geography, latitude is a geographic coordinate that specifies the north–south position of a point on the Earth's surface. Latitude is an angle (defined below) which ranges from 0° at the Equator to 90° (North or South) at the poles. Lines of constant latitude, or parallels, run east–west as circles parallel to the equator. Latitude is used together with longitude to specify the precise location of features on the surface of the Earth. On its own, the term latitude should be taken to be the geodetic latitude as defined below. Briefly, geodetic latitude at a point is the angle formed by the vector perpendicular (or normal) to the ellipsoidal surface from that point, and the equatorial plane. Also defined are six auxiliary latitudes which are used in special applications.

Metres above sea level

Metres above mean sea level (MAMSL) or simply metres above sea level (MASL or m a.s.l.) is a standard metric measurement in metres of vertical distance (height, elevation or altitude) of a location in reference to a historic mean sea level taken as a vertical datum. Mean sea levels are affected by climate change and other factors and change over time. For this and other reasons, recorded measurements of elevation above sea level might differ from the actual elevation of a given location over sea level at a given moment.

Normalnull

Normalnull ("standard zero") or Normal-Null (short N. N. or NN ) is an outdated official vertical datum used in Germany. Elevations using this reference system were to be marked "Meter über Normal-Null" (“meters above standard zero”). Normalnull has been replaced by Normalhöhennull (short NHN).

Palestine grid

The British Mandate Palestine grid (Arabic: التربيع الفلسطيني) was the geographic coordinate system used in Mandatory Palestine.

The system was chosen by the Survey Department of the Government of Palestine in 1922. The projection used was the Cassini-Soldner projection. The central meridian (the line of longitude along which there is no local distortion) was chosen as that passing through a marker on the hill of Mar Elias Monastery south of Jerusalem. The false origin (zero point) of the grid was placed 100 km to the south and west of the Ali el-Muntar hill that overlooks Gaza city. The unit length for the grid was the kilometre; the British units were not even considered.At the time the grid was established, there was no intention of mapping the lower reaches of the Negev Desert, but this did not remain true. The fact that those southern regions would have negative north-south coordinate then became a source of confusion, which was solved by adding 1000 to the northern coordinate in that case. For some military purposes, 1000 was added to the north-south coordinates of all locations, so that they then ranged uniformly from about 900 to about 1300.

During World War II, a Military Palestine Grid was used that was similar to the Palestine Grid but used the transverse Mercator projection. The difference between the two projections was only a few meters.After the establishment of the State of Israel, the Palestine grid continued to be used under the name of the Israel Grid or the Israeli Cassini Soldner (ICS) grid, now called the "Old Israeli Grid", with 1000km added to the northing component to make the north-south range continuous. It was replaced by the Israeli Transverse Mercator grid in 1994. The Palestine grid is still commonly used to specify locations in the historical and archaeological literature.

Planetary science

Planetary science or, more rarely, planetology, is the scientific study of planets (including Earth), moons, and planetary systems (in particular those of the Solar System) and the processes that form them. It studies objects ranging in size from micrometeoroids to gas giants, aiming to determine their composition, dynamics, formation, interrelations and history. It is a strongly interdisciplinary field, originally growing from astronomy and earth science, but which now incorporates many disciplines, including planetary geology (together with geochemistry and geophysics), cosmochemistry, atmospheric science, oceanography, hydrology, theoretical planetary science, glaciology, and exoplanetology. Allied disciplines include space physics, when concerned with the effects of the Sun on the bodies of the Solar System, and astrobiology.

There are interrelated observational and theoretical branches of planetary science. Observational research can involve a combination of space exploration, predominantly with robotic spacecraft missions using remote sensing, and comparative, experimental work in Earth-based laboratories. The theoretical component involves considerable computer simulation and mathematical modelling.

Planetary scientists are generally located in the astronomy and physics or Earth sciences departments of universities or research centres, though there are several purely planetary science institutes worldwide. There are several major conferences each year, and a wide range of peer-reviewed journals. Some planetary scientists work at private research centres and often initiate partnership research tasks.

Satellite geodesy

Satellite geodesy is geodesy by means of artificial satellites — the measurement of the form and dimensions of Earth, the location of objects on its surface and the figure of the Earth's gravity field by means of artificial satellite techniques. It belongs to the broader field of space geodesy. Traditional astronomical geodesy is not commonly considered a part of satellite geodesy, although there is considerable overlap between the techniques.The main goals of satellite geodesy are:

Determination of the figure of the Earth, positioning, and navigation (geometric satellite geodesy)

Determination of geoid, Earth's gravity field and its temporal variations (dynamical satellite geodesy)

Measurement of geodynamical phenomena, such as crustal dynamics and polar motionSatellite geodetic data and methods can be applied to diverse fields such as navigation, hydrography, oceanography and geophysics. Satellite geodesy relies heavily on orbital mechanics.

Summit

A summit is a point on a surface that is higher in elevation than all points immediately adjacent to it. The topographic terms acme, apex, peak (mountain peak), and zenith are synonymous.

The term top (mountain top) is generally used only for a mountain peak that is located at some distance from the nearest point of higher elevation. For example, a big massive rock then to the main summit of a mountain is not considered a summit. Summits near a higher peak, with some prominence or isolation, but not reaching a certain cutoff value for the quantities, are often considered subsummits (or subpeaks) of the higher peak, and are considered part of the same mountain. A pyramidal peak is an exaggerated form produced by ice erosion of a mountain top. Summit may also refer to the highest point along a line, trail, or route.

The highest summit in the world is Everest with height of 8844.43 m above sea level (29,029 ft). The first official ascent was made by Tenzing Norgay and Sir Edmund Hillary. They reached the mountain's peak in 1953.Whether a highest point is classified as a summit, a sub peak or a separate mountain is subjective. The UIAA definition of a peak is that it has a prominence of 30 metres (98 ft) or more; it is a mountain summit if it has a prominence of at least 300 metres (980 ft). Otherwise, it's a subpeak.

In many parts of the western United States, the term summit refers to the highest point along a road, highway, or railroad. For example, the highest point along Interstate 80 in California is referred to as Donner Summit and the highest point on Interstate 5 is Siskiyou Mountain Summit.

Very-long-baseline interferometry

Very-long-baseline interferometry (VLBI) is a type of astronomical interferometry used in radio astronomy. In VLBI a signal from an astronomical radio source, such as a quasar, is collected at multiple radio telescopes on Earth. The distance between the radio telescopes is then calculated using the time difference between the arrivals of the radio signal at different telescopes. This allows observations of an object that are made simultaneously by many radio telescopes to be combined, emulating a telescope with a size equal to the maximum separation between the telescopes.

Data received at each antenna in the array include arrival times from a local atomic clock, such as a hydrogen maser. At a later time, the data are correlated with data from other antennas that recorded the same radio signal, to produce the resulting image. The resolution achievable using interferometry is proportional to the observing frequency. The VLBI technique enables the distance between telescopes to be much greater than that possible with conventional interferometry, which requires antennas to be physically connected by coaxial cable, waveguide, optical fiber, or other type of transmission line. The greater telescope separations are possible in VLBI due to the development of the closure phase imaging technique by Roger Jennison in the 1950s, allowing VLBI to produce images with superior resolution.VLBI is best known for imaging distant cosmic radio sources, spacecraft tracking, and for applications in astrometry. However, since the VLBI technique measures the time differences between the arrival of radio waves at separate antennas, it can also be used "in reverse" to perform earth rotation studies, map movements of tectonic plates very precisely (within millimetres), and perform other types of geodesy. Using VLBI in this manner requires large numbers of time difference measurements from distant sources (such as quasars) observed with a global network of antennas over a period of time.

World Geodetic System

The World Geodetic System (WGS) is a standard for use in cartography, geodesy, and satellite navigation including GPS. This standard includes the definition of the coordinate system's fundamental and derived constants, the ellipsoidal (normal) Earth Gravitational Model (EGM), a description of the associated World Magnetic Model (WMM), and a current list of local datum transformations.The latest revision is WGS 84 (also known as WGS 1984, EPSG:4326), established in 1984 and last revised in 2004. Earlier schemes included WGS 72, WGS 66, and WGS 60. WGS 84 is the reference coordinate system used by the Global Positioning System.

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