Latitude is the angle formed by a plumb line passing through a given point on the Earth's surface and the plane of the equator (in Fig. 3 for point M angle MOS).
No matter where the observer is on the globe, his force of gravity will always be directed towards the center of the Earth. This direction is called plumb or vertical.
Latitude is measured by the arc of the meridian from the equator to the parallel of a given point in the range from 0 to 90° and is designated by the letter f. Thus, the geographic parallel eabq is the locus of points that have the same latitude.
Depending on which hemisphere the point is located in, the latitude is given the name northern (N) or southern (S).
Longitude is called the dihedral angle between the planes of the initial meridian and the meridian of a given point (in Fig. 3 for point M angle AOS). Longitude is measured by the smaller of the arcs of the equator between the prime meridian and the meridian of a given point in the range from 0 to 180° and is designated by the letter l. Thus, the geographic meridian PN MCPs is the locus of points having the same longitude.
Depending on which hemisphere the point is located in, the longitude is called eastern (O st) or western (W).
Rice. 4
The magnitude of the change in longitude Al resulting from the passage of a ship from the departure point M1 to the arrival point C2 is called difference in longitude(RD). The taxiway is measured by the smaller arc of the equator between the meridians of the point of departure and the point of arrival MCN (see Fig. 4). If, during the passage of the vessel, the eastern longitude increases or the western one decreases, then the taxiway is considered to be made to O st, and if the eastern longitude decreases or the western longitude increases, then to W. To determine the taxiway and taxiway, the formulas are used:
РШ = φ1 - φ2; (1)
RD = λ1 - λ2 (2)
Where φ1 is the latitude of the departure point;
φ2 - latitude of arrival point;
λ1 - longitude of departure point;
λ2 - longitude of the point of arrival.
In this case, northern latitudes and eastern longitudes are considered positive and are assigned a plus sign, while southern latitudes and western longitudes are considered negative and are assigned a minus sign. When solving problems using formulas (1) and (2), in the case of positive RS results, it will be done to N, and RD - to O st (see example 1), and in the case of negative RS results, it will be made to S, and RD - to W (see example 2). If a RD result is more than 180° with a negative sign, you need to add 360° (see example 3), and if the RD result is more than 180° with a positive sign, you need to subtract 360° (see example 4).
Example 1. Known: φ1 = 62°49" N; λ1 = 34°49" O st ; φ2 = 72°50"N; λ2 = 80°56" O st .
Find RS and RD.
Solution.
Find RS and RD.
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 the southern hemisphere is considered 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- 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.
To completely determine the position of a point in 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 the geographic envelope, the “height above sea level” is usually used, measured from the level of the “smoothed” surface - the geoid. Such a three-coordinate system 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
The main disadvantage in the practical application of the GSK in navigation is the large 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.
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.
The WGS84 system is used to record geographic coordinates.
Coordinates (latitude from -90° to +90°, longitude from -180° to +180°) can be written:
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.
Search engine maps by default show coordinates in degrees and decimals, with "-" signs for negative longitude. On Google maps and Yandex maps, latitude comes first, then longitude (until October 2012, the reverse order was adopted on Yandex maps: 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. / 55.755831 , 37.617673 37°37′03.62″ E. d.:
Notes
AIESEC See what “Geographic coordinates” are in other dictionaries: Geographical coordinates
- see Coordinates. Mountain encyclopedia. M.: Soviet Encyclopedia. Edited by E. A. Kozlovsky. 1984 1991 … Geological encyclopedia GEOGRAPHICAL COORDINATES
- see Coordinates. Mountain encyclopedia. M.: Soviet Encyclopedia. Edited by E. A. Kozlovsky. 1984 1991 …- 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
AIESEC- angular values 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 of the earth’s equator, measured from 0 to 90° (north of the equator is northern latitude and south of southern latitude); longitude... ...Nautical Dictionary
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 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
| 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 |
Astronomy first hand
Geographic coordinates, latitude and longitude, which determine the position of a point on the earth's surface, were known back in ancient Greece. However, among the Hellenes these concepts were significantly different from our modern ones.
Now we measure latitude in degrees from the equator, and longitude from some arbitrarily chosen meridian, for example, from Greenwich.
The ancients had no idea about the degree grid and determined latitude either by the height of the Polar, or by the duration of the longest day of daylight in the year, or by the length of the shortest shadow. It was more difficult with longitude or the difference in longitude, which can only be defined as the difference in local times measured at two points at the same physical moment. The problem was to either somehow deliver the time of one point to another, or to register some phenomenon simultaneously observed from two points. Hipparchus proposed using lunar eclipses as such a phenomenon, but, unfortunately, did not indicate methods for measuring local time. It was impossible to directly use a sundial for this purpose, since during an eclipse of the Moon the Sun is below the horizon. The accuracy of determining the same phase of the eclipse was also very low.
It took about a millennium before people learned to determine latitude and longitude with sufficiently high accuracy.
This problem became especially acute during the era of great geographical discoveries, when navigators needed knowledge of the coordinates of their ships.
In 1567, the Spanish King Philip II offered a reward for solving the problem of determining longitude on the high seas. In 1598, Philip III promised 6 thousand ducats as a permanent contribution, 2 thousand ducats as a life annuity and 1 thousand ducats to assist anyone who could “discover longitude”.
The United Provinces of Holland awarded a prize of 30 thousand florins. Portugal and Venice also promised rewards.
One of the most famous contenders for longitude prizes was Galileo Galilei. Using the telescope he designed, Galileo observed the eclipses of the moons of Jupiter, compiled tables predicting these eclipses, and proposed using the moments of the eclipses to determine the longitude of the observer.
Navigators, having their local time, say, from observations of the Sun, and knowing from tables the time when eclipses of Jupiter's satellites occur on a certain reference meridian, could calculate the time difference, that is, the longitude of their ship from the reference meridian.
Another, also astronomical, method of determining longitude was proposed: by observing the position of the Moon among the stars. This method, in principle, is similar to Galileo’s method, only in it it was not eclipses of Jupiter’s satellites that were observed, but the distances of the lunar disk from reference, well-known stars were determined. Tables were compiled giving the position of the Moon among the stars on the meridian for a certain point in time.
Unfortunately, both astronomical methods have not found wide application in maritime navigation.
Firstly, they are only possible on clear nights.
Secondly, they require a good theory of the motion of the satellites of Jupiter and the Moon; theories, especially for the Moon, a very capricious luminary, were absent in the 17th-18th centuries.
Thirdly, the moments of eclipse of satellites from the ship are determined with large errors. This also applies to the positions of the Moon among the stars.
Fourthly, astronomical observations require highly trained navigators, which was also not always the case.
Therefore, scientists diligently searched for another, simpler way to determine longitude. The idea of this method was obvious - it was necessary to create a watch with the help of which the time of the reference meridian could be carried with you on a ship.
Clocks with a pendulum were unsuitable for this purpose; they did not tolerate pitching.
In 1714, the English Parliament passed a bill providing for a reward for a person or group of people who could determine longitude at sea. A reward of £10,000 was offered if the method could determine longitude to within one degree of the great circumference, or sixty geographical miles. If the accuracy doubled, the amount doubled and amounted to 20 thousand pounds sterling. It was truly a royal prize!
This prize, although not entirely, went to the inventor of the chronometer, London watchmaker John Harrison. His first chronometer was made in 1735, then for several decades Harrison improved his brainchild.
With the advent of the chronometer, the problem of transporting accurate time was solved.
When setting sail, the ship's navigator checked his chronometers, and there were usually several of them, with the observatory clock, the longitude of which was well known. The local time and latitude of the ship were determined using a sextant from the Sun or the stars.
This method of determining coordinates made it possible to find the position of the ship with an accuracy of seconds, which was a distance of about 1 km at the equator.
Such accuracy suited sailors quite well on the open sea, but was insufficient near the coast, and here lighthouses equipped with light and sound signals came to their aid.
In the last century, an urgent need arose for precise coordinates on the Earth's surface. This was mainly due to the compilation of maps. The principle of determining exact coordinates was the same as at sea, but instead of a sextant, a universal instrument and a theodolite were used - instruments that made it possible to determine latitude and local time from observations of stars with great accuracy. The main difficulty, as before, was the problem of storing Greenwich time. Even good chronometers without control quickly moved ahead or fell behind, and an error of, say, one second in determining longitude was completely unsuitable for precise geodetic work.
A real revolution in determining coordinates was made by the invention of the telegraph, and then the radio. Now exact time signals from Greenwich, or from a point with a known longitude, could be received anywhere on Earth. Everything depended on the power of the transmitter and the sensitivity of the receiver.
The problem of determining longitude was solved for many decades.
However, this problem still had one weak point - astronomy.
It is not always possible to make astronomical observations; they require special skills, they are very inconvenient to make from an airplane, from a rocking ship, and on Earth, without stationary pillars, it is also impossible to get good results.
In the second half of our century, a fundamentally new idea arose for determining coordinates on the Earth's surface. The essence of this idea is this.
Three radio stations transmit precise time signals at the same physical moment. Let's say, for example, that these stations are located on different continents. One in Europe and two in North and South America. Then, the ship's navigator, receiving these signals on his watch, which is synchronized with the clocks of the supply stations, finds the time delays of the signals t 1, t 2, t 3, i.e., the times during which the radio wave must travel from the station transmitters to the receiver. Then multiplying the t values by the speed of light, the navigator finds the distance l 1, l 2, l 3 from all three stations. Drawing circles on the map around the station with radii l 1, l 2, l 3, the navigator determines his place on the map at their intersection. This is just a principle. In reality, the matter is much more complicated. It is necessary to take into account the curvature of the Earth, features in the speed of propagation of radio waves, errors in receiving equipment, and much more. It is especially difficult to synchronize a ship's clock and maintain this synchronization over a certain period of time.
However, with the advent of computers and atomic standards that store time with the stability of a second with an accuracy of 10 -12 s, all these problems were resolved. If the accuracy of clock synchronization and signal reception errors were 3-5 microseconds, then the on-board computer could determine the position of a ship or aircraft with an error of about 1 km. Moreover, these data, in the presence of a large number of special radio stations, could be issued continuously.
Systems such as the American Laurent and the Soviet RNS have completely solved navigation problems with an accuracy of several hundred meters.
Artificial Earth satellites made a great contribution to the task of determining coordinates. If a satellite is equipped with an atomic frequency standard, it can perform the tasks of a transmitting station. The advantages are obvious - the influence of the atmosphere when receiving signals from a satellite is minimal, reception errors are small.
There are also difficulties - the satellite is mobile, and therefore its coordinates are constantly changing. But these difficulties can be overcome.
The satellite’s on-board computer stores data about its trajectory, that is, its coordinates, which it continuously transmits along with time signals in a special code. The code is needed so that it is known from which satellite the information is coming.
Any consumer of these signals, receiving them on his watch, determines the time delay t and, therefore, the distance to the satellite, at some moment equal to l=tc, where c is the speed of radio waves. That is, the principle is the same as in the Laurent system, but there are improvements. The consumer clock synchronization error is considered as an unknown quantity, therefore it is determined not by l=tc, but by l 1 =t+t 1 c, where t 1 is the consumer clock synchronization error. The value l 1 is called pseudorange. If you receive signals from not one, but from four or more navigation satellites, you can obtain a system of equations from which the coordinates of the observation location and, separately, the synchronization error of the local clock are determined on a computer. Considering that the stability of modern atomic clocks has increased sharply (the stability of the second is now about 5 * 10 -14), it is possible to obtain the position on the earth's surface with the help of navigation satellites with an accuracy of several meters, and this is not the limit. Special, more advanced equipment allows us to talk about centimeter accuracy. And finally, the last question - where to get satellite coordinates? This requires special trajectory measurements, as well as a center for processing them. In the USA there is a GPS radio navigation system, we also have such a system in Russia, it is called GLONASS.
This system should consist of 24 satellites located in different orbits so that at least four satellites are visible from each location on the earth's surface served by the system.
There are many different coordinate systems, all of which are used to determine the position of points on the earth's surface. These include mainly geographic coordinates, plane rectangular and polar coordinates. In general, coordinates are usually called angular and linear quantities that define points on any surface or in space.
Geographic coordinates are angular values - latitude and longitude - that determine the position of a point on the globe. Geographic latitude is the angle formed by the equatorial plane and a plumb line at a given point on the earth's surface. This angle value shows how far a particular point on the globe is north or south of the equator.
If a point is located in the Northern Hemisphere, then its geographic latitude will be called northern, and if in the Southern Hemisphere - southern latitude. The latitude of points located on the equator is zero degrees, and at the poles (North and South) - 90 degrees.
Geographic longitude is also an angle, but formed by the plane of the meridian, taken as the initial (zero), and the plane of the meridian passing through a given point. For uniformity of definition, we agreed to consider the prime meridian to be the meridian passing through the astronomical observatory in Greenwich (near London) and call it Greenwich.
All points located to the east of it will have eastern longitude (up to the meridian 180 degrees), and to the west of the initial one will have western longitude. The figure below shows how to determine the position of point A on the earth's surface if its geographic coordinates (latitude and longitude) are known.
Note that the difference in longitude of two points on Earth shows not only their relative position in relation to the prime meridian, but also the difference in these points at the same moment. The fact is that every 15 degrees (24th part of the circle) in longitude is equal to one hour of time. Based on this, it is possible to determine the time difference at these two points using geographic longitude.
Moscow has a longitude of 37°37′ (east), and Khabarovsk -135°05′, that is, lies east of 97°28′. What time do these cities have at the same moment? Simple calculations show that if it is 13 hours in Moscow, then in Khabarovsk it is 19 hours 30 minutes.
The figure below shows the design of the frame of a sheet of any card. As can be seen from the figure, in the corners of this map the longitude of the meridians and the latitude of the parallels that form the frame of the sheet of this map are written.
On all sides the frame has scales divided into minutes. For both latitude and longitude. Moreover, each minute is divided into 6 equal sections by dots, which correspond to 10 seconds of longitude or latitude.
Thus, in order to determine the latitude of any point M on the map, it is necessary to draw a line through this point, parallel to the lower or upper frame of the map, and read the corresponding degrees, minutes, seconds on the right or left along the latitude scale. In our example, point M has a latitude of 45°31’30”.
Similarly, drawing a vertical line through point M parallel to the lateral (closest to this point) meridian of the border of a given map sheet, we read the longitude (eastern) equal to 43°31’18”.
Drawing a point on a map at specified geographic coordinates is done in the reverse order. First, the indicated geographic coordinates are found on the scales, and then parallel and perpendicular lines are drawn through them. Their intersection will show a point with the given geographic coordinates.
Based on materials from the book “Map and Compass are My Friends.”
Klimenko A.I.
