Meridian arcIn geodesy and navigation, a meridian arc is the curve between two points on the Earth's surface having the same longitude. The term may refer either to a segment of the meridian, or to its length. The purpose of measuring meridian arcs is to determine a figure of the Earth. One or more measurements of meridian arcs can be used to infer the shape of the reference ellipsoid that best approximates the geoid in the region of the measurements.
History of geodesyThe history of geodesy deals with the historical development of measurements and representations of the Earth. The corresponding scientific discipline, geodesy (/dʒiːˈɒdɪsi/), began in pre-scientific antiquity and blossomed during the Age of Enlightenment. Early ideas about the figure of the Earth held the Earth to be flat (see flat Earth) and the heavens a physical dome spanning over it. Two early arguments for a spherical Earth were that lunar eclipses were seen as circular shadows and that Polaris is seen lower in the sky as one travels South.
Figure of the EarthFigure 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. A sphere is a well-known historical approximation of the figure of the Earth that is satisfactory for many purposes. Several models with greater accuracy (including ellipsoid) have been developed so that coordinate systems can serve the precise needs of navigation, surveying, cadastre, land use, and various other concerns.
Earth ellipsoidAn Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations. It is a spheroid (an ellipsoid of revolution) whose minor axis (shorter diameter), which connects the geographical North Pole and South Pole, is approximately aligned with the Earth's axis of rotation.
Earth radiusEarth radius (denoted as R🜨 or ) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly (equatorial radius, denoted a) to a minimum of nearly (polar radius, denoted b). A nominal Earth radius is sometimes used as a unit of measurement in astronomy and geophysics, which is recommended by the International Astronomical Union to be the equatorial value. A globally-average value is usually considered to be with a 0.
Spherical EarthSpherical Earth or Earth's curvature refers to the approximation of figure of the Earth as a sphere. The earliest documented mention of the concept dates from around the 5th century BC, when it appears in the writings of Greek philosophers. In the 3rd century BC, Hellenistic astronomy established the roughly spherical shape of Earth as a physical fact and calculated the Earth's circumference. This knowledge was gradually adopted throughout the Old World during Late Antiquity and the Middle Ages.
Paris meridianThe Paris meridian is a meridian line running through the Paris Observatory in Paris, France – now longitude 2°20′14.02500′′ East. It was a long-standing rival to the Greenwich meridian as the prime meridian of the world. The "Paris meridian arc" or "French meridian arc" (French: la Méridienne de France) is the name of the meridian arc measured along the Paris meridian. The French meridian arc was important for French cartography, inasmuch as the triangulations of France began with the measurement of the French meridian arc.
ZenithThe zenith (ˈzɛnɪθ, ˈziːnɪθ) is an imaginary point directly "above" a particular location, on the celestial sphere. "Above" means in the vertical direction (plumb line) opposite to the gravity direction at that location (nadir). The zenith is the "highest" point on the celestial sphere. The word zenith derives from an inaccurate reading of the Arabic expression سمت الرأس (), meaning "direction of the head" or "path above the head", by Medieval Latin scribes in the Middle Ages (during the 14th century), possibly through Old Spanish.
Vertical deflectionThe vertical deflection (VD) or deflection of the vertical (DoV), also known as deflection of the plumb line and astro-geodetic deflection, is a measure of how far the gravity direction at a given point of interest is rotated by local mass anomalies such as nearby mountains. They are widely used in geodesy, for surveying networks and for geophysical purposes. The vertical deflection are the angular components between the true zenith–nadir curve (plumb line) tangent line and the normal vector to the surface of the reference ellipsoid (chosen to approximate the Earth's sea-level surface).
Geographical distanceGeographical distance or geodetic distance is the distance measured along the surface of the earth. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude. This distance is an element in solving the second (inverse) geodetic problem. Calculating the distance between geographical coordinates is based on some level of abstraction; it does not provide an exact distance, which is unattainable if one attempted to account for every irregularity in the surface of the earth.
