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 height systems that also determine the altitude location of a point on the Earth's surface.
What are coordinates
Coordinates are numeric or alphabetic values that can be used to determine the location of a point on the terrain. As a result, a coordinate system is a set of values of the same type that have the same principle for finding a point or object.
Finding the location of a point 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 on which all subsequent work is based.
Most coordinate systems, as a rule, define the location of a point on a plane limited by only two axes. To determine the position of a pointin 3D space, the height system is also applied. With its help, you can find out the exact location of the desired object.
Briefly about coordinate systems used in geodesy
Coordinate systems define 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.
Basic spatial coordinate systems used in geodesy:
- Geodesics.
- Geographic.
- Polar.
- Rectangular.
- Zonal Gauss-Kruger coordinates.
All systems have their own starting point, values for the location of the object and scope.
Geodetic coordinates
The main figure used to measure geodetic coordinates is the earth 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, it is an ellipsoid that is used instead to determine geodetic coordinates. This makes it easier to perform many calculations to determine the position of the body on the surface.
Geodetic coordinates are defined by three values: geodetic latitude, longitude and altitude.
- Geodetic latitude is an angle whose beginning lies on the plane of the equator, and the end lies at the perpendicular,drawn to the desired point.
- Geodesic longitude is the angle that is measured from the zero meridian to the meridian on which the desired point is located.
- Geodesic height - the value of the normal drawn to the surface of the Earth's rotation ellipsoid from a given point.
Geographic coordinates
To solve high-precision problems of higher geodesy, it is necessary to distinguish between geodetic and geographical coordinates. In the system used in engineering geodesy, such differences, as a rule, are not made due to the small space covered by the work.
To determine geodetic coordinates, an ellipsoid is used as a reference plane, and a geoid is used to determine geographic coordinates. The geoid is a mathematically incorrect figure that is closer to the actual figure of the Earth. Its level surface is taken to be that which is continued under sea level in its calm state.
The geographic coordinate system used in geodesy describes the position of a point in space with three values. The definition of geographic longitude coincides with the geodesic, since the zero meridian, called the Greenwich meridian, will also be the reference point. 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.
Height 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 Unionthe mark from which the heights are determined is the Kronstadt footstock. It is located at the level of the B altic Sea.
Polar coordinates
The polar coordinate system used in geodesy has other nuances of measuring. It is used in small areas of terrain to determine the relative location of a point. The reference point can be any object marked as a source. Thus, using polar coordinates, it is impossible to determine the unambiguous location of a point on the territory of the globe.
Polar coordinates are defined 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, so a radius vector is introduced - the distance from the standing point to the desired object. With these two options, you can determine the location of the point in the local system.
Typically, this coordinate system is used for engineering work carried out on a small area.
Rectangular coordinates
The rectangular coordinate system used in geodesy is also used in small areas of the terrain. The main element of the system is the coordinate axis from which the reference is made. Point coordinates are found as the length of perpendiculars drawn from the abscissa and ordinate axes 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 considered negative. Depending on the signs and quarters, they determine the location of a point in space.
Gauss-Kruger coordinates
The Gauss-Kruger coordinate zonal system is similar to the rectangular one. The difference is that it can be applied to the whole area of the globe, 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 to depict large areas of the Earth on paper. Transferring distortion is considered negligible.
According to this system, the globe is divided by longitude into six-degree zones with the axial meridian in the middle. The equator is in the center along a horizontal line. In total, there are 60 such zones.
zone number.
The X-axis values in Russia are usually positive, while the Y-values can be negative. In order to avoid the minus sign in the values of the abscissa axis, the axial meridian of each zone is conditionally moved 500 meters to the west. Then all coordinates becomepositive.
The coordinate system was proposed by Gauss as possible and calculated mathematically by Krueger in the middle of the twentieth century. Since then, it has been used in geodesy as one of the main ones.
Height system
The systems of coordinates and heights used in geodesy are used to accurately determine the position of a point on the Earth. 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 an excess from the desired point to any other. They are convenient to use for working in the local coordinate system in order to simplify the subsequent processing of the results.
Application of coordinate systems in geodesy
In addition to the above, there are other coordinate systems used in geodesy. Each of them has its own advantages and disadvantages. There are also their own areas of work for which this or that method of determining the location is relevant.
It is the purpose of the work that determines which coordinate systems used in geodesy are best used. For work in small areas, it is convenient to use rectangular and polar coordinate systems, and for solving large-scale problems, systems are needed that allow covering the entire territory of the earth's surface.
