Geographic coordinates of the city. Determining geographic coordinates and plotting objects on a map using known coordinates
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Lesson questions:
1. Coordinate systems used in topography: geographic, flat rectangular, polar and bipolar coordinates, their essence and use.
Coordinates are called angular and linear quantities (numbers) that determine the position of a point on any surface or in space.
In topography, coordinate systems are used that make it possible to most simply and unambiguously determine the position of points earth's surface both from the results of direct measurements on the ground and using maps. Such systems include geographic, flat rectangular, polar and bipolar coordinates.
Geographical coordinates
(Fig. 1) – angular values: latitude (j) and longitude (L), which determine the position of an object on the earth’s surface relative to the origin of coordinates – the point of intersection of the prime (Greenwich) meridian with the equator. On a map, the geographic grid is indicated by a scale on all sides of the map frame. The western and eastern sides of the frame are meridians, and the northern and southern sides are parallels. In the corners of the map sheet, the geographical coordinates of the intersection points of the sides of the frame are written.
Rice. 1. System of geographical coordinates on the earth's surface |
In the geographic coordinate system, the position of any point on the earth's surface relative to the origin of coordinates is determined in angular measure. In our country and in most other countries, the point of intersection of the prime (Greenwich) meridian with the equator is taken as the beginning. Being thus uniform for our entire planet, the system of geographic coordinates is convenient for solving problems of determining the relative position of objects located at significant distances from each other. Therefore, in military affairs this system is used mainly for conducting calculations related to the use of combat weapons. long range, For example ballistic missiles, aviation, etc.
Plane rectangular coordinates(Fig. 2) - linear quantities that determine the position of an object on a plane relative to the accepted origin of coordinates - the intersection of two mutually perpendicular lines (coordinate axes X and Y).
In topography, each 6-degree zone has its own system of rectangular coordinates. The X axis is the axial meridian of the zone, the Y axis is the equator, and the point of intersection of the axial meridian with the equator is the origin of coordinates.
The plane rectangular coordinate system is zonal; it is established for each six-degree zone into which the Earth’s surface is divided when depicting it on maps in the Gaussian projection, and is intended to indicate the position of images of points of the earth’s surface on a plane (map) in this projection.
The origin of coordinates in a zone is the point of intersection of the axial meridian with the equator, relative to which the position of all other points in the zone is determined in a linear measure. The origin of the zone and its coordinate axes occupy a strictly defined position on the earth's surface. Therefore, the system of flat rectangular coordinates of each zone is connected both with the coordinate systems of all other zones, and with the system of geographical coordinates.
Application linear quantities to determine the position of points makes the system of flat rectangular coordinates very convenient for carrying out calculations both when working on the ground and on the map. Therefore, this system is most widely used among the troops. Rectangular coordinates indicate the position of terrain points, their battle formations and targets, and with their help determine the relative position of objects within one coordinate zone or in adjacent areas of two zones.
Polar and bi systems polar coordinates
are local systems. In military practice, they are used to determine the position of some points relative to others in relatively small areas of the terrain, for example, when designating targets, marking landmarks and targets, drawing up terrain diagrams, etc. These systems can be associated with systems of rectangular and geographic coordinates.
2. Determining geographic coordinates and plotting objects on a map using known coordinates.
The geographic coordinates of a point located on the map are determined from the nearest parallel and meridian, the latitude and longitude of which are known.
Frame topographic map divided into minutes, which are separated by dots into divisions of 10 seconds each. Latitudes are indicated on the sides of the frame, and longitudes are indicated on the northern and southern sides.
Using the minute frame of the map you can:
1
. Determine the geographic coordinates of any point on the map.
For example, the coordinates of point A (Fig. 3). To do this, you need to use a measuring compass to measure shortest distance from point A to the southern frame of the map, then attach the meter to the western frame and determine the number of minutes and seconds in the measured segment, add the resulting (measured) value of minutes and seconds (0"27") with the latitude of the southwestern corner of the frame - 54°30 ".
Latitude points on the map will be equal to: 54°30"+0"27" = 54°30"27".
Longitude is defined similarly.
Using a measuring compass, measure the shortest distance from point A to the western frame of the map, apply the measuring compass to the southern frame, determine the number of minutes and seconds in the measured segment (2"35"), add the resulting (measured) value to the longitude of the southwestern corner frames - 45°00".
Longitude points on the map will be equal to: 45°00"+2"35" = 45°02"35"
2. Plot any point on the map according to the given geographical coordinates.
For example, point B latitude: 54°31 "08", longitude 45°01 "41".
To plot a point in longitude on a map, it is necessary to draw the true meridian through this point, for which you connect the same number of minutes along the northern and southern frames; To plot a point in latitude on a map, it is necessary to draw a parallel through this point, for which you connect the same number of minutes along the western and eastern frames. The intersection of two lines will determine the location of point B.
3. Rectangular coordinate grid on topographic maps and its digitization. Additional grid at the junction of coordinate zones.
The coordinate grid on the map is a grid of squares, formed by lines, parallel coordinate axes zones. Grid lines are drawn through an integer number of kilometers. Therefore, the coordinate grid is also called the kilometer grid, and its lines are kilometer.
On a 1:25000 map, the lines forming the coordinate grid are drawn through 4 cm, that is, through 1 km on the ground, and on maps 1:50000-1:200000 through 2 cm (1.2 and 4 km on the ground, respectively). On a 1:500000 map, only the outputs of the coordinate grid lines are plotted on the inner frame of each sheet every 2 cm (10 km on the ground). If necessary, coordinate lines can be drawn on the map along these outputs.
On topographic maps, the values of the abscissa and ordinate of coordinate lines (Fig. 2) are signed at the exits of the lines outside the inner frame of the sheet and in nine places on each sheet of the map. Full values The abscissa and ordinate in kilometers are signed near the coordinate lines closest to the corners of the map frame and near the intersection of the coordinate lines closest to the northwestern corner. The remaining coordinate lines are abbreviated with two numbers (tens and units of kilometers). The labels near the horizontal grid lines correspond to the distances from the ordinate axis in kilometers.
Labels near the vertical lines indicate the zone number (one or two first digits) and the distance in kilometers (always three digits) from the origin, conventionally moved west of the zone’s axial meridian by 500 km. For example, the signature 6740 means: 6 - zone number, 740 - distance from the conventional origin in kilometers.
On the outer frame there are outputs of coordinate lines ( additional mesh) coordinate system of the adjacent zone.
4. Determination of rectangular coordinates of points. Drawing points on a map according to their coordinates.
Using a coordinate grid using a compass (ruler), you can:
1.
Determine the rectangular coordinates of a point on the map.
For example, points B (Fig. 2).
To do this you need:
- write X - digitization of the bottom kilometer line of the square in which point B is located, i.e. 6657 km;
- measure the perpendicular distance from the bottom kilometer line of the square to point B and, using the linear scale of the map, determine the size of this segment in meters;
- add the measured value of 575 m with the digitization value of the lower kilometer line of the square: X=6657000+575=6657575 m.
The Y ordinate is determined in the same way:
- write down the Y value - digitization of the left vertical line of the square, i.e. 7363;
- measure the perpendicular distance from this line to point B, i.e. 335 m;
- add the measured distance to the Y digitization value of the left vertical line of the square: Y=7363000+335=7363335 m.
2.
Plot the target on the map given coordinates.
For example, point G at coordinates: X=6658725 Y=7362360.
To do this you need:
- find the square in which point G is located according to the value of whole kilometers, i.e. 5862;
- set aside from the lower left corner of the square a segment on the map scale equal to the difference between the abscissa of the target and the bottom side of the square - 725 m;
- - from the obtained point, along the perpendicular to the right, plot a segment equal to the difference between the ordinates of the target and the left side of the square, i.e. 360 m.
The accuracy of determining geographic coordinates using 1:25000-1:200000 maps is about 2 and 10"" respectively.
The accuracy of determining the rectangular coordinates of points from a map is limited not only by its scale, but also by the magnitude of errors allowed when shooting or drawing up a map and drawing it on it. various points and terrain objects
Most accurately (with an error not exceeding 0.2 mm) geodetic points and are plotted on the map. objects that stand out most sharply in the area and are visible from a distance, having the significance of landmarks (individual bell towers, factory chimneys, tower-type buildings). Therefore, the coordinates of such points can be determined with approximately the same accuracy with which they are plotted on the map, i.e. for a map of scale 1:25000 - with an accuracy of 5-7 m, for a map of scale 1:50000 - with an accuracy of 10-15 m, for a map of scale 1:100000 - with an accuracy of 20-30 m.
The remaining landmarks and contour points are plotted on the map, and, therefore, determined from it with an error of up to 0.5 mm, and points related to contours that are not clearly defined on the ground (for example, the contour of a swamp), with an error of up to 1 mm.
6. Determining the position of objects (points) in polar and bipolar coordinate systems, plotting objects on a map by direction and distance, by two angles or by two distances.
System flat polar coordinates(Fig. 3, a) consists of point O - the origin, or poles, and the initial direction of the OR, called polar axis.
System flat bipolar (two-pole) coordinates(Fig. 3, b) consists of two poles A and B and a common axis AB, called the basis or base of the notch. The position of any point M relative to two data on the map (terrain) of points A and B is determined by the coordinates that are measured on the map or on the terrain.
These coordinates can be either two position angles that determine the directions from points A and B to the desired point M, or the distances D1=AM and D2=BM to it. The position angles in this case, as shown in Fig. 1, b, are measured at points A and B or from the direction of the basis (i.e. angle A = BAM and angle B = ABM) or from any other directions passing through points A and B and taken as the initial ones. For example, in the second case, the location of point M is determined by the position angles θ1 and θ2, measured from the direction of the magnetic meridians.
Drawing a detected object on a map
This is one of the most important moments in object detection. The accuracy of determining its coordinates depends on how accurately the object (target) is plotted on the map.
Having discovered an object (target), you must first accurately determine by various signs what has been detected. Then, without stopping observing the object and without detecting yourself, put the object on the map. There are several ways to plot an object on a map.
Visually: A feature is plotted on the map if it is near a known landmark.
By direction and distance: to do this, you need to orient the map, find the point of your standing on it, indicate on the map the direction to the detected object and draw a line to the object from the point of your standing, then determine the distance to the object by measuring this distance on the map and comparing it with the scale of the map.
 Rice. 4. Drawing the target on the map using a straight line |
If it is graphically impossible to solve the problem in this way (the enemy is in the way, poor visibility, etc.), then you need to accurately measure the azimuth to the object, then translate it into a directional angle and draw on the map from the standing point the direction at which to plot the distance to the object. |
7. Methods of target designation on the map: in graphic coordinates, flat rectangular coordinates (full and abbreviated), by kilometer grid squares (up to a whole square, up to 1/4, up to 1/9 square), from a landmark, from a conventional line, in azimuth and target range, in a bipolar coordinate system.
The ability to quickly and correctly indicate targets, landmarks and other objects on the ground has important to control units and fire in battle or to organize combat.
Targeting in geo graphic coordinates
used very rarely and only in cases where targets are distant from given point on the map at a considerable distance, expressed in tens or hundreds of kilometers. In this case, geographic coordinates are determined from the map, as described in question No. 2 of this lesson.
The location of the target (object) is indicated by latitude and longitude, for example, height 245.2 (40° 8" 40" N, 65° 31" 00" E). On the eastern (western), northern (southern) sides of the topographic frame, marks of the target position in latitude and longitude are applied with a compass. From these marks, perpendiculars are lowered into the depth of the topographic map sheet until they intersect (commander’s rulers and standard sheets of paper are applied). The point of intersection of the perpendiculars is the position of the target on the map.
For approximate target designation by rectangular coordinates It is enough to indicate on the map the grid square in which the object is located. The square is always indicated by the numbers of the kilometer lines, the intersection of which forms the southwest (lower left) corner. When indicating the square of the map, the following rule is followed: first they call two numbers signed at the horizontal line (on the western side), that is, the “X” coordinate, and then two numbers at the vertical line (the southern side of the sheet), that is, the “Y” coordinate. In this case, “X” and “Y” are not said. For example, enemy tanks were spotted. When transmitting a report by radiotelephone, the square number is pronounced: "eighty eight zero two."
If the position of a point (object) needs to be determined more accurately, then full or abbreviated coordinates are used.
Work with full coordinates. For example, you need to determine the coordinates of a road sign in square 8803 on a map at a scale of 1:50000. First, determine the distance from the bottom horizontal side of the square to the road sign (for example, 600 m on the ground). In the same way, measure the distance from the left vertical side of the square (for example, 500 m). Now, by digitizing kilometer lines, we determine the full coordinates of the object. The horizontal line has the signature 5988 (X), adding the distance from this line to the road sign, we get: X = 5988600. We define the vertical line in the same way and get 2403500. The full coordinates of the road sign are as follows: X=5988600 m, Y=2403500 m.
Abbreviated coordinates respectively will be equal: X=88600 m, Y=03500 m.
If it is necessary to clarify the position of a target in a square, then target designation is used in an alphabetic or digital way inside the square of a kilometer grid.
During target designation literal way inside the square of the kilometer grid, the square is conditionally divided into 4 parts, each part is assigned capital letter Russian alphabet.
Second way - digital way target designation inside the square kilometer grid (target designation by snail
). This method got its name from the arrangement of conventional digital squares inside the square of the kilometer grid. They are arranged as if in a spiral, with the square divided into 9 parts.
When designating targets in these cases, they name the square in which the target is located, and add a letter or number that specifies the position of the target inside the square. For example, height 51.8 (5863-A) or high-voltage support (5762-2) (see Fig. 2).
Target designation from a landmark is the simplest and most common method of target designation. With this method of target designation, the landmark closest to the target is first named, then the angle between the direction to the landmark and the direction to the target in protractor divisions (measured with binoculars) and the distance to the target in meters. For example: “Landmark two, forty to the right, further two hundred, near a separate bush there is a machine gun.”
Target designation from the conditional line usually used in motion on combat vehicles. With this method, two points are selected on the map in the direction of action and connected by a straight line, relative to which target designation will be carried out. This line is denoted by letters, divided into centimeter divisions and numbered starting from zero. This construction is done on the maps of both transmitting and receiving target designation.
Target designation from a conventional line is usually used in movement on combat vehicles. With this method, two points are selected on the map in the direction of action and connected by a straight line (Fig. 5), relative to which target designation will be carried out. This line is denoted by letters, divided into centimeter divisions and numbered starting from zero.
 Rice. 5. Target designation from the conditional line |
This construction is done on the maps of both transmitting and receiving target designation. |
Target designation from a conventional line can be given by indicating the direction to the target at an angle from the conventional line and the distance to the target, for example: “Straight AC, right 3-40, one thousand two hundred – machine gun.”
Target designation in azimuth and range to the target. The azimuth of the direction to the target is determined using a compass in degrees, and the distance to it is determined using an observation device or by eye in meters. For example: “Azimuth thirty-five, range six hundred—a tank in a trench.”
This method is most often used in areas where there are few landmarks.
8. Problem solving.
Determining the coordinates of terrain points (objects) and target designation on the map is practically practiced educational maps at previously prepared points (marked objects).
Each student determines geographic and rectangular coordinates (maps objects according to known coordinates).
Methods of target designation on the map are being worked out: in flat rectangular coordinates(full and abbreviated), by kilometer grid squares (up to a whole square, up to 1/4, up to 1/9 square), from a landmark, by azimuth and target range.
Notes
Military topography
Military ecology
Military medical training
Engineering training
Fire training
And it allows you to find the exact location of objects on the earth’s surface degree network - a system of parallels and meridians. It serves to determine the geographic coordinates of points on the earth's surface - their longitude and latitude.
Parallels(from Greek parallelos- walking next to) are lines conventionally drawn on the earth's surface parallel to the equator; equator - a line of section of the earth's surface by a depicted plane passing through the center of the Earth perpendicular to its axis of rotation. The longest parallel is the equator; the length of the parallels from the equator to the poles decreases.
Meridians(from lat. meridianus- midday) - lines conventionally drawn on the earth's surface from one pole to another along the shortest path. All meridians are equal in length. All points of a given meridian have the same longitude, and all points of a given parallel have the same latitude.
Rice. 1. Elements of the degree network
Geographic latitude and longitude
Geographic latitude of a point is the magnitude of the meridian arc in degrees from the equator to a given point. It varies from 0° (equator) to 90° (pole). There are northern and southern latitudes, abbreviated as N.W. and S. (Fig. 2).
Any point south of the equator will have a southern latitude, and any point north of the equator will have a northern latitude. Determining the geographic latitude of any point means determining the latitude of the parallel on which it is located. On maps, the latitude of parallels is indicated on the right and left frames.
Rice. 2. Geographical latitude
Geographic longitude of a point is the magnitude of the parallel arc in degrees from the prime meridian to a given point. The prime (prime, or Greenwich) meridian passes through the Greenwich Observatory, located near London. To the east of this meridian the longitude of all points is eastern, to the west - western (Fig. 3). Longitude varies from 0 to 180°.
Rice. 3. Geographical longitude
Determining the geographic longitude of any point means determining the longitude of the meridian on which it is located.
On maps, the longitude of the meridians is indicated on the upper and lower frames, and on the map of the hemispheres - on the equator.
The latitude and longitude of any point on Earth make up its geographical coordinates. Thus, the geographical coordinates of Moscow are 56° N. and 38°E
Geographic coordinates of cities in Russia and CIS countries
| City | Latitude | Longitude |
| Abakan | 53.720976 | 91.44242300000001 |
| Arkhangelsk | 64.539304 | 40.518735 |
| Astana(Kazakhstan) | 71.430564 | 51.128422 |
| Astrakhan | 46.347869 | 48.033574 |
| Barnaul | 53.356132 | 83.74961999999999 |
| Belgorod | 50.597467 | 36.588849 |
| Biysk | 52.541444 | 85.219686 |
| Bishkek (Kyrgyzstan) | 42.871027 | 74.59452 |
| Blagoveshchensk | 50.290658 | 127.527173 |
| Bratsk | 56.151382 | 101.634152 |
| Bryansk | 53.2434 | 34.364198 |
| Velikiy Novgorod | 58.521475 | 31.275475 |
| Vladivostok | 43.134019 | 131.928379 |
| Vladikavkaz | 43.024122 | 44.690476 |
| Vladimir | 56.129042 | 40.40703 |
| Volgograd | 48.707103 | 44.516939 |
| Vologda | 59.220492 | 39.891568 |
| Voronezh | 51.661535 | 39.200287 |
| Grozny | 43.317992 | 45.698197 |
| Donetsk, Ukraine) | 48.015877 | 37.80285 |
| Ekaterinburg | 56.838002 | 60.597295 |
| Ivanovo | 57.000348 | 40.973921 |
| Izhevsk | 56.852775 | 53.211463 |
| Irkutsk | 52.286387 | 104.28066 |
| Kazan | 55.795793 | 49.106585 |
| Kaliningrad | 55.916229 | 37.854467 |
| Kaluga | 54.507014 | 36.252277 |
| Kamensk-Uralsky | 56.414897 | 61.918905 |
| Kemerovo | 55.359594 | 86.08778100000001 |
| Kyiv(Ukraine) | 50.402395 | 30.532690 |
| Kirov | 54.079033 | 34.323163 |
| Komsomolsk-on-Amur | 50.54986 | 137.007867 |
| Korolev | 55.916229 | 37.854467 |
| Kostroma | 57.767683 | 40.926418 |
| Krasnodar | 45.023877 | 38.970157 |
| Krasnoyarsk | 56.008691 | 92.870529 |
| Kursk | 51.730361 | 36.192647 |
| Lipetsk | 52.61022 | 39.594719 |
| Magnitogorsk | 53.411677 | 58.984415 |
| Makhachkala | 42.984913 | 47.504646 |
| Minsk, Belarus) | 53.906077 | 27.554914 |
| Moscow | 55.755773 | 37.617761 |
| Murmansk | 68.96956299999999 | 33.07454 |
| Naberezhnye Chelny | 55.743553 | 52.39582 |
| Nizhny Novgorod | 56.323902 | 44.002267 |
| Nizhny Tagil | 57.910144 | 59.98132 |
| Novokuznetsk | 53.786502 | 87.155205 |
| Novorossiysk | 44.723489 | 37.76866 |
| Novosibirsk | 55.028739 | 82.90692799999999 |
| Norilsk | 69.349039 | 88.201014 |
| Omsk | 54.989342 | 73.368212 |
| Eagle | 52.970306 | 36.063514 |
| Orenburg | 51.76806 | 55.097449 |
| Penza | 53.194546 | 45.019529 |
| Pervouralsk | 56.908099 | 59.942935 |
| Permian | 58.004785 | 56.237654 |
| Prokopyevsk | 53.895355 | 86.744657 |
| Pskov | 57.819365 | 28.331786 |
| Rostov-on-Don | 47.227151 | 39.744972 |
| Rybinsk | 58.13853 | 38.573586 |
| Ryazan | 54.619886 | 39.744954 |
| Samara | 53.195533 | 50.101801 |
| Saint Petersburg | 59.938806 | 30.314278 |
| Saratov | 51.531528 | 46.03582 |
| Sevastopol | 44.616649 | 33.52536 |
| Severodvinsk | 64.55818600000001 | 39.82962 |
| Severodvinsk | 64.558186 | 39.82962 |
| Simferopol | 44.952116 | 34.102411 |
| Sochi | 43.581509 | 39.722882 |
| Stavropol | 45.044502 | 41.969065 |
| Sukhum | 43.015679 | 41.025071 |
| Tambov | 52.721246 | 41.452238 |
| Tashkent (Uzbekistan) | 41.314321 | 69.267295 |
| Tver | 56.859611 | 35.911896 |
| Tolyatti | 53.511311 | 49.418084 |
| Tomsk | 56.495116 | 84.972128 |
| Tula | 54.193033 | 37.617752 |
| Tyumen | 57.153033 | 65.534328 |
| Ulan-Ude | 51.833507 | 107.584125 |
| Ulyanovsk | 54.317002 | 48.402243 |
| Ufa | 54.734768 | 55.957838 |
| Khabarovsk | 48.472584 | 135.057732 |
| Kharkov, Ukraine) | 49.993499 | 36.230376 |
| Cheboksary | 56.1439 | 47.248887 |
| Chelyabinsk | 55.159774 | 61.402455 |
| Mines | 47.708485 | 40.215958 |
| Engels | 51.498891 | 46.125121 |
| Yuzhno-Sakhalinsk | 46.959118 | 142.738068 |
| Yakutsk | 62.027833 | 129.704151 |
| Yaroslavl | 57.626569 | 39.893822 |
For determining latitude It is necessary, using a triangle, to lower the perpendicular from point A to the degree frame onto the line of latitude and read the corresponding degrees, minutes, seconds on the right or left along the latitude scale. φА= φ0+ Δφ
φА=54 0 36 / 00 // +0 0 01 / 40 //= 54 0 37 / 40 //
For determining longitude you need to use a triangle to lower a perpendicular from point A to the degree frame of the line of longitude and read the corresponding degrees, minutes, seconds from above or below.
Determining the rectangular coordinates of a point on the map
The rectangular coordinates of the point (X, Y) on the map are determined in the square of the kilometer grid as follows: 
1. Using a triangle, perpendiculars are lowered from point A to the kilometer grid line X and Y and the values are taken XA=X0+Δ X; UA=U0+Δ U
For example, the coordinates of point A are: XA = 6065 km + 0.55 km = 6065.55 km;
UA = 4311 km + 0.535 km = 4311.535 km. (the coordinate is reduced);
Point A is located in the 4th zone, as indicated by the first digit of the coordinate at given.
9. Measuring the lengths of lines, directional angles and azimuths on the map, determining the angle of inclination of the line specified on the map.
Measuring lengths
To determine on a map the distance between terrain points (objects, objects), using a numerical scale, you need to measure on the map the distance between these points in centimeters and multiply the resulting number by the scale value. 
A small distance is easier to determine using a linear scale. To do this, a measuring compass is sufficient, the solution of which equal to the distance between given points on the map, apply it to a linear scale and take a reading in meters or kilometers. 
To measure curves, the “step” of the measuring compass is set so that it corresponds to an integer number of kilometers, and an integer number of “steps” is plotted on the segment measured on the map. The distance that does not fit into the whole number of “steps” of the measuring compass is determined using a linear scale and added to the resulting number of kilometers.
Measuring directional angles and azimuths on a map
.
We connect points 1 and 2. We measure the angle. The measurement is carried out using a protractor, it is located parallel to the median, then the angle of inclination is reported clockwise.
Determining the angle of inclination of a line specified on the map.
The determination follows exactly the same principle as finding the directional angle.
10. Direct and inverse geodetic problem on a plane. When computationally processing measurements taken on the ground, as well as when designing engineering structures and making calculations to transfer projects into reality, the need arises to solve direct and inverse geodetic problems. Direct geodetic problem . By known coordinates X 1 and at 1 point 1, directional angle 1-2 and distance d 1-2 to point 2 you need to calculate its coordinates X 2 ,at 2 .
|
|
Rice. 3.5. To the solution of direct and inverse geodetic problems |
The coordinates of point 2 are calculated using the formulas (Fig. 3.5): (3.4) where X,atcoordinate increments equal to
(3.5)
Inverse geodetic problem .
By known coordinates X 1 ,at 1 points 1 and X 2 ,at 2 points 2 need to calculate the distance between them d 1-2 and directional angle 1-2. From formulas (3.5) and Fig. 3.5 it is clear that. (3.6) To determine the directional angle 1-2, we use the arctangent function. At the same time, we take into account that computer programs and microcalculators give the main value of the arctangent= 
, lying in the range90+90, while the desired directional anglecan have any value in the range 0360.
The formula for transition from kdepends on coordinate quarter, in which the given direction is located or, in other words, from the signs of the differences y=y 2 y 1 and x=X 2 X 1 (see table 3.1 and figure 3.6). Table 3.1
Rice. 3.6. Directional angles and main arctangent values in the I, II, III and IV quarters
The distance between points is calculated using the formula
(3.6) or in another way - according to the formulas 
(3.7)
In particular, electronic tacheometers are equipped with programs for solving direct and inverse geodetic problems, which makes it possible to directly determine the coordinates of observed points during field measurements and calculate angles and distances for alignment work.
Counted from 0° to 90° on both sides of the equator. The geographic latitude of points lying in the northern hemisphere (northern latitude) is usually considered positive, the latitude of points in southern hemisphere- negative. It is customary to speak of latitudes close to the poles as high, and about those close to the equator - as about low.
Due to the difference in the shape of the Earth from a sphere, the geographic latitude of points differs somewhat from their geocentric latitude, that is, from the angle between the direction to a given point from the center of the Earth and the plane of the equator.
Longitude
Longitude- angle λ between the plane of the meridian passing through a given point and the plane of the initial prime meridian from which longitude is measured. Longitudes from 0° to 180° east of the prime meridian are called eastern, and to the west - western. Eastern longitudes are considered to be positive, western longitudes are considered negative.
Height
To completely determine the position of a point three-dimensional space, a third coordinate is needed - height. The distance to the center of the planet is not used in geography: it is convenient only when describing very deep regions of the planet or, on the contrary, when calculating orbits in space.
Within geographic envelope Usually “height above sea level” is used, measured from the level of the “smoothed” surface - the geoid. Such system of three coordinates turns out to be orthogonal, which simplifies a number of calculations. Altitude above sea level is also convenient because it is related to atmospheric pressure.
Distance from the earth's surface (up or down) is often used to describe a place, however Not serves coordinate
Geographic coordinate system
The main disadvantage in practical application GSK in navigation is large quantities angular velocity of this system at high latitudes, increasing to infinity at the pole. Therefore, instead of the GSK, a semi-free CS in azimuth is used.
Semi-free in azimuth coordinate system
The azimuth-semi-free CS differs from the GSK in only one equation, which has the form:
Accordingly, the system also has the initial position that the GCS and their orientation also coincide with the only difference that its axes and are deviated from the corresponding axes of the GCS by an angle for which the equation is valid
The conversion between the GSK and the semi-free CS in azimuth is carried out according to the formula
In reality, all calculations are carried out in this system, and then, to produce output information, the coordinates are converted into the GSK.
Geographic coordinate recording formats
The WGS84 system is used to record geographic coordinates.
Coordinates (latitude from -90° to +90°, longitude from -180° to +180°) can be written:
- in ° degrees as a decimal (modern version)
- in ° degrees and "minutes s decimal
- in ° degrees, "minutes and" seconds with decimal fraction (historical form of notation)
The decimal separator is always a dot. Positive coordinate signs are represented by a (in most cases omitted) "+" sign, or by the letters: "N" - north latitude and "E" - east longitude. Negative coordinate signs are represented either by a “-” sign or by the letters: “S” is south latitude and “W” is west longitude. Letters can be placed either in front or behind.
There are no uniform rules for recording coordinates.
On the maps search engines By default, coordinates are shown in degrees with decimal fractions, with “-” signs for negative longitude. On Google maps and Yandex maps, first latitude, then longitude (until October 2012, Yandex maps adopted reverse order: first longitude, then latitude). These coordinates are visible, for example, when plotting routes from arbitrary points. Other formats are also recognized when searching.
In navigators, by default, degrees and minutes with a decimal fraction with a letter designation are often shown, for example, in Navitel, in iGO. You can enter coordinates in accordance with other formats. The degrees and minutes format is also recommended for maritime radio communications.
At the same time, the original method of recording with degrees, minutes and seconds is often used. Currently, coordinates can be written in one of many ways or duplicated in two main ways (with degrees and with degrees, minutes and seconds). As an example, options for recording the coordinates of the sign “Zero kilometer of highways of the Russian Federation” - 55.755831 , 37.617673 55°45′20.99″ n. w. 37°37′03.62″ E. d. / 55.755831 , 37.617673 (G) (O) (I):
- 55.755831°, 37.617673° -- degrees
- N55.755831°, E37.617673° -- degrees (+ additional letters)
- 55°45.35"N, 37°37.06"E -- degrees and minutes (+ additional letters)
- 55°45"20.9916"N, 37°37"3.6228"E -- degrees, minutes and seconds (+ additional letters)
Links
- Geographic coordinates of all cities on Earth (English)
- Geographic coordinates of populated areas on Earth (1) (English)
- Geographic coordinates of populated areas on Earth (2) (English)
- Converting coordinates from degrees to degrees/minutes, to degrees/minutes/seconds and back
- Converting coordinates from degrees to degrees/minutes/seconds and back
see also
Notes
Wikimedia Foundation. 2010.
See what “Geographic coordinates” are in other dictionaries:
See Coordinates. Mountain encyclopedia. M.: Soviet encyclopedia. Edited by E. A. Kozlovsky. 1984 1991 … Geological encyclopedia
- (latitude and longitude), determine the position of a point on the earth’s surface. Geographic latitude j is the angle between the plumb line at a given point and the plane of the equator, measured from 0 to 90 latitude on both sides of the equator. Geographical longitude l angle… … Modern encyclopedia
Latitude and longitude determine the position of a point on the earth's surface. Geographic latitude? the angle between the plumb line at a given point and the plane of the equator, measured from 0 to 90. in both directions from the equator. Geographic longitude? angle between... ... Big Encyclopedic Dictionary
Angular quantities that determine the position of a point on the Earth’s surface: latitude – the angle between the plumb line at a given point and the plane earth's equator, counted from 0 to 90° (north of the equator is northern latitude and to the south is southern latitude); longitude... ...Nautical Dictionary
Video lesson “Geographical latitude and geographic longitude. Geographic Coordinates" will help you get an idea of geographic latitude and geographic longitude. The teacher will tell you how to correctly determine geographic coordinates.
Geographic latitude- arc length in degrees from the equator to a given point.
To determine the latitude of an object, you need to find the parallel on which this object is located.
For example, the latitude of Moscow is 55 degrees and 45 minutes north latitude, it is written like this: Moscow 55°45" N; latitude of New York - 40°43" N; Sydney - 33°52" S
Geographic longitude is determined by meridians. Longitude can be western (from the 0 meridian to the west to the 180 meridian) and eastern (from the 0 meridian to the east to the 180 meridian). Longitude values are measured in degrees and minutes. Geographic longitude can have values from 0 to 180 degrees.
Geographic longitude- length of the equatorial arc in degrees from the prime meridian (0 degrees) to the meridian of a given point.
The prime meridian is considered to be the Greenwich meridian (0 degrees).
Rice. 2. Determination of longitudes ()
To determine longitude, you need to find the meridian on which a given object is located.
For example, the longitude of Moscow is 37 degrees and 37 minutes east longitude, it is written like this: 37°37" east; the longitude of Mexico City is 99°08" west.
Rice. 3. Geographical latitude and geographic longitude
For precise definition To locate an object on the surface of the Earth, you need to know its geographic latitude and geographic longitude.
Geographical coordinates- quantities that determine the position of a point on the earth’s surface using latitudes and longitudes.
For example, Moscow has the following geographic coordinates: 55°45"N and 37°37"E. The city of Beijing has the following coordinates: 39°56′ N. 116°24′ E First the latitude value is recorded.
Sometimes you need to find an object at already given coordinates; to do this, you must first guess in which hemispheres the object is located.
Homework
Paragraphs 12, 13.
1. What is geographic latitude and longitude?
Bibliography
Main
1. Basic course in geography: Textbook. for 6th grade. general education institutions / T.P. Gerasimova, N.P. Neklyukova. - 10th ed., stereotype. - M.: Bustard, 2010. - 176 p.
2. Geography. 6th grade: atlas. - 3rd ed., stereotype. - M.: Bustard, DIK, 2011. - 32 p.
3. Geography. 6th grade: atlas. - 4th ed., stereotype. - M.: Bustard, DIK, 2013. - 32 p.
4. Geography. 6th grade: cont. cards. - M.: DIK, Bustard, 2012. - 16 p.
Encyclopedias, dictionaries, reference books and statistical collections
1. Geography. Modern illustrated encyclopedia / A.P. Gorkin. - M.: Rosman-Press, 2006. - 624 p.
Literature for preparing for the State Exam and the Unified State Exam
1. Geography: initial course. Tests. Textbook manual for 6th grade students. - M.: Humanite. ed. VLADOS center, 2011. - 144 p.
2. Tests. Geography. 6-10 grades: Educational and methodological manual/ A.A. Letyagin. - M.: LLC "Agency "KRPA "Olympus": "Astrel", "AST", 2001. - 284 p.
Materials on the Internet
1. Federal Institute pedagogical measurements ().
2. Russian Geographical Society ().
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