home

Geographic latitude and longitude. Determining geographic latitude from astronomical observations

Determining geographic latitude from astronomical observations

The abstract was completed by Belaya Ekaterina

11th grade

Determination of geographic latitude in ancient times. In ancient times, and especially in the era of the great geographical discoveries, determining the coordinates of a place was a necessary and priority task. Each ship had an astronomer who, with the help of the simplest instruments, was able to determine the latitude and longitude of the ship's location.

For a long time, a Jacobs scale was used to determine the coordinates - a tool that is a long graduated bar equipped with a shorter movable transverse bar. When sighting, it was necessary to put the end of the bar to the eye, and move the transverse bar until its lower end touches the horizon, and the upper one touches a given star or the Sun. Thus, the height of the luminary was determined, and with its help, the latitude of the place and time. The Jacobs staff was used until the middle of the 18th century, until it was replaced by a mirror sextant - an astronomical goniometer consisting of a telescope, two mirrors, filters and a scale. The sextant was so important to navigators that it was even placed in the sky, calling this word a constellation.

The system of geographic coordinates on the surface of the Earth. The globe is divided by the plane of the equator into two equal hemispheres - Northern and Southern. The plane of the equator is perpendicular to the Earth's axis of rotation. The axis of rotation intersects with the earth's surface at the North and South Poles of the Earth.

If you mentally cross the globe with planes parallel to the equator, you get circles - parallels. The globe can be mentally crossed by planes perpendicular to the equator and passing through the earth's axis, which are called meridian planes, and the lines formed by their intersection with the surface of the globe are called meridians. Any point on the surface of the globe can be given two coordinates. One coordinate is called longitude and is measured from the zero, conventionally accepted meridian passing through the Greenwich Observatory. The second coordinate is called latitude and is measured from the earth's equator to the poles.

The height of the world pole above the horizon. The height of the world pole above the horizon h p =ÐPCN, and the geographical latitude of the place j=ÐCOR. These two angles (ÐPCN and ÐCOR) are equal as angles with mutually perpendicular sides: [OC]^ ,^. The equality of these angles gives the simplest way to determine the geographic latitude of the area j: the angular distance of the celestial pole from the horizon is equal to the geographic latitude of the area. To determine the geographic latitude of the area, it is enough to measure the height of the celestial pole above the horizon, since:

Daily movement of luminaries at different latitudes. With a change in the geographical latitude of the place of observation, the orientation of the axis of rotation of the celestial sphere relative to the horizon changes. It is necessary to consider what will be the apparent movements of celestial bodies in the region of the North Pole, at the equator and at the middle latitudes of the Earth.

At the Earth's pole, the celestial pole is at its zenith, and the stars move in circles parallel to the horizon. Here the stars do not set and do not rise, their height above the horizon is unchanged.

At middle geographic latitudes, there are both rising and setting stars, as well as those that never sink below the horizon. For example, circumpolar constellations at the geographic latitudes of the USSR never set. Constellations farther from the north celestial pole appear briefly above the horizon. And the constellations lying near the south pole of the world are non-ascending.

To an observer at the equator, all stars rise and set perpendicular to the horizon plane. Each star here passes over the horizon exactly half of its path. The north pole of the world for him coincides with the point of the north, and the south pole of the world coincides with the point of the south. The axis of the world is located in the plane of the horizon.

The height of the luminaries at the climax. The pole of the world, with the apparent rotation of the sky, reflecting the rotation of the earth around its axis, occupies a constant position above the horizon at a given latitude. During the day, the stars describe circles above the horizon around the axis of the world, parallel to the celestial equator. At the same time, each luminary crosses the celestial meridian twice a day.

The phenomena of the passage of luminaries through the celestial meridian are called climaxes. In the upper climax, the height of the luminary is maximum, in the lower culmination - minimal. The time interval between climaxes is equal to half a day.

Both climaxes are visible for the luminary M, which does not set at a given latitude j, for the stars that rise and set, the lower culmination occurs under the horizon, below the north point. At the luminary M 4, located far to the south of the celestial equator, both climaxes can be invisible.

The moment of the upper culmination of the center of the Sun is called true noon, and the moment of the lower climax is called true midnight.

Let us find the relationship between the height h of the luminary M at the upper culmination, its declination d and the latitude of the area j. ZZ / - plumb line, PP / - axis of the world, QQ / - projection of the celestial equator, NS - horizon line on the plane of the celestial meridian (PZSP / N).

The height of the world pole above the horizon is equal to the geographical latitude of the place, i.e. h p = j. Consequently, the angle between the noon line NS and the axis of the world PP / is equal to the latitude of the area j, i.e. ÐPON=h p = j. Obviously, the inclination of the plane of the celestial equator to the horizon, measured by ÐQOS, will be equal to 90 0 - j, since ÐQOZ=ÐPON as angles with mutually perpendicular sides. Then the star M with declination d, culminating south of the zenith, has a height at the upper culmination

h \u003d 90 o - j + d.

From this formula it can be seen that the geographical latitude can be determined by measuring the height of any luminary with a known declination d at the upper climax. In this case, it should be borne in mind that if the luminary at the moment of climax is located south of the equator, then its declination is negative.

Determining geographic latitude from astronomical observations

For a long time, a Jacobs scale was used to determine the coordinates - a tool that is a long graduated bar equipped with a shorter movable transverse bar. When sighting, it was necessary to put the end of the bar to the eye, and move the transverse bar until its lower end touches the horizon, and the upper one touches a given star or the Sun. Thus, the height of the luminary was determined, and with its help - the latitude of the place and time. The Jacobs staff was used until the middle of the 18th century, until it was supplanted by the mirror sextant, an astronomical goniometer consisting of a telescope, two mirrors, light filters and a scale. The sextant was so important to navigators that it was even placed in the sky, calling this word a constellation.

The height of the world pole above the horizon. The height of the celestial pole above the horizon is hp = PCN, and the geographical latitude of the place = COR. These two angles (PCN and COR) are equal as angles with mutually perpendicular sides: [OS] ,. The equality of these angles gives the simplest way to determine the geographic latitude of the area: the angular distance of the celestial pole from the horizon is equal to the geographic latitude of the area. To determine the geographic latitude of the area, it is enough to measure the height of the celestial pole above the horizon, since:

To an observer at the equator, all stars rise and set perpendicular to the horizon plane. Each star here passes over the horizon exactly half of its path. The north pole of the world for him coincides with the point of the north, and the south pole of the world - with the point of the south. The axis of the world is located in the plane of the horizon.

The height of the luminaries at the climax. The pole of the world, with the apparent rotation of the sky, reflecting the rotation of the earth around its axis, occupies a constant position above the horizon at a given latitude. During the day, the stars describe circles above the horizon around the axis of the world, parallel to the celestial equator. At the same time, each luminary crosses the celestial meridian twice a day.

Both climaxes are visible for the luminary M, which does not set at a given latitude, for stars that rise and set, the lower culmination occurs under the horizon, below the north point. At the luminary M4, located far to the south of the celestial equator, both climaxes may be invisible.

The moment of the upper climax of the center of the Sun is called true noon, and the moment of the lower climax is called true midnight.

Let us find the relationship between the height h of the luminary M at the upper culmination, its declination and the latitude of the area. ZZ/ - plumb line, PP/ - axis of the world, QQ/ - projection of the celestial equator, NS - horizon line on the plane of the celestial meridian (PZSP/N).

The height of the world pole above the horizon is equal to the geographical latitude of the place, i.e. hp=. Consequently, the angle between the noon line NS and the world axis PP/ is equal to the latitude of the area, i.e. PON=hp= . Obviously, the inclination of the plane of the celestial equator to the horizon, measured by QOS, will be equal to 900-, since QOZ = PON as angles with mutually perpendicular sides. Then the star M with declination, culminating south of the zenith, has a height at the upper culmination

From this formula it can be seen that the geographical latitude can be determined by measuring the height of any luminary with a known declination at the upper climax. In this case, it should be borne in mind that if the luminary at the moment of climax is located south of the equator, then its declination is negative.

Every place on earth can be identified by a global coordinate system of latitude and longitude. Knowing these parameters, it is easy to find any location on the planet. The coordinate system has been helping people in this for several centuries in a row.

Historical prerequisites for the emergence of geographical coordinates

When people began to travel long distances across deserts and seas, they needed a way to fix their position and know in which direction to move so as not to get lost. Before latitude and longitude were on a map, the Phoenicians (600 BC) and Polynesians (400 AD) used the starry sky to calculate latitude.

Quite complex devices have been developed over the centuries, such as the quadrant, the astrolabe, the gnomon, and the Arabic kamal. All of them were used to measure the height of the sun and stars above the horizon and thereby measure latitude. And if the gnomon is just a vertical stick that casts a shadow from the sun, then the kamal is a very peculiar device.

It consisted of a rectangular wooden plank measuring 5.1 by 2.5 cm, to which a rope with several equally spaced knots was attached through a hole in the middle.

These instruments determined latitude even after their invention, until a reliable method of determining latitude and longitude on a map was invented.

Navigators for hundreds of years did not have an accurate idea of the location due to the lack of a concept of the value of longitude. There was no precise time device in the world, such as a chronometer, so calculating longitude was simply impossible. Not surprisingly, early navigation was problematic and often resulted in shipwrecks.

Without a doubt, the pioneer of revolutionary navigation was Captain James Cook, who traveled the expanses of the Pacific Ocean thanks to the technical genius of Henry Thomas Harrison. Harrison developed the first navigational clock in 1759. Keeping accurate Greenwich Mean Time, Harrison's clock allowed sailors to determine how many hours were at a point and at a location, after which it became possible to determine longitude from east to west.

Geographic coordinate system

The geographic coordinate system defines two-dimensional coordinates based on the surface of the Earth. It has an angular unit, a prime meridian, and an equator with zero latitude. The globe is conditionally divided into 180 degrees of latitude and 360 degrees of longitude. Lines of latitude are placed parallel to the equator, they are horizontal on the map. Lines of longitude connect the North and South Poles and are vertical on the map. As a result of the overlay, geographic coordinates are formed on the map - latitude and longitude, with which you can determine the position on the surface of the Earth.

This geographic grid gives a unique latitude and longitude for every position on Earth. To increase the accuracy of measurements, they are further subdivided into 60 minutes, and each minute into 60 seconds.

The equator is located at right angles to the Earth's axis, approximately halfway between the North and South Poles. At an angle of 0 degrees, it is used in the geographic coordinate system as the starting point for calculating latitude and longitude on the map.

Latitude is defined as the angle between the equatorial line of the Earth's center and the location of its center. The North and South Poles have a width angle of 90. To distinguish places in the Northern Hemisphere from the Southern Hemisphere, the width is additionally provided in the traditional spelling with N for north or S for south.

The earth is tilted about 23.4 degrees, so to find the latitude at the summer solstice, you need to add 23.4 degrees to the angle you are measuring.

How to determine the latitude and longitude on the map during the winter solstice? To do this, subtract 23.4 degrees from the angle that is being measured. And in any other period of time, you need to determine the angle, knowing that it changes by 23.4 degrees every six months and, therefore, about 0.13 degrees per day.

In the northern hemisphere, one can calculate the tilt of the Earth, and therefore latitude, by looking at the angle of the North Star. At the North Pole it will be 90 from the horizon, and at the equator it will be directly ahead of the observer, 0 degrees from the horizon.

Important latitudes:

North and South polar circles, each is at 66 degrees 34 minutes north and south latitude respectively. These latitudes limit the areas around the poles where the sun does not set at the summer solstice, so the midnight sun dominates there. On the winter solstice, the sun does not rise here, the polar night sets in.
Tropics are located at 23 degrees 26 minutes in the northern and southern latitudes. These latitudinal circles mark the solar zenith with the summer solstice of the northern and southern hemispheres.
Equator lies at latitude 0 degrees. The equatorial plane runs approximately in the middle of the Earth's axis between the north and south poles. The equator is the only circle of latitude that corresponds to the circumference of the earth.

Latitude and longitude on the map are important geographic coordinates. Longitude is much more difficult to calculate than latitude. The earth rotates 360 degrees a day, or 15 degrees an hour, so there is a direct relationship between longitude and the times the sun rises and sets. The Greenwich meridian is indicated by 0 degrees of longitude. The sun sets an hour earlier every 15 degrees east of it and an hour later every 15 degrees west. If you know the difference between the sunset time of a location and another known place, you can understand how far east or west is from it.

The lines of longitude run from north to south. They converge at the poles. And the longitude coordinates are between -180 and +180 degrees. The Greenwich meridian is the zero line of longitude, which measures the east-west direction in a system of geographic coordinates (such as latitude and longitude on a map). In fact, the zero line passes through the Royal Observatory in Greenwich (England). The Greenwich meridian, as the prime meridian, is the starting point for calculating longitude. Longitude is specified as the angle between the center of the prime meridian of the center of the Earth and the center of the center of the Earth. The Greenwich meridian has an angle of 0, and the opposite longitude along which the date line runs has an angle of 180 degrees.

How to find latitude and longitude on a map?

Determining the exact geographic location on a map depends on its scale. To do this, it is enough to have a map with a scale of 1/100000, or better - 1/25000.

First, the longitude D is determined by the formula:

D \u003d G1 + (G2 - G1) * L2 / L1,

where G1, G2 - the value of the right and left nearest meridians in degrees;

L1 - distance between these two meridians;

Calculation of longitude, for example, for Moscow:

G1 = 36°,

G2 = 42°,

L1 = 252.5 mm,

L2 = 57.0 mm.

Search longitude = 36 + (6) * 57.0 / 252.0 = 37° 36".

We determine the latitude L, it is determined by the formula:

L \u003d G1 + (G2 - G1) * L2 / L1,

where G1, G2 - the value of the lower and upper nearest latitude in degrees;

L1 - distance between these two latitudes, mm;

L2 - distance from the definition point to the left nearest one.

For example, for Moscow:

L1 = 371.0 mm,

L2 = 320.5 mm.

Desired width L = 52" + (4) * 273.5 / 371.0 = 55 ° 45.

We check the correctness of the calculation, for this it is necessary to find the coordinates of latitude and longitude on the map using online services on the Internet.

We establish that the geographical coordinates for the city of Moscow correspond to the calculations:

55° 45" 07" (55° 45" 13) north latitude;
37° 36" 59" (37° 36" 93) East.

Determining location coordinates using iPhone

The acceleration of the pace of scientific and technological progress at the present stage has led to revolutionary discoveries of mobile technology, with the help of which a faster and more accurate determination of geographic coordinates has become available.

There are various mobile applications for this. On iPhones, this is very easy to do using the Compass app.

Definition order:

To do this, click "Settings", and then - "Privacy".
Now click "Location Services" at the very top.
Scroll down until you see the compass and tap it.
If you see that it says "When used on the right side", you can start the definition.
If not, tap it and select "When using the app".
Open the Compass app and you will see your current location and current GPS coordinates at the bottom of the screen.

Determination of coordinates in an Android phone

Unfortunately, Android doesn't have an official built-in way to get GPS coordinates. However, it is possible to get Google Maps coordinates, which requires some additional steps:

Open Google Maps on your Android device and find the desired definition point.
Press and hold it anywhere on the screen and drag it to Google Maps.
An informational or detailed map will appear at the bottom.
Find the Share option on the information card in the upper right corner. This will bring up a menu with the Share option.

This setup can be done in Google Maps on iOS.

This is a great way to get coordinates without the need to install any additional apps.

In Chapter 1, it was noted that the Earth has the shape of a spheroid, that is, an oblate ball. Since the terrestrial spheroid differs very little from a sphere, this spheroid is usually called the globe. The earth rotates around an imaginary axis. The points of intersection of an imaginary axis with the globe are called poles. north geographic pole (PN) is considered to be the one from which the Earth's own rotation is seen counterclockwise. south geographic pole (PS) is the pole opposite to the north.
If we mentally cut the globe with a plane passing through the axis (parallel to the axis) of the Earth's rotation, we get an imaginary plane, which is called meridian plane . The line of intersection of this plane with the earth's surface is called geographic (or true) meridian .
The plane perpendicular to the earth's axis and passing through the center of the earth is called equatorial plane , and the line of intersection of this plane with the earth's surface - equator .
If you mentally cross the globe with planes parallel to the equator, then circles are obtained on the surface of the Earth, which are called parallels .
Parallels and meridians plotted on globes and maps make up degree grid (Fig. 3.1). The degree grid makes it possible to determine the position of any point on the earth's surface.
For the initial meridian in the preparation of topographic maps taken Greenwich astronomical meridian passing through the former Greenwich Observatory (near London from 1675 - 1953). Currently, the buildings of the Greenwich Observatory house a museum of astronomical and navigational instruments. The modern Prime Meridian passes through Hirstmonceau Castle 102.5 meters (5.31 seconds) east of the Greenwich Astronomical Meridian. The modern prime meridian is used for satellite navigation.

Rice. 3.1. Degree grid of the earth's surface

Coordinates - angular or linear quantities that determine the position of a point on a plane, surface or in space. To determine coordinates on the earth's surface, a point is projected by a plumb line onto an ellipsoid. To determine the position of horizontal projections of a terrain point in topography, systems are used geographical , rectangular And polar coordinates .
Geographical coordinates determine the position of a point relative to the earth's equator and one of the meridians, taken as the initial one. Geographic coordinates may be derived from astronomical observations or geodetic measurements. In the first case they are called astronomical , in the second - geodetic . For astronomical observations, the projection of points onto the surface is carried out by plumb lines, for geodetic measurements - by normals, therefore the values of astronomical and geodetic geographical coordinates are somewhat different. To create small-scale geographical maps, the compression of the Earth is neglected, and the ellipsoid of revolution is taken as a sphere. In this case, the geographic coordinates will be spherical .
Latitude - angular value that determines the position of a point on Earth in the direction from the equator (0º) to the North Pole (+90º) or South Pole (-90º). Latitude is measured by the central angle in the meridian plane of a given point. On globes and maps, latitude is shown using parallels.

Rice. 3.2. Geographic latitude

Longitude - angular value that determines the position of a point on Earth in the West-East direction from the Greenwich meridian. Longitudes are counted from 0 to 180 °, to the east - with a plus sign, to the west - with a minus sign. On globes and maps, latitude is shown using meridians.

Rice. 3.3. Geographic longitude

3.1.1. Spherical coordinates

spherical geographic coordinates called the angular quantities (latitude and longitude) that determine the position of terrain points on the surface of the earth's sphere relative to the plane of the equator and the initial meridian.

spherical latitude (φ) call the angle between the radius vector (the line connecting the center of the sphere and a given point) and the equatorial plane.

spherical longitude (λ) is the angle between the zero meridian plane and the meridian plane of the given point (the plane passes through the given point and the axis of rotation).

Rice. 3.4. Geographic spherical coordinate system

In the practice of topography, a sphere with a radius R = 6371 is used km, whose surface is equal to the surface of the ellipsoid. On such a sphere, the arc length of the great circle is 1 minute (1852 m) called nautical mile.

3.1.2. Astronomical coordinates

Astronomical geographical coordinates are latitude and longitude, which determine the position of points on geoid surface relative to the plane of the equator and the plane of one of the meridians, taken as the initial one (Fig. 3.5).

Astronomical latitude (φ) called the angle formed by a plumb line passing through a given point and a plane perpendicular to the axis of rotation of the Earth.

Plane of the astronomical meridian - a plane passing through a plumb line at a given point and parallel to the axis of rotation of the Earth.
astronomical meridian - the line of intersection of the surface of the geoid with the plane of the astronomical meridian.

Astronomical longitude (λ) called the dihedral angle between the plane of the astronomical meridian passing through a given point, and the plane of the Greenwich meridian, taken as the initial one.

Rice. 3.5. Astronomical latitude (φ) and astronomical longitude (λ)

3.1.3. Geodetic coordinate system

IN geodetic geographic coordinate system for the surface on which the positions of the points are found, the surface is taken reference -ellipsoid . The position of a point on the surface of the reference ellipsoid is determined by two angular values - the geodetic latitude (IN) and geodetic longitude (L).
Plane of the geodesic meridian - a plane passing through the normal to the surface of the earth's ellipsoid at a given point and parallel to its minor axis.
geodetic meridian - the line along which the plane of the geodesic meridian intersects the surface of the ellipsoid.
Geodetic parallel - the line of intersection of the surface of an ellipsoid by a plane passing through a given point and perpendicular to the minor axis.

Geodetic latitude (IN)- the angle formed by the normal to the surface of the earth's ellipsoid at a given point and the plane of the equator.

Geodetic longitude (L)- dihedral angle between the plane of the geodesic meridian of the given point and the plane of the initial geodesic meridian.

Rice. 3.6. Geodetic latitude (B) and geodetic longitude (L)

3.2. DETERMINATION OF GEOGRAPHICAL COORDINATES OF POINTS ON THE MAP

Topographic maps are printed in separate sheets, the sizes of which are set for each scale. The side frames of the sheets are the meridians, and the upper and lower frames are the parallels. . (Fig. 3.7). Consequently, geographic coordinates can be determined by the side frames of the topographic map . On all maps, the top frame always faces north.
Geographic latitude and longitude are signed in the corners of each sheet of the map. On maps of the Western Hemisphere, in the northwestern corner of the frame of each sheet, to the right of the longitude of the meridian, the inscription is placed: "West of Greenwich."
On maps of scales 1: 25,000 - 1: 200,000, the sides of the frames are divided into segments equal to 1 ′ (one minute, Fig. 3.7). These segments are shaded through one and divided by dots (except for the map of scale 1: 200,000) into parts of 10 "(ten seconds). On each sheet, maps of scales 1: 50,000 and 1: 100,000 show, in addition, the intersection of the middle meridian and the middle parallel with digitization in degrees and minutes, and along the inner frame - outputs of minute divisions with strokes 2 - 3 mm long.This allows, if necessary, to draw parallels and meridians on a map glued from several sheets.

Rice. 3.7. Side frames of the card

When compiling maps of scales 1: 500,000 and 1: 1,000,000, a cartographic grid of parallels and meridians is applied to them. Parallels are drawn, respectively, through 20′ and 40 "(minutes), and meridians - through 30" and 1 °.
The geographical coordinates of a point are determined from the nearest southern parallel and from the nearest western meridian, the latitude and longitude of which are known. For example, for a map with a scale of 1: 50,000 "ZAGORYANI", the nearest parallel located to the south of a given point will be the parallel 54º40′ N, and the nearest meridian located to the west of the point will be the meridian 18º00′ E. (Fig. 3.7).

Rice. 3.8. Determination of geographical coordinates

To determine the latitude of a given point, you must:

set one leg of the measuring compass to a given point, set the other leg along the shortest distance to the nearest parallel (for our map 54º40 ′);
without changing the solution of the measuring compass, install it on the side frame with minute and second divisions, one leg should be on the south parallel (for our map 54º40 ′), and the other between the 10-second points on the frame;
count the number of minutes and seconds from the south parallel to the second leg of the measuring compass;
add the result obtained to the south latitude (for our map 54º40 ′).

To determine the longitude of a given point, you must:

set one leg of the measuring compass to a given point, set the other leg along the shortest distance to the nearest meridian (for our map 18º00′);
without changing the solution of the measuring compass, set it to the nearest horizontal frame with minute and second divisions (for our map, the lower frame), one leg should be on the nearest meridian (for our map 18º00 ′), and the other between the 10-second points on horizontal frame;
count the number of minutes and seconds from the western (left) meridian to the second leg of the measuring compass;
add the result to the longitude of the western meridian (for our map 18º00′).

note that this method of determining the longitude of a given point for maps at a scale of 1:50,000 and smaller has an error due to the convergence of the meridians that limit the topographic map from the east and west. The north side of the frame will be shorter than the south side. Therefore, the discrepancies between the measurements of longitude on the northern and southern frames may differ by several seconds. To achieve high accuracy in the measurement results, it is necessary to determine the longitude on both the south and north sides of the frame, and then interpolate.
To improve the accuracy of determining geographic coordinates, you can use graphic method. To do this, it is necessary to connect with straight lines the ten-second divisions of the same name nearest to the point in latitude south of the point and in longitude west of it. Then determine the dimensions of the segments in latitude and longitude from the drawn lines to the position of the point and summarize them, respectively, with the latitude and longitude of the drawn lines.
The accuracy of determining geographical coordinates on maps of scales 1: 25,000 - 1: 200,000 is 2" and 10", respectively.

3.3. POLAR COORDINATE SYSTEM

polar coordinates are called the angular and linear quantities that determine the position of a point on the plane relative to the origin, taken as a pole ( ABOUT), and the polar axis ( OS) (Fig. 3.1).

The location of any point ( M) is determined by the position angle ( α ), measured from the polar axis to the direction to the determined point, and the distance (horizontal distance - the projection of the terrain line on the horizontal plane) from the pole to this point ( D). Polar angles are usually measured from the polar axis in a clockwise direction.

Rice. 3.9. Polar coordinate system

For the polar axis can be taken: the true meridian, the magnetic meridian, the vertical line of the grid, the direction to any landmark.

3.2. BIPOLAR COORDINATE SYSTEMS

Bipolar coordinates call two angular or two linear quantities that determine the location of a point on a plane relative to two starting points (poles ABOUT 1 And ABOUT 2 rice. 3.10).

The position of any point is determined by two coordinates. These coordinates can be either two position angles ( α 1 And α 2 rice. 3.10), or two distances from the poles to the determined point ( D 1 And D 2 rice. 3.11).

Rice. 3.10. Determining the location of a point at two angles (α 1 and α 2 )

Rice. 3.11. Determining the location of a point by two distances

In a bipolar coordinate system, the position of the poles is known, i.e. the distance between them is known.

3.3. POINT HEIGHT

Previously reviewed plan coordinate systems , defining the position of any point on the surface of the earth's ellipsoid, or the reference ellipsoid , or on the plane. However, these planned coordinate systems do not allow obtaining an unambiguous position of a point on the physical surface of the Earth. Geographic coordinates refer the position of the point to the surface of the reference ellipsoid, polar and bipolar coordinates refer the position of the point to the plane. And all these definitions have nothing to do with the physical surface of the Earth, which is more interesting for a geographer than a reference ellipsoid.
Thus, the planned coordinate systems do not make it possible to unambiguously determine the position of a given point. It is necessary to somehow define your position, at least with the words “above”, “below”. Just about what? To obtain complete information about the position of a point on the physical surface of the Earth, the third coordinate is used - height . Therefore, it becomes necessary to consider the third coordinate system - height system .

The distance along a plumb line from the level surface to a point on the physical surface of the Earth is called height.

There are heights absolute if they are counted from the level surface of the Earth, and relative (conditional ) if they are counted from an arbitrary level surface. Usually, the level of the ocean or the open sea in a calm state is taken as the origin of absolute heights. In Russia and Ukraine, the absolute heights are taken as the origin zero of the Kronstadt footstock.

Footstock- a rail with divisions, fixed vertically on the shore so that it is possible to determine from it the position of the water surface, which is in a calm state.
Kronstadt footstock- a line on a copper plate (board) mounted in the granite abutment of the Blue Bridge of the Obvodny Canal in Kronstadt.
The first footstock was installed during the reign of Peter the Great, and since 1703 regular observations of the level of the Baltic Sea began. Soon the footstock was destroyed, and only from 1825 (and up to the present time) regular observations were resumed. In 1840, hydrographer M.F. Reinecke calculated the average height of the Baltic Sea and recorded it on the granite abutment of the bridge in the form of a deep horizontal line. Since 1872, this feature has been taken as a zero mark when calculating the heights of all points on the territory of the Russian state. The Kronstadt footstock was repeatedly modified, however, the position of its main mark was kept the same during design changes, i.e. determined in 1840
After the collapse of the Soviet Union, Ukrainian surveyors did not begin to invent their own national system of heights, and at present, Ukraine still uses Baltic height system.

It should be noted that, in every necessary case, measurements are not taken directly from the level of the Baltic Sea. There are special points on the ground, the heights of which were previously determined in the Baltic system of heights. These points are called benchmarks .
Absolute heights H can be positive (for points above the Baltic Sea level) and negative (for points below the Baltic Sea level).
The difference between the absolute heights of two points is called relative height or excess (h):
h = H BUT-H IN .
The excess of one point over another can also be positive and negative. If the absolute height of the point BUT greater than the absolute height of the point IN, i.e. is above the point IN, then the excess of the point BUT over the dot IN will be positive, and vice versa, exceeding the point IN over the dot BUT- negative.

Example. Absolute heights of points BUT And IN: H BUT = +124,78 m; H IN = +87,45 m. Find Mutual Exceedances of Points BUT And IN.

Solution. Exceeding point BUT over the dot IN
h A(B) = +124,78 - (+87,45) = +37,33 m.
Exceeding point IN over the dot BUT
h B(A) = +87,45 - (+124,78) = -37,33 m.

Example. Point absolute height BUT is equal to H BUT = +124,78 m. Exceeding point FROM over the dot BUT equals h C(A) = -165,06 m. Find the absolute height of a point FROM.

Solution. Point absolute height FROM is equal to
H FROM = H BUT + h C(A) = +124,78 + (-165,06) = - 40,28 m.

The numerical value of the height is called the elevation of the point (absolute or conditional).
For example, H BUT = 528.752 m - absolute mark of the point BUT; H" IN \u003d 28.752 m - conditional elevation of the point IN .

Rice. 3.12. Heights of points on the earth's surface

To move from conditional to absolute heights and vice versa, it is necessary to know the distance from the main level surface to the conditional one.

Video
Meridians, parallels, latitudes and longitudes
Determining the position of points on the earth's surface

Questions and tasks for self-control

Expand the concepts: pole, equatorial plane, equator, meridian plane, meridian, parallel, degree grid, coordinates.
Relative to what planes on the globe (ellipsoid of revolution) are geographic coordinates determined?
What is the difference between astronomical geographic coordinates and geodetic coordinates?
Using the drawing, expand the concepts of "spherical latitude" and "spherical longitude".
On what surface is the position of points in the astronomical coordinate system determined?
Using the drawing, expand the concepts of "astronomical latitude" and "astronomical longitude".
On what surface is the position of points in the geodetic coordinate system determined?
Using the drawing, expand the concepts of "geodesic latitude" and "geodesic longitude".
Why, in order to improve the accuracy of determining longitude, is it necessary to connect the nearest ten-second divisions of the same name to the point with straight lines?
How can you calculate the latitude of a point if you determine the number of minutes and seconds from the northern frame of a topographic map?
What are the polar coordinates?
What is the purpose of the polar axis in a polar coordinate system?
What coordinates are called bipolar?
What is the essence of the direct geodetic problem?

The ability to “read” a map is a very interesting and useful activity. Today, when with the help of innovative technologies it is possible to virtually visit any corner of the world, the possession of such skills is very rare. Geographic latitude is studied in the school curriculum, but without constant practice it is impossible to consolidate the theoretical knowledge gained in the general education course. Cartographic skills develop not only imagination, but also are a necessary basis for many complex disciplines. Those wishing to acquire the profession of navigator, surveyor, architect and military simply need to know the basic principles of working with a map and plan. Determination of geographic latitude is a mandatory skill that a real travel lover and just an educated person should have.

globe

Before moving on to the magnitude algorithm, it is necessary to become more familiar with the globe and map. Because it is on them that you will have to train your skills. A globe is a miniature model of our Earth, which depicts its surface. M. Behaim, the creator of the famous "Earth Apple" in the 15th century, is considered the author of the very first model. The history of the development of cartographic knowledge has information about other famous globes.

Multitouch. This interactive model is a modern invention that allows you to "visit" anywhere in the world without spending a lot of time and effort!
Heavenly. This globe shows the location of cosmic bodies - mirrored. After all, when we admire the beautiful night sky, we are “inside” the dome, and we are forced to look at this globe from the outside!
One of the collectors - Sh.Missine - has a globe carved from an ostrich egg. This is one of the very first maps of this continent.

On the globe, you can accurately determine the geographical latitude, because it has the least distortion. But for greater reliability, it is necessary to use a special flexible ruler.

Cards

The globe is not very convenient to take with you on a trip, besides, it becomes more useless the smaller it is. And over time, people began to use the card. It, of course, has more errors, since it is very difficult to accurately depict the convex shape of the Earth on a piece of paper, but it is more convenient and easy to use. Maps have several classifications, but we will focus on their difference in scale, as we are talking about acquiring the skills of determining coordinates.

Large scale. This is the name of drawings with a scale (M) from 1:100,000 to 1:10,000. If the map has M 1:5,000, and larger, then it is already called a plan.
Medium scale. This is the name of the drawings of the Earth's surface, which have MM from 1:1,000,000 to 1:200,000.
Small scale. These are drawings with M 1:1,000,000 or less, for example - MM 1:2,000,000, 1:50,000,000, etc.

On a large-scale map, the geographic latitude is most easily determined, since the image is plotted on it in more detail. This is due to the fact that the grid lines are located at a small distance.

Geographic latitude

This is the name of the angle between the zero parallel and the plumb line at a given point. The resulting value can only be within 90 degrees. It is important to remember: the equator divides our Earth into the south, and therefore the latitude of all points on the Earth that are located above will be north, and below - south. How to determine the geographic latitude of an object? It is necessary to carefully look at which parallel it is located. If it is not indicated, then it is necessary to calculate what is the distance between adjacent lines and determine the degree of the desired parallel.

Geographic longitude

This is the meridian of a particular point on the Earth and which has the name Greenwich Mean. All objects to the right of it are considered eastern, and to the left - western. Longitude shows on which meridian the desired object is located. If the point to be determined is not located on the meridian indicated on the map, then we proceed in the same way as in the case of determining the desired parallel.

Geographic address

It is present in every object on our Earth. The intersection of parallels and meridians on a map or globe is called a grid (degree grid), along which the coordinates of the desired point are determined. Knowing them, you can not only determine the place where the object is located, but also correlate its position with others. Having information about the geographical address of a particular point, it is possible to correctly plot the boundaries of territories on contour maps.

Five main latitudes

On any map, the main parallels are highlighted, which facilitate the determination of coordinates. The territories that are between these main latitude lines, depending on location, may be included in the following areas: the Arctic, the tropics, equatorial and temperate.

The equator is the longest parallel. The length of lines located above or below it becomes shorter towards the poles. What is the geographic latitude of the equator? It is equal to 0 degrees, as it is considered the starting point of the parallels to the north and south. The territories that are located from the equator to the tropics are called the equatorial regions.

The northern tropic is the main parallel, which is always marked on world maps of the Earth. It is located 23 degrees 26 minutes and 16 seconds north of the equator. Another name for this parallel is the Tropic of Cancer.
The Southern Tropic is a parallel that is located 23 degrees 26 minutes and 16 seconds south of the equator. It also has a second name - the Tropic of Capricorn. The territories that are located between these lines and the equator are called tropical regions.
located 66 degrees 33 minutes and 44 seconds above the equator. It limits the territory beyond which the time of night increases, closer to the pole it reaches 40 days.

South polar circle. Its geographic latitude is 66 degrees 33 minutes and 44 seconds. This parallel is also the boundary beyond which phenomena such as polar night and day begin. The territories that are located between these lines and the tropics are called temperate regions, and beyond them - polar.

What else to read

Why cucumbers in the greenhouse became bitter Cucumber beds in a summer cottage always occupy the most fertile and lighted areas, and the fruits are used ...

Where are comets born in the solar system? A comet is a celestial body of small size, consisting of ice interspersed with dust and stone fragments. At...

Rudeness and aggressive behavior of a teenager: what should parents do We often receive questions from parents of teenagers about the nature of their children's behavior. Often understand students ...