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Category# Geodesy

Summary

Geodesy is the science of measuring and representing the geometry, gravity, and spatial orientation of the Earth in temporally varying 3D. It is called planetary geodesy when studying other astronomical bodies, such as planets or circumplanetary systems.
Geodynamical phenomena, including crustal motion, tides, and polar motion, can be studied by designing global and national control networks, applying space geodesy and terrestrial geodetic techniques, and relying on datums and coordinate systems. The job titles are geodesist and geodetic surveyor.
History of geodesy
Geodesy began in pre-scientific antiquity, so the very word geodesy comes from the Ancient Greek word γεωδαισία or geodaisia (literally, "division of Earth").
Early ideas about the figure of the Earth held the Earth to be flat and the heavens a physical dome spanning over it. Two early arguments for a spherical Earth were that lunar eclipses appear to an observer as circular shadows and that Polaris appears lower and lower in the sky to a traveler headed South.
In the English-speaking world, geodesy refers to the science of measuring and representing geospatial information, while geomatics encompasses practical applications of geodesy on local and regional scales, including surveying.
Geodesy in the German-speaking world consists of higher geodesy (höhere Geodäsie or Erdmessung, literally "geomensuration") — concerned with measuring Earth on the global scale, and practical geodesy or engineering geodesy (Ingenieurgeodäsie) that includes surveying — measuring parts or regions of Earth.
For the longest time, geodesy was the science of measuring and understanding Earth's geometric shape, orientation in space, and gravitational field; however, geodetic science and operations are applied to other astronomical bodies in our Solar System also.
To a large extent, Earth's shape is the result of rotation, which causes its equatorial bulge, and the competition of geological processes such as the collision of plates, as well as of volcanism, resisted by Earth's gravitational field.

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Solar zenith angle

The solar zenith angle is the zenith angle of the sun, i.e., the angle between the sun’s rays and the vertical direction. It is the complement to the solar altitude or solar elevation, which is the altitude angle or elevation angle between the sun’s rays and a horizontal plane. At solar noon, the zenith angle is at a minimum and is equal to latitude minus solar declination angle. This is the basis by which ancient mariners navigated the oceans.

Gravimetry

Gravimetry is the measurement of the strength of a gravitational field. Gravimetry may be used when either the magnitude of a gravitational field or the properties of matter responsible for its creation are of interest. Gravity is usually measured in units of acceleration. In the SI system of units, the standard unit of acceleration is 1 metre per second squared (abbreviated as m/s2). Other units include the cgs gal (sometimes known as a galileo, in either case with symbol Gal), which equals 1 centimetre per second squared, and the g (gn), equal to 9.

Flat Earth

Flat Earth is an archaic and scientifically disproven conception of the Earth's shape as a plane or disk. Many ancient cultures subscribed to a flat-Earth cosmography. The idea of a spherical Earth appeared in ancient Greek philosophy with Pythagoras (6th century BC). However, most pre-Socratics (6th–5th century BC) retained the flat-Earth model. In the early 4th century BC, Plato wrote about a spherical Earth. By about 330 BC, his former student Aristotle had provided strong empirical evidence for a spherical Earth.

Explores additional transformations between geocentric and geodetic systems, map projections, and vertical reference systems.

Covers advanced physics topics related to Earth dynamics and the Foucault pendulum experiment.

Explores the geoid, gravity conditions, geoid elevation, and reference systems.

Using an algebraic formalism based on matrices in SL(2,R), we explicitly give the Teichmüller spaces of Riemann surfaces of signature (0,4) (X pieces), (1,2) ("Fish" pieces) and (2,0) in trace coordinates. The approach, based upon gluing together two building blocks (Q and Y pieces), is then extended to tree-like pants decomposition for higher signatures (g,n) and limit cases such as surfaces with cusps or cone-like singularities. Given the Teichmüller spaces, we establish a set of generators of their modular groups for signatures (0,4), (1,2) and (2,0) in trace coordinates using transformations acting separately on the building blocks and an algorithm on dividing geodesics. The fact that these generators act particularly nice in trace coordinates gives further motivation to this choice (rather then the one of Fenchel-Nielsen coordinates). This allows us to solve the Riemann moduli problem for X pieces, "Fish" pieces and surfaces of genus 2; i.e. to give the moduli spaces as the fundamental domains for the action of the modular groups on the Teichmüller spaces. In this context, we also give an algorithm deciding whether two Riemann surfaces of signatures (0,4), (1,2) or (2,0) given by points in the Teichmüller space are isometric or not. As a consequence, we show the following two results concerning simple closed geodesics: On any purely hyperbolic Riemann surface (containing neither cusps nor cone-like singularities), the longest of two simple closed geodesics that intersect one another n times is of length at least ln, a sharp constant independent of the surface. We explicitly give ln for n = 1,2,3 and study its behaviour when n goes to infinity. X pieces are spectrally rigid with respect to the length spectrum of simple closed geodesics.

Observational astronomy

Observational astronomy is a division of astronomy that is concerned with recording data about the observable universe, in contrast with theoretical astronomy, which is mainly concerned with calculating the measurable implications of physical models. It is the practice and study of observing celestial objects with the use of telescopes and other astronomical instruments. As a science, the study of astronomy is somewhat hindered in that direct experiments with the properties of the distant universe are not possible.

Euclidean geometry

Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems.

Atmosphere

An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A stellar atmosphere is the outer region of a star, which includes the layers above the opaque photosphere; stars of low temperature might have outer atmospheres containing compound molecules. The atmosphere of Earth is composed of nitrogen (78 %), oxygen (21 %), argon (0.