Major axle shaft A= 6,378,245 m.
Minor shaft b= 6,356,863.019 m.
Radius of a sphere of the same volume with Krasovsky's ellipsoid R= 6,371,110 m.
Radius of a sphere with the same surface as the Krasovsky ellipsoid R= 6,371,116 m.
Radius of a ball of the same circumference of a great circle with the length of the meridian of the Krasovsky ellipsoid R= 6,367,559 m.
Radius of a sphere, one minute of great circle arc of which is equal to a nautical mile (1852 m) R= 6,366,707 m.
When solving problems that do not require high accuracy, the compression of the Earth is neglected, i.e. mistake the earth for a ball.
Ball radius are chosen based on certain conditions. For example, when measuring distances at sea, the radius of the ball R = 6366 km 707 m(L E= 39,983 km).
R SR = 6371.1 km(L E= 40,010.5 km).
2. Basic points, lines and planes of the Earth
Rice. 2.1. Basic points, lines and planes of the Earth
Earth's axis (Fig. 2.1) – an imaginary straight line around which the Earth makes its daily rotation (≈ 0.5 km/s = 0.464 km/s).
This axis ( P N P S) coincides with the minor axis of the earth's ellipsoid and intersects the surface of the ellipsoid at two points called geographic poles Lands: – northern – P N , – southern – P S .
North geographic pole (P N) is considered to be the one from which the Earth’s own rotation is seen counterclockwise.
South geographic pole (P S) – the pole opposite to the north.
Equator plane – a plane perpendicular to the earth’s axis and passing through the center of the ball (ellipsoid).
Earth's equator – a line (circle) formed from the intersection of the ellipsoid surface with the equatorial plane.
Earth's equator (line EAQB) divides the globe into two hemispheres:
northern hemisphere (from P N);
southern hemisphere (from P S).
Planes of parallels – planes parallel to the equatorial plane.
Parallels - small circles formed on the surface of the earth's ellipsoid when it intersects parallel planes.
Normal (plumb line) – a straight line that coincides with the direction of gravity at a given point. For T. WITH– the normal is a straight line SOS', passing through the center of the Earth.
Planes of true meridians – planes passing through the Earth’s axis ( P N P S).
The meridian passing through the observer's place is usually called true (geographical) meridian of the observer
3. Basic lines and planes of the observer
Rice. 2.2. Basic lines and planes of the observer
The surface of the Earth observed by humans is perceived as flat, therefore, for orientation on a small area of the Earth's surface, certain imaginary lines and planes are used. Many navigation problems are solved with the help of these lines and planes.
For orientation at any point on the Earth's surface, the following lines and planes are used, associated with the observer's position.
Vertical (plumb) line – straight Zn, coinciding with the direction of gravity at the observer's location.
Observer's zenith - dot Z the intersection of a vertical line with an imaginary celestial sphere above the observer's head.
Nadir of the observer - dot n the intersection of a vertical line with an imaginary celestial sphere under the observer.
Horizontal plane - any plane perpendicular to a plumb line.
Observer's true horizon plane – horizontal plane HH’ passing through the observer's eye.
Vertical plane (vertical plane) - any plane passing through a plumb line.
Observer true meridian plane – vertical plane MM’ , passing through the Earth's poles and the observer's position.
True (geographical) meridians – lines (circles) formed on the surface of the ellipsoid when it intersects the planes of the true meridians.
Observer Meridian – big circle R N AR S, formed by a section of the Earth's surface by the plane of the observer's true meridian.
Observer's true meridian line (noon line) – line N.S. intersection of the plane of the observer's true meridian with the plane of the observer's true horizon.
Prime (prime, Greenwich) meridian .
According to the International Agreement, since 1884, the Greenwich meridian has been taken as the prime (zero) meridian - the meridian that passed through the axis of the main telescope of the former Greenwich Observatory (which existed for 278 years, 1675–1953) on the outskirts of London (England).
Since 1953, the new Greenwich Observatory has been located at Herstmonceux Castle (south of England 15 km from the English Channel coast east of the prime meridian at 20′25″).
The prime (Greenwich) meridian divides the globe into the eastern and western hemispheres.
Main directions.
The intersection of the plane of the observer's true meridian and the plane of the first vertical with the plane of the true horizon forms two mutually perpendicular lines N–S and E–W in the plane of the true horizon. The N–S line is the noon line. It fixes the direction to the north and south geographic poles. Line E–W determines the east–west direction. Four mutually perpendicular directions in the plane of the true horizon: N (north), S (south), E (east - east), W (west) form the main directions. Orientation on the Earth's surface is carried out relative to these directions.
Such a system of lines and planes is called a horizontal coordinate system.
The earth has a spherical shape, or rather, it is slightly flattened along the edges at the points that are its poles. But this is not particularly noticeable on a planetary scale, because it is assumed that the Earth is a ball, and its surface is taken to be spherical.
Marking the Earth with meridians and parallels made it possible to accurately determine the coordinates of any object that moves (airplane, thunderclouds) or that occupies a certain place on the planet (city, island). This provided quite a lot of benefits for any objects moving in space. Previously, people were guided by the stars, by the position of the sun in the sky. This was not as accurate as with the help of modern technologies, although if you suddenly find yourself on a desert island without the means so familiar in our lives - smartphones, tablets, laptops, respectively, without Internet access, without a navigator and so on, then It would not be superfluous to know those very “inconvenient” methods for calculating coordinates.
You can use a navigation system into which the necessary coordinates will be entered, and autopilot devices will be able to move themselves where necessary, without a person. But first things first. Let's look at the main points and circles on the globe.
Some historical information
Questions about coordinates have preoccupied the minds of people for a long time, even before our era. Outstanding scientists on the path of developing the coordinate system were Hipparchus and Ptolemy. These people lived in the second and first centuries BC, but, nevertheless, they could already determine with dividing accuracy. These were the great people of their era, powerful geographers and astronomers. It was they who introduced the concept that we now call a coordinate system, and from their works it already becomes clear what it is. At that time, these people did not know that the Earth revolves around the Sun. Hipparchus proposed that the surface of our planet can be considered an ideal sphere, and using this as an example, he explained various fundamentals regarding spherical geometry.
Globe - the most accurate model of the Earth
It is with the help of a globe that you can easily determine the coordinates of any country, island or other object. With its help, it is easiest to show what meridians and parallels, geographic poles, and other points and lines of the Earth are.
By the way, the first globe was created a long time ago, even before our era, and it was done by a certain Crates of Mallus in 150 BC, at the same time when Hipparchus and Ptolemy lived. Of course, the globe cannot demonstrate all the small details, but in general it allows you to perfectly describe the overall picture of what our planet is, and perfectly demonstrates, for example, which points of the earth are called geographic poles,
On the globe it is easy to see where a country, sea, ocean, location of continents or even their relief is located. It depends on what will be depicted by the creator of this or that globe. It can be purely political, only with the division of continents into countries and with the indication of large objects such as oceans. Most likely, it will be a small decorative globe. Educational copies contain much more information about the geographic poles and geographical location of any part of the world.
In general, there are three parameters by which the Earth is characterized in geographical coordinate terms. Therefore, let's look at the main points, lines and planes on the Earth's surface.
What is the Earth's axis
If we take the Earth to be a sphere, then it becomes clear that it has such a line, which also serves as an instrumental line in a stereometric figure. What exactly are we talking about? This is a line that is the diameter, rotating around which the semicircle creates a whole sphere. What diameter in comparison with the Earth is called the axis. This is an imaginary line that does not actually exist, but there is a daily rotation around it, and it is generally accepted that it passes through the North and South Poles.
Poles of planet Earth
Which points of the earth are called geographic poles? These are the well-known cold, deserted north and south poles. In stereometry, what is called the “geographical pole” is the point at which the earth’s axis of rotation (the diagonal of a spherical body) intersects the sphere. The last one in this case is
All the meridians, which we will discuss below, pass through these two poles.
What are parallels
Let's continue to consider the Earth as a sphere and determine what the parallels are in this case. If we assume that the planet, like the ball, has a center, then the Earth’s axis will pass through it and be divided into two equal parts, like a diameter into radii.
If you draw a certain plane that runs perpendicular to the axis, then it will intersect the sphere along a certain circle, that is, the Earth along a line called a parallel. The parallel with the largest diameter passes through the center of the Earth, which is a great circle and is called the equator. It divides the sphere into two equal hemispheres. All similar circles that are created by planes perpendicular to the axis are also called parallels, but are small circles compared to the equator. And the lines passing through the geographic poles will be called meridians. By the way, it is thanks to the equator that our Earth is divided into two parts - northern and southern. Accordingly, there are geographic poles of planet Earth, which are named depending on what part of the world they are located in.
Meridian
If we draw a large plane through the axis itself and through the poles, we end up with a circle called the “full meridian.” All meridians are the same in length, since they pass through a straight line and two points on it in different planes. Only their location changes.
The system of meridians and parallels, which are depicted on the map and on the globe, is a degree network.
It is two-dimensional, since it is specified by only two coordinates - the parallel coordinate and the latitude coordinate. That is, what are geographic coordinates? These are two numbers, indicators of latitude and longitude. Such numbers have dimensions in degrees and minutes.
At the beginning of the article it was said that the Earth is not quite a sphere, that it is slightly flattened. What does this mean? The length of the equator is 40075.7 kilometers, when the length of the meridian is 40008.5 kilometers. The poles are slightly closer to the equator, although on a planetary scale this is not very noticeable.
Planes of the earth's spheroid
It is those imaginary planes that run parallel or perpendicular to the earth’s axis that are the main ones. The area of the plane that passes through the meridian is called, accordingly, the plane of the earth's meridian. The most prominent of them is the Greenwich Meridian. It divides the earth into the eastern and main plane, which passes through the equator and divides the earth into two parts - the Northern and Southern Hemispheres.
Initial reference lines
All coordinates are calculated using conventional stereometry. Reference points have been selected, more precisely, a reference meridian and a reference parallel, from which the coordinates of any place on Earth are calculated. The prime meridian was chosen to be the one that passes through London, namely the Greenwich Observatory. It is customary to take the longest meridian - the equator - as the line that is considered the origin of geographic latitude.
Interesting fact about the Greenwich meridian. There is a system for assigning certain coordinates to a point, and it is called World Geodetic System-84, or WGS-84 for short, (84 is the year the system was adopted), which is used by the whole world, and in which the prime meridian is the ERS Reference Meridian, passing near Greenwich, just 5.31 arcminutes to the east.
Which lines of the Earth give width and longitude
Children at school often confuse these concepts - meridians and parallels, which of them is width and which is longitude. So, the equator is the origin of geographic latitude, while the Greenwich meridian is the starting line for calculating longitude.
Geographic latitude can range from 0 to 90 degrees. Depending on which side of the equator the point is located, it is assigned the value of northern or southern latitude. So, let's say New York has a latitude of 40 degrees 43 minutes north, and Sydney has a latitude of 33 degrees 52 minutes south. It is written as follows: 40 about 43’, 33 about 52’.
Same with geographic longitude. It can also be calculated using degrees and minutes, but longitude ranges from 0 to 180 degrees. It can be western, if it goes west from the prime meridian, and eastern (similarly, to the east from the prime meridian).
As previously stated, the prime meridian passes through Greenwich and has a value of 0 degrees. Which points of the Earth are called the geographic poles of the planet and what are their coordinates? These are those points that have values of ninety degrees in latitude and zero degrees in longitude.
Let's sum it up
On planet Earth, like on a sphere, there are basic points, lines and planes. We have already figured out which points of the earth are called geographic poles. These are the points through which the daily axis passes. If a plane passes through this axis and intersects the geographic poles, then it forms intersections of the Earth's sphere, which are called meridians.
There is one taking place in London, and several others that have dimensions up to 180 degrees (there can be a minimum of 180). If a certain plane passes through the axis of rotation of the Earth, namely perpendicular to it, then their intersection with the sphere of the Earth is a parallel. The parallel that has the greatest longitude is called the equator. It is this that is the starting point for measuring the latitude coordinate. All coordinates are measured in degrees and smaller fractions - minutes, seconds. There are sixty minutes in one degree, and sixty seconds in one minute. Two strokes are used to indicate seconds (the same as for minutes).
Geographic coordinates are numbers used to indicate the position of an arbitrary point on the surface or near the surface of the Earth. These numbers are called longitude and latitude.
A geographic coordinate system is defined in relation to certain basic points and lines on the surface of the globe. Two of these points are the Earth's poles. The geographic poles of the Earth are the points at which the Earth's axis of rotation intersects the surface of the globe. The one of the two poles, when observed from which the Earth rotates counterclockwise, is called the North. The opposite pole is called the South Pole.
The plane passing through the center of the Earth perpendicular to the axis of rotation is called the plane of the Earth's equator. The circle along which this plane intersects the surface of the Earth is called the equator. The equator divides the globe into two equal hemispheres: Northern and Southern.
A plane passing through an arbitrary point M of the earth's surface and the axis of rotation of the Earth intersects the earth's surface along a line called the meridian of point M. The meridians together form a system of imaginary lines connecting the North and South geographic poles. The position of each meridian is determined in relation to one or another meridian, taken as the initial one. The prime meridian and equator are the main lines with which the geographic coordinate system is defined.
At different times, different meridians were taken as the initial one. Since 1634 it was carried out through the island of Ferro. This tiny island is considered the westernmost point of the Old World, and thus the prime meridian symbolically divided the countries of the Old and New Worlds into two hemispheres.
Since 1884, by decision of the International Meridian Conference, it was agreed that the initial meridian was the one that passes through one of the oldest astronomical observatories in the world - the Greenwich Observatory, which at that time was located on the outskirts of London.
The dihedral angle between the planes of the prime meridian and the meridian of a given point on the earth's surface represents one of the geographical coordinates - longitude. Geographic longitude can be measured either east (east longitude) or west (west longitude) of the prime meridian.
To distinguish points lying on the same meridian from each other, enter a second geographic coordinate - latitude. Latitude is the angle formed by a plumb line drawn at a given place on the Earth's surface with the plane of the equator.
For points in the Northern Hemisphere of the Earth, latitudes are considered positive, or northern; for points in the Southern Hemisphere - negative, or southern.
Latitudes can have values from -90° to +90° (or from 90° south latitude to 90° north latitude). The terms “longitude” and “latitude” came to us from ancient sailors who described the length and width of the Mediterranean Sea. The coordinate that corresponded to the measurements of the length of the Mediterranean Sea became longitude, and the one that corresponded to the width became modern latitude.
Determining latitude, like determining the direction of the meridian, is closely related to the observation of stars. Already astronomers of antiquity proved that the height of the celestial pole above the horizon is equal to the geographical latitude of the place.
A line on the Earth's surface connecting points with the same latitudes is called a parallel. The plane of any parallel is parallel to the plane of the earth's equator. Among the parallels, the tropics and polar circles occupy a special place.
The Sun makes a circuit of the celestial sphere throughout the year, moving along the ecliptic, inclined to the celestial equator (see Celestial Sphere) at an angle of 23.5°. On the day of the vernal equinox, it is located at the point of intersection of the ecliptic with the celestial equator and therefore at noon is observed at the zenith at the earth's equator.
Day by day, the Sun moves along the ecliptic into the northern hemisphere of the sky, its declination (see Celestial coordinates) increases, and in subsequent days at noon it passes overhead no longer at the Earth’s equator, but at a latitude numerically equal to the declination of the Sun. This continues until the summer solstice, when the declination of the Sun reaches a maximum value of +23.5°. On this day, it passes through the zenith at the northern parallel of +23.5° for the only time a year at noon. This parallel is called the Tropic of the North, or the Tropic of Cancer (after the name of the zodiac constellation in which the summer solstice point was located in ancient times). On the day of the summer solstice, the polar day zone around the Earth's North Pole extends to the parallel of +66.5°, which is called the Arctic Circle (see Day length).
Six months later, on the day of the winter solstice, the Sun, whose declination is -23.5°, passes overhead for the only time a year at the latitude of the Tropic of Capricorn, i.e., on a parallel with latitude -23.5°. The southern parallel with a latitude of -66.5° is called the Antarctic Circle.
The astronomical determination of one of the geographical coordinates - latitude - is relatively simple. To do this, as mentioned above, it is enough to determine the height of the pole above the horizon. Ancient astronomers were able to do this already in the 3rd century. BC e. Measuring longitude is fraught with much greater difficulties. Neither in antiquity nor in the Middle Ages could they determine longitude from astronomical observations alone, without the use of additional information. This is connected, in particular, with the great delusion of Christopher Columbus, who, due to errors in determining longitude, having discovered the Bahamas, believed that he was sailing near the tip of Asia.
Geographic longitude is obtained as the difference between the local time (see Measuring time) of a given point and the local time of the original point, taken as the prime meridian.
Previously, to determine longitude, observations were made of phenomena that occur almost simultaneously over vast areas of the earth's surface, for example, solar and lunar eclipses or eclipses of Jupiter's satellites.
It was done like this. Astronomers working on the prime meridian, using the results of many years of observations, pre-calculated those moments at which the desired phenomenon occurs according to the local time of the prime meridian. These pre-calculations were published in special tables. Subsequently, the astronomer-navigator or astronomer-traveler, from his measurements, established the moment of local time when the expected phenomenon occurred at the observation point. The result was compared with the table data. Since the phenomenon chosen for observation had to occur simultaneously for all parts of the Earth, the difference between the local time at the observation point and the local time indicated in the table for the prime meridian corresponded to the difference in longitude. A much more convenient way is “time transport”. This method is as follows. The watch, set according to the local time of the prime meridian, is transported to a given point on the Earth, and there its readings are compared with local time. But to apply the “time transport” method in practice, you need a very reliable watch that can store the time of the prime meridian during a long journey. After all, a clock error of just 1 minute when determining longitude near the equator leads to an inaccuracy in determining the location on the Earth’s surface of almost 30 km. Reliable mechanical chronometer watches appeared only in the second half of the 18th century. in England.
With the invention of the telegraph, the time of the prime meridian began to be transmitted to observation points via electric wires. And later the telegraph replaced the radio. The problem of determining geographical longitudes has ceased to exist in our time.
The geographic coordinates described above are called astronomical. Astronomical coordinates are inconvenient for constructing accurate topographic maps, since the plumb lines with which latitude measurements are associated change incorrectly when moving from one point on the earth's surface to another. The direction of plumb lines is greatly influenced by gravitational anomalies (see Gravimetry) associated with the terrain and other reasons.
For solving geodesy problems, geodetic coordinates are more convenient. In the geodetic coordinate system, the plumb line is the perpendicular to the earth's ellipsoid. Thus, geodetic latitude is equal to the angle between the direction of the perpendicular to the earth's ellipsoid drawn through a given point and the equatorial plane of the ellipsoid. It differs only slightly from astronomical latitude.
Instead of a plumb line, you can use the radius vector of a given point on the Earth's surface drawn from its center. A system of geographic coordinates that is half-valued in this way is called geocentric.
The figure (p. 65) shows a cross section of the Earth along the meridian and the difference in geographical latitudes - astronomical, geodetic and geocentric.
By analogy with the system of geographic coordinates on Earth, similar systems are introduced on the surfaces of other planets and their satellites.
Two geographic coordinates - latitude and longitude - determine the position of a point on a regular geometric figure - a sphere or on the earth's ellipsoid. For points on the real physical surface of the Earth, a third coordinate is introduced. The height above the geoid, the so-called altitude above sea level, is most often used for this purpose.
Measuring the height of points on the earth's surface above sea level is not an astronomical, but a geodetic task. The beginning of the calculation of heights is usually set by the results of long-term averaged observations of water levels in the seas using special water meters - foot rods. The height system on the territory of the USSR is based on the average water level of the Baltic Sea and originates from the zero of the Kronstadt water gauge.
The earth's axis intersects the surface of the planet at the points of the geographic poles.
Geographic poles
As you know, there are two poles of the Earth: the North (located in the Arctic Ocean in the central part of the Arctic) and the South (located on the continent of Antarctica). These places do not belong to any state.
The South Pole is the southernmost point of the planet, and the North Pole, accordingly, is the northernmost. A person standing exactly at the pole (for example, at the South Pole) takes every step towards the north.
The areas surrounding the poles are the coldest on the planet and are called the Arctic. There are also two seasons of the year: polar night and polar day. This is due to the fact that the illumination here is different from the rest of the planet due to the deviation of the earth's axis from the orbital plane by about 20°.
Conquest of the Poles
The conquest of the poles was very slow and occurred only at the beginning of the twentieth century. People have tried to conquer the North Pole since the seventeenth and eighteenth centuries, since all the continents around were inhabited for a long time and voyages in the southern parts of the Arctic Ocean took place for centuries. However, during the short Arctic summer it was not possible to sail there by sea, and icebreakers did not yet exist.
In this regard, the North Pole was explored only in 1909. The success of the expedition of the discoverer Robert Peary was guaranteed, in many respects, by the fact that the northern coast of Greenland, located closest to the pole, was chosen as the starting point. Other explorers tried to reach the Arctic from Europe, and they simply did not have enough supplies to complete the trip.
Other famous travelers who attempted to reach the North Pole included:
- F. Nansen.
- W. Parry.
- F. Cook.
- C. Hall.
Research in Antarctica began much later, because the continent itself was only discovered in the first half of the nineteenth century. It was reached by the Russian expedition of Bellingshausen. Only a few decades after this, people first set foot on Antarctic soil. In 1911, several pioneers went to the pole at once, and in the end the victory went to the Norwegian R. Amundsen.
The earth's axis intersects the surface of the planet at the points of the geographic poles.
Geographic poles
As you know, there are two poles of the Earth: the North (located in the Arctic Ocean in the central part of the Arctic) and the South (located on the continent of Antarctica). These places do not belong to any state.
The South Pole is the southernmost point of the planet, and the North Pole, accordingly, is the northernmost. A person standing exactly at the pole (for example, at the South Pole) takes every step towards the north.
The areas surrounding the poles are the coldest on the planet and are called the Arctic. There are also two seasons of the year: polar night and polar day. This is due to the fact that the illumination here is different from the rest of the planet due to the deviation of the earth's axis from the orbital plane by about 20°.
Conquest of the Poles
The conquest of the poles was very slow and occurred only at the beginning of the twentieth century. People have tried to conquer the North Pole since the seventeenth and eighteenth centuries, since all the continents around were inhabited for a long time and voyages in the southern parts of the Arctic Ocean took place for centuries. However, during the short Arctic summer it was not possible to sail there by sea, and icebreakers did not yet exist.
In this regard, the North Pole was explored only in 1909. The success of the expedition of the discoverer Robert Peary was guaranteed, in many respects, by the fact that the northern coast of Greenland, located closest to the pole, was chosen as the starting point. Other explorers tried to reach the Arctic from Europe, and they simply did not have enough supplies to complete the trip.
Other famous travelers who attempted to reach the North Pole included:
- F. Nansen.
- W. Parry.
- F. Cook.
- C. Hall.
Research in Antarctica began much later, because the continent itself was only discovered in the first half of the nineteenth century. It was reached by the Russian expedition of Bellingshausen. Only a few decades after this, people first set foot on Antarctic soil. In 1911, several pioneers went to the pole at once, and in the end the victory went to the Norwegian R. Amundsen.
