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Coordinate systems used in geodesy and topography

To solve most problems in applied sciencesyou need to know the location of the object or point, which is determined by using one of the adopted coordinate systems. In addition, there are elevation systems that also determine the high-altitude location of a point on the surface of the Earth.

What are coordinates

Coordinates - numeric or alphabetic values, withusing which you can determine the place where the point is located on the ground. As a result, the coordinate system is a set of similar values ​​having the same principle of finding a point or object.

Нахождение местоположения точки требуется для solving many practical problems. In such a science as geodesy, locating a point in a given space is the main goal, on the achievement of which all subsequent work is built.

coordinate systems used in geodesy

Most coordinate systems tend to bedetermine the location of a point on a plane bounded by only two axes. In order to determine the position of a point in three-dimensional space, the system of heights is also used. With its help you can find out the exact location of the desired object.

Briefly about the coordinate systems used in geodesy

Coordinate systems determine the location of a point on the earth’s surface by giving it three values. The principles of their calculation are different for each coordinate system.

what coordinate systems are used in geodesy

The main spatial coordinate systems used in geodesy:

  1. Geodesic.
  2. Geographical.
  3. Polar
  4. Rectangular.
  5. Zonal coordinates of Gauss-Kruger.

All systems have their starting point, values ​​for the location of the object and application.

Geodetic coordinates

The main figure used for reference geodetic coordinates, is the terrestrial ellipsoid.

An ellipsoid is a three-dimensional compressed figure thatthe best way is the figure of the globe. Due to the fact that the globe is a mathematically irregular figure, instead of it, it is the ellipsoid that is used to determine the geodetic coordinates. This facilitates the implementation of many calculations to determine the position of the body on the surface.

coordinate systems used in engineering geodesy

Geodetic coordinates are determined by three values: geodetic latitude, longitude and height.

  1. Geodesic latitude is the angle, the beginning of which lies on the equatorial plane, and the end is at the perpendicular to the desired point.
  2. Geodetic longitude is the angle that is measured from the zero meridian to the meridian on which the desired point is located.
  3. Geodesic height is the magnitude of the normal drawn to the surface of the ellipsoid of Earth's rotation from a given point.

Geographical coordinates

Для решения высокоточных задач высшей геодезии it is necessary to distinguish between geodetic and geographic coordinates. In the system used in engineering geodesy, such differences, due to the small space covered by the work, as a rule, do not.

Для определения геодезических координат в the ellipsoid is used as the reference plane, and the geoid is used to determine the geographical. A geoid is a mathematically irregular figure, more close to the actual figure of the Earth. For its flattened surface, they take the one that is continued below sea level in its calm state.

coordinate systems and heights used in geodesy

The geographical coordinate system used ingeodesy, describes the position of a point in space with the indication of three values. The definition of geographic longitude coincides with the geodesic, since the point of reference will also be the zero meridian, called Greenwich. It passes through the observatory of the same name in the city of London. Geographic latitude is determined from the equator, held on the surface of the geoid.

Высота в системе местных координат, применяемой в geodesy, measured from sea level in its calm state. On the territory of Russia and the countries of the former Soviet Union, the mark from which heights are determined is the Kronstadt tide gauge. It is located at the level of the Baltic Sea.

Polar coordinates

Полярная система координат, применяемая в geodesy, has other nuances of the work of measurement. It is used on small areas to determine the relative location of the point. The starting point can be any object marked as the original. Thus, using the polar coordinates it is impossible to determine the unique location of a point on the territory of the globe.

coordinate systems used in geodesy briefly

Polar coordinates are determined by two values:angle and distance. The angle is measured from the north direction of the meridian to a given point, determining its position in space. But one angle will not be enough; therefore, a radius vector is introduced — the distance from the point of standing to the desired object. Using these two parameters, you can locate a point in the local system.

As a rule, this coordinate system is used to perform engineering work carried out on a small portion of the terrain.

Rectangular coordinates

The rectangular coordinate system used inGeodesy, also used in small areas of terrain. The main element of the system is the coordinate axis from which the readout originates. The coordinates of the point are the length of the perpendiculars drawn from the abscissa and ordinate axes to the desired point.

local coordinate systems used in geodesy

The north direction of the X axis and the east Y axis are considered positive, while the south and west axes are considered negative. Depending on the signs and quarters determine the location of a point in space.

Gauss-Kruger coordinates

The Gauss-Kruger zonal coordinate system is similar to a rectangular one. The difference is that it can be applied to the entire territory of the globe, and not just to small areas.

The rectangular coordinates of the Gauss-Kruger zonesEssentially, they are a projection of the globe onto a plane. It originated for practical purposes for the image of large areas of the Earth on paper. Distortions arising from the transfer are considered insignificant.

According to this system, the globe is divided in longitude into six-degree zones with an axial meridian in the middle. The equator is in the center of the horizontal line. As a result, there are 60 such zones.

spatial coordinate systems used in geodesy

Each of the sixty zones has its ownthe system of rectangular coordinates, measured on the ordinate axis from the axial meridian X, and on the abscissa axis - from the portion of the Earth's equator, U. To uniquely determine the location in the entire globe, before the values ​​X and Y put the zone number.

Значения оси Х на территории России, как правило, are positive, while Y values ​​may be negative. In order to avoid the minus sign in the values ​​of the abscissa axis, the axial meridian of each zone is conventionally transferred 500 meters to the west. Then all the coordinates become positive.

The coordinate system was proposed by Gauss as possible and calculated mathematically by Kruger in the middle of the twentieth century. Since then, it has been used in geodesy as one of the main ones.

Elevation system

Системы координат и высот, применяемые в geodesies are used to accurately determine the position of a point on the Earth’s territory. Absolute heights are measured from sea level or other surface taken as the original. In addition, there are relative heights. The latter are counted as the excess from the desired point to any other. They are conveniently used for work in the local coordinate system in order to simplify the subsequent processing of the results.

Application of coordinate systems in geodesy

Помимо вышеперечисленных, имеются и другие coordinate systems used in geodesy. Each of them has its advantages and disadvantages. There are also areas of work for which this or that method of positioning is relevant.

It is the purpose of the work that determines which systemscoordinates used in geodesy, it is better to use. To work in small areas, it is convenient to use a rectangular and polar coordinate systems, and for solving large-scale tasks, systems are needed to cover the entire territory of the earth's surface.

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