To solve most problems in applied sciences, it is necessary to know the location of an object or point, which is determined using one of the accepted coordinate systems. In addition, there are altitude systems that also determine the altitude location of a point on the surface of the Earth.
What are coordinates
Coordinates - numeric or alphabetic values with which you can determine the place where the point is located on the ground. As a result, a coordinate system is a collection of the same type of values that have the same principle of finding a point or object.
Finding a point location is required to solve many practical problems. In a science such as geodesy, determining the location of a point in a given space is the main goal upon which all subsequent work is built.
Most coordinate systems, as a rule, determine 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, a height system is also used. With its help, you can find out the exact location of the desired object.
Briefly about coordinate systems used in surveying
Coordinate systems determine the location of a point on the earth's surface, giving it three values. The principles of their calculation are different for each coordinate system.
The main spatial coordinate systems used in geodesy:
- Geodetic.
- Geographical.
- Polar.
- Rectangular
- The Gauss-Kruger area coordinates.
All systems have their own starting point, values for the location of the object and scope.
Geodetic coordinates
The main figure used to read the geodetic coordinates is the Earth's ellipsoid.
An ellipsoid is a three-dimensional compressed figure that best represents the shape of the globe. Due to the fact that the globe is a mathematically incorrect figure, an ellipsoid is used instead of it to determine the geodetic coordinates. This facilitates the implementation of many calculations to determine the position of the body on the surface.
Geodetic coordinates are determined by three values: geodetic latitude, longitude and height.
- Geodetic latitude is an angle whose beginning lies on the plane of the equator, and the end is at the perpendicular drawn to the desired point.
- Geodetic longitude is the angle that is measured from the zero meridian to the meridian at which the desired point is located.
- Geodesic height - the magnitude of the normal drawn to the surface of the ellipsoid of rotation of the Earth from a given point.
Geographical coordinates
To solve high-precision tasks of higher geodesy, it is necessary to distinguish between geodetic and geographical coordinates. In the system used in engineering surveying, such differences, as a rule, are not made due to the small space covered by the work.
To determine the geodetic coordinates, an ellipsoid is used as a reference plane, and a geoid is used to determine geographic coordinates. A geoid is a mathematically incorrect figure, closer to the actual figure of the Earth. For its level surface, take the one that is continued below sea level in its calm state.
The geographic coordinate system used in surveying describes the position of a point in space with three values. The definition of geographical longitude coincides with the geodetic, since the reference point 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 drawn on the surface of the geoid.
The altitude in the local coordinate system used in geodesy is measured from sea level in its calm state. On the territory of Russia and the countries of the former Union, the mark from which the heights are determined is the Kronstadt footstock. It is located at the level of the Baltic Sea.
Polar coordinates
The polar coordinate system used in surveying has other nuances of measuring. It is used in small areas to determine the relative location of a point. The reference point can be any object marked as the source. Thus, using polar coordinates it is impossible to determine the unambiguous location of a point on the territory of the globe.
The polar coordinates are determined by two quantities: the angle and the 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 standing point to the desired object. Using these two parameters, you can determine the location of a point in the local system.
Typically, this coordinate system is used to perform engineering work carried out on a small area.
Rectangular coordinates
The rectangular coordinate system used in surveying is also used in small areas. The main element of the system is the coordinate axis, from which the reading takes place. The coordinates of the point are found as the length of the perpendiculars drawn from the abscissa and ordinate to the desired point.
The north direction of the X axis and the east of the Y axis are considered positive, while the south and west are negative. Depending on the signs and quarters, the location of a point in space is determined.
Gauss-Krueger coordinates
The coordinate system of the Gauss-Krueger 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 zones, in fact, are the projection of the globe onto a plane. It arose for practical purposes for depicting large tracts of the Earth on paper. Distortions arising from the transfer are considered minor.
According to this system, the globe is divided by longitude into six-degree zones with an axial meridian in the middle. The equator is in the center in a horizontal line. As a result, there are 60 such zones.
Each of the sixty zones has its own system of rectangular coordinates, counted along the ordinate from the axial meridian of X, and along the abscissa from the portion of the Earth’s equator U. To uniquely determine the location on the territory of the entire globe, the zone number is put in front of the values X and Y.
The values of the X axis on the territory of Russia, as a rule, are positive, while the values of Y can be negative. In order to avoid the minus sign in the abscissa axis, the axial meridian of each zone is conventionally transferred to the west for 500 meters. Then all coordinates become positive.
The coordinate system was proposed by Gauss as possible and mathematically calculated by Krueger in the mid-twentieth century. Since then, it has been used in surveying as one of the main ones.
Height system
The coordinate systems and heights used in geodesy are used to accurately determine the position of a point on Earth. Absolute heights are measured from sea level or other surface, taken as the initial one. In addition, there are relative heights. The latter are counted as an excess from the desired point to any other. They are conveniently used to work in the local coordinate system in order to simplify the subsequent processing of the results.
The use of coordinate systems in geodesy
In addition to the above, there are other coordinate systems used in geodesy. Each of them has its advantages and disadvantages. There are also areas of work for which a particular location method is relevant.
It is the purpose of the work that determines which coordinate systems used in surveying are best used. For work in small territories it is convenient to use rectangular and polar coordinate systems, and for solving large-scale tasks, systems are needed that cover the entire territory of the earth's surface.