# Coordinate systems for GPS navigators, geographical coordinates. Earth, its shape and coordinates.

As you know, for most of us, the Earth appears in a form close to a ball, but everyone knows that it is not a ball. The difference is very significant for accurate navigation and coordinate system. The complex surface of the Earth was called a geoid in the 19th century. The surface of the geoid coincides with the surface of the seas and oceans in their calm state and virtually continues under the continents.

## Earth, its shape and coordinates.

For practical use, two models of the Earth’s shape are widespread: spherical with a simplified representation of it in the form of a ball with a radius of 6371.1 kilometers and spheroidal in the form of an ellipse of revolution (ellipsoid). By it is meant a geometric figure that is formed when the ellipse rotates around its minor axis. The dimensions of the ellipsoid of revolution, its orientation and location relative to the center of mass of the Earth can vary to achieve the greatest accuracy in approaching the real earth’s surface. It should be understood that each model used also has its own coordinate system.

When we speak of any coordinate system, we also mean the corresponding ellipsoid model. But this is not all the differences that the user of the GPS system needs to know. If the parameters of the ellipsoid are selected for the Earth as a whole, then such an ellipsoid is called the common terrestrial ellipsoid (OZE). In order to describe the local (partial) region of the Earth’s surface, an ellipsoid with other parameters can be used with greater accuracy.

Such an ellipsoid, legally adopted for measuring and processing geodetic data, is called a reference ellipsoid (RE), and the reference coordinate system formed by it. In a reference ellipsoid, its minor axis does not coincide with the axis of rotation of the Earth, but should be parallel to it. In the OZE, the semi-minor axis always coincides with the axis of rotation, and the center of the ellipsoid coincides with the center of mass of the Earth.

In the CIS, two common Earth coordinate systems are used, PZ-90 and International WGS-84 (Wordl Geodetic System 1984). The numbers in the designation of the system indicate the year of its creation. Both systems are close to each other. PZ-90 is used in the CIS for geodetic support of orbital flights, and WGS-84 is used worldwide for processing satellite GPS measurements. Russian reference systems include the SK-42 (Pulkovo) and SK-95 systems. Both systems use the Krasovsky ellipsoid (introduced since 1946) and are used when performing geodetic and cartographic work.

## Coordinate Systems for GPS.

When navigating and using GPS navigators, it is very important to understand that displaying GPS positions on maps with different coordinate systems without recounting them will lead to big errors. Therefore, cartographic programs are used to transfer data, for example, from the WGS-84 system to local coordinate systems. Fortunately, users of portable GPS navigators do not have this problem at all. When using a paper map with a grid in conjunction with a GPS navigator, it is necessary to verify the coincidence of the coordinate systems of the map and the navigator.

If necessary, you can configure the navigator’s coordinate system by setting parameters called datum in it, corresponding to the loaded map, or by choosing a custom datum. The navigator will then perform the coordinate conversion automatically. A datum is a geodetic coordinate system, uniquely determined by the size of its ellipsoid and its position with respect to the center of the earth. The number of different datums, or more simply, the coordinate systems used in world cartography, is more than a hundred. Different datums were proposed in order to get the best approximation of the model they determined to the real Earth’s surface in a given region.

For example, the local North American datum NAD-27 is designed to best represent North America, and the local European datum ED-50 is designed for use in Europe. Local datums cannot be used outside the area for which they were developed. For the convenience of the user of GPS navigators, the parameters of many datums are stored in their memory, which makes it possible to use electronic maps in them from different sources without any difficulties.

On many paper maps, an amendment is indicated for the transition from the map coordinate system to the international WGS-84, in which GPS works. For example, in order to place a point located in the Baltic Sea and Ladoga region, with coordinates according to the WGS-84 system, on a Russian map built in the 1942 Pulkovo Observatory system, you need to shift this point by 0.14 minutes to the east. At the latitude of St. Petersburg This difference corresponds to approximately 130 meters.

## Geographical coordinates.

To determine the position of any object on the surface of the Earth, a system of geographical coordinates and two special points of the poles of the North and South is used. Poles are, as you know, the points of intersection of the axis of rotation of the Earth with the surface of an ellipsoid. Most clearly, the geographical coordinates are represented in a spherical model of the Earth. In it, the geographical coordinates, latitude and longitude, are determined using circles formed at the cross-section of the spherical model of the Earth by planes: for latitude, in the horizontal direction, and for longitude, in the vertical.

The circle EQ, formed on the surface of the ball by a horizontal secant plane perpendicular to the earth’s axis and passing through the center of the ball, is called the equator. It divides the globe into the northern and southern hemispheres. The circles of small circles whose planes are parallel to the equator’s plane form parallels (PP). The circles formed by the planes passing through the earth’s axis are called meridians (geographic or true). Among all the meridians, it is necessary to distinguish the initial (zero) PnGPs, called Greenwich, since it passes through the astronomical observatory in Greenwich (England). This meridian divides the globe into eastern and western hemispheres..

## Geographic latitude.

The geographic latitude of a point on the surface of the terrestrial spheroid is the angle between the equatorial plane and the normal (vertical line) to this surface. For a model of the Earth in the form of a ball, the normal coincides with the Earth’s radius OM, drawn through a given point M to the center of the ball. Latitude is measured by the arc of the meridian (MOT angle) from the equator to the parallel of this point. Latitude takes values ​​in the range from 0 to 90 degrees. If the point is in the northern hemisphere, then the name N (northern) is assigned to latitude, if in the southern – S.

## Geographic longitude.

The geographic longitude of a point is called the dihedral angle between the planes of the initial (zero) meridian and the meridian passing through a given point. So, the longitude of point M is determined by the angle GOL. Longitude is measured by a smaller arc of the equator GL, but, for example, not by a GEQL arc. Longitude counts lead east or west of the initial meridian, from 0 to 180 degrees.

If the point is in the eastern hemisphere, then the longitude is attributed to the name E (eastern), if in the western – W (western). Sometimes, to indicate the hemispheres of a point, +/- signs are used in coordinates. Moreover, the minus sign is attributed to coordinates located in the southern and western hemispheres. The following formats are used for geographic coordinates in GPS navigators:

ddd.mm.ss.s degrees, minutes, seconds,
ddd.dddd degrees, decimal degrees,
ddd.mm.mmm degrees, minutes, decimal minutes.

Based on materials from the book All About GPS Navigators.
Naiman V.S., Samoilov A.E., Ilyin N.R., Sheinis A.I..