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In the 18th and 19th centuries, astronomers used the exact method of triangulation to measure the Earth.
In this case, the direct measurement of large lengths on the Earth is replaced by the determination of angles in a system of triangles, divided on a convex earth surface. Comparison of such measured arcs, drawn both along the meridians and in longitude, across different continents, made it possible to form an idea of the shape and actual dimensions of the Earth's solid shell.
The earth turned out to be different from a sphere; only in the coarsest approximation can it be taken for a ball with a radius of 6371 km. In fact, it is flattened at the poles in accordance with the laws of rotation of bodies and Newton's theory of gravitation. The polar radius is almost 21 km shorter than the equatorial radius. Therefore, in the second approximation, the Earth can be considered a slightly oblate sphere, the so-called spheroid, or ellipsoid of revolution. The elements of this ellipsoid serve as the basis for building accurate maps of the earth's surface.
We present data on the ellipsoid, which were established in 1940 by Soviet scientists: the equatorial radius is 6378 km, the polar radius is 6356.9 km. Therefore, the length of the Earth's meridian, ie, the circle passing through the poles, is 40,010 km, and the area of the entire surface is 510 million km 2. Of these, land accounts for only 29%; the rest, that is, almost three quarters of the entire surface, is a gigantic area of oceans and seas.
However, the real shape of the Earth is different from the ellipsoid; continents protrude somewhat above the surface of the oceans, and land is much larger in the Northern Hemisphere of the Earth than in the Southern Hemisphere. Finding out the exact figure of the Earth is of great interest. Therefore, scientists continue accurate measurements using geodesy methods, determining the sides and angles of triangles and building geodesic signs that are located at the vertices of these triangles. The force of gravity is measured at all accessible points of the Earth, for which extremely accurate gravimeters have recently been used. The data obtained make it possible not only to judge about inhomogeneities in the earth's crust, mineral deposits, but also to study the shape of the Earth.
The mass of the Earth (the amount of its substance) is 6000 billion billion tons. Dividing the mass by volume, we get the average density of the terrestrial substance, which turns out to be 5.5 times more than water. And since the average density at the surface is only 2.6 in relation to water, the substance of the inner regions of the Earth must be very strongly compacted and correspond to the density of iron or steel.
Recently, artificial satellites have begun to be used to study the size and shape of the Earth. Based on the laws of celestial mechanics, astronomers are able to determine the exact orbits of satellites and, through continuous observations, monitor all changes in their movement. Therefore, you can always know where, when and at what altitude the satellite is flying. Accurate measurements of the position of the satellite in the sky, made from several points on the Earth, make it possible to judge the positions of the observers themselves, that is, they make it possible to check geodetic data on the earth's surface. The results are obtained in a number of cases more accurate than with geodetic determinations.
The method of observing satellites is especially important in clarifying the question: are the continents shifting relative to each other? Is it true that the American continent drifted long ago from the western borders of Europe and Africa, as some scholars suggest? Indeed, the line of the east coast of America fits well with the outlines of the western coasts of Europe and Africa. To clarify this issue, a large number of accurate observations are needed. Some time will pass, and scientists will be able to answer the question about the movement of continents.
Rockets and satellites are also increasingly used for direct observation of the Earth from great heights, from interplanetary space. Everything. saw the remarkable color photographs of the earth's surface, taken by GS Titov from the Vostok-2 satellite. A permanent meteorological service is already being conducted from satellites equipped with television installations. From the images on the screens of terrestrial televisions, one can monitor the state of the weather in various regions of the Earth, and study the movement of cyclones.
Devices raised on satellites record the state of the magnetic field around the Earth, the number and characteristics of cosmic particles, meteoric particles, ultraviolet and X-rays, and much more. The use of satellites allowed in 1958-1959. discover the existence of the Earth's corona - two or even three belts of high energy particles - fast protons and electrons held by the earth's magnetic field. These radiation belts seem to play a very important role in various atmospheric phenomena and in life on Earth.
Man has always been interested in everything that surrounded him: minerals, rocks, water, fire, air, plants, animals.
Ancient scientists collected facts, and then systematized them and established patterns. In their work, they used various methods and techniques, that is, methods (from the Greek word "methodos" - a way of research, theory, teaching).
Like all sciences, geography has special research methods. Let's take a look at some of them.
Geographical description
This method was usually used by explorers, navigators, travelers, who recorded the first information about the open lands and peoples inhabiting them. They tried to answer the questions: where is it located? What does it look like? What features does it have?
Now this method is widely used by participants in field research and expeditions studying the relief, the World Ocean, the Earth's atmosphere, as well as the Arctic and Antarctica.
Cartographic method
The map is a special source of geographic knowledge. It reflects and organizes information obtained through observations and descriptions.
The first geographical maps appeared in Ancient Greece in the VIII-VI centuries. BC er .. Time passed. Maps were refined and improved. Nowadays, computer maps are widely used.
Cartographers create various maps - geographical, climatic, minerals, etc. Thus, the cartographic method of research is the use of maps for the scientific and practical knowledge of the objects and phenomena depicted on them. It is an integral part of most geographic exploration.
Comparative geographical method
The comparative geographical method is one of the oldest in geography. It allows, by means of comparison, to identify the general and the special in geographic objects, phenomena, processes.
Aerospace method
Currently, this method has become one of the most important in geography. Observations and images from airplanes, satellites, space stations make it possible not only to draw up very accurate maps, but also to find new deposits of minerals, to monitor human activities, pollution of the earth's surface, to receive information about other planets of the solar system, the Galaxy, and the Universe.
Statistical method
The statistical method is used to analyze statistical - quantitative and qualitative - data. Statistical accounting was carried out in ancient times. For example, in ancient China, population censuses were conducted. Currently, the statistical method is used in almost all industries. In geography, statistical material is presented in the text of textbooks, in maps, as well as in the form of diagrams, graphs, tables.
- How did ancient people study the Earth?
- What is the method of geographic description?
- What role does the cartographic method play in our time?
- What does the aerospace method give to modern geography?
- Are the methods of geographical research used by ancient scientists in the age of computer technology?
The Earth is a unique planet: only on it there is life. are closely interrelated, they change and complement each other. Processes occurring in nature and changing it - - are divided into physical and biological. Man has a huge impact on changing the face of the Earth.
They are called natural sciences. These include astronomy, physics, chemistry, geography, biology, geology, ecology.
Forms a group of interrelated sciences, the number of which is constantly increasing. There are two main sections: physical and socio-economic geography.
Special methods of geographical research are geographical description, cartographic, comparative geographical, aerospace and statistical methods.
Basic concepts and terms of the section:
- Live nature
- inanimate nature
- natural phenomena: physical, biological
- natural Sciences
- physical geography
- socio-economic geography
- methods of geographic research
Site search.
What are modern methods of studying the Earth for?
Answers:
Research methods in geography today remain the same as before. However, this does not mean at all that they do not undergo changes. The newest methods of geographical research appear, allowing to significantly expand the possibilities of mankind and the boundaries of the unknown. But before considering these innovations, you need to understand the usual classification. Geographic research methods are different ways of obtaining information within the framework of the science of geography. They are divided into several groups. So, the cartographic method is the use of maps as the main source of information. They can give an idea not only of the mutual arrangement of objects, but also of their sizes, the degree of distribution of various phenomena and a lot of useful information. The statistical method says that it is impossible to consider and study peoples, countries, natural objects without using statistical data. That is, it is very important to know what is the depth, height, reserves of natural resources of a particular territory, its area, the population of a particular country, its demographic indicators, as well as production indicators. The historical method implies that our world has developed and everything on the planet has its own rich history. Thus, in order to study modern geography, it is necessary to have knowledge about the history of the development of the Earth itself and of humanity living on it. Geographic research methods continue the economic and mathematical method. These are nothing more than numbers: calculations of mortality, fertility, population density, resource availability The comparative-geographical method helps to more fully assess and describe the differences and similarities of geographical objects. After all, everything in this world is subject to comparison: less or more, slower or faster, lower or higher, and so on. This method makes it possible to compile classifications of geographic objects and predict their changes. Geographic research methods cannot be imagined without observation. They can be continuous or periodic, areal and route, remote or stationary, the less they all provide the most important data on the development of geographic objects and the changes they undergo. It is impossible to study geography while sitting at the desk in the office or at the school desk in the classroom; you need to learn how to extract useful information from what you can see with your own eyes. One of the important methods of studying geography has been and remains the method of geographic regionalization. This is the allocation of economic and natural (physical and geographical) regions. The method of geographic modeling is no less important. We all know the most striking example of a geographic model from school - the globe. But modeling can be machine, mathematical, and graphical. Geographic forecasting is the ability to predict the consequences that may arise as a result of human development. This method allows you to reduce the negative impact of human activities on the environment, avoid undesirable phenomena, rationally use all kinds of resources, and so on. Modern methods of geographical research have revealed to the world GIS - geographic information systems, that is, a complex of digital maps, software tools and statistics linked to them, which enable people to work with maps directly on a computer. And thanks to the Internet, satellite positioning systems appeared, popularly known as GPS. They consist of ground tracking devices, navigation satellites and various devices that receive information and determine coordinates. All these methods are interconnected. For example, it is impossible to study any country completely, if you exclude at least one of these methods. There are many examples, knowing the methods, you can compose them yourself ...
Introduction
A brief historical overview
Study of the shape and size of the Earth at the present stage
Methods for studying the figure of the Earth
1 Gravimetric method
2 Definition of a common terrestrial spheroid
3 Space method
4 Geometric method
Conclusion
List of sources used
Introduction
Determining the shape and size of the Earth is one of the main tasks of modern science.
Man has always wanted to navigate the world around him. Man strove to represent the Earth in the form of an image that would help him navigate in the world around him.
So, even in the Stone Age, the surface of the Earth was depicted in the form of a drawing on the bones of animals, on the walls of caves, etc. These drawings showed places of residence, main paths, rivers, in general, everything necessary for human life at that time.
With the advent of time, they began to depict the boundaries of the possessions of different states on the maps, and it was after this that a person had a serious question - How to depict the surface of the Earth as accurately as possible for better orientation in this world?
But the Earth is neither a ball nor an ellipse and does not have a form that can be expressed mathematically. Therefore, humanity has sought to determine as accurately as possible the true shape of the Earth, using various methods.
Later, with the study of gravimetry, humans had a new goal in studying the shape of the Earth - this is to determine the shape and size of the Earth as accurately as possible, not only for making maps, but also for constructing physical theorems. Knowing which people perceived the nature and the processes taking place in it better.
Therefore, I can say with confidence that this topic is very relevant at the present stage.
The main purpose of this course work is to describe the basic methods for determining the shape and size of the Earth.
To achieve this goal, you need to complete the following tasks:
give a brief historical overview in the study of the shape and size of the Earth.
to characterize the study of the shape and size of the Earth at the present stage.
This course work consists of an introduction, 3 sections, which are structured into paragraphs, conclusions and a list of sources used, and contains 3 figures.
1. A brief historical overview
Earth is the third planet from the sun and the largest and most complex dynamic object of all the inner planets. (picture 1)
Picture 1
The earth has a shape close to spherical. The radius of the sphere, equal to the size of the Earth, is 6371 km. The earth revolves around the sun and revolves around its axis. One natural satellite revolves around the Earth - the Moon.
Usually, the figure of the Earth is understood as a body bounded by its physical surface and the undisturbed surface of the seas and oceans. When determining the shape of the Earth, it is not necessary to depict its physical surface in detail in the form of maps; it is enough to determine the position of a network of points on it in a single spatial coordinate system. In the formation of the Earth, the heat of the interior and the processes of radioactive decay played an essential role. The formation of the earth's crust took place over a long period, which, according to paleontology, is divided into eras, periods, epochs, centuries. The presence of the hydrosphere and the emergence of organic life on it played an important role in the evolution of the Earth.
Ideas about the shape of the Earth. Since school years, we have become accustomed to considering the Earth as a ball, and we have no doubts about this. Meanwhile, the question of the shape of the Earth is far from being as simple as it seems to us at the present time. It took a lot of work and time before humanity was able to resolve this very important and complex issue.
The idea of the most ancient peoples about the Earth was based on what they saw. The earth is a vast flat space, over which the solid vault of the sky, strewn with stars, is toppled over. We meet this representation in various variations among all the ancient peoples who inhabited western Asia and southeastern Europe.
However, with the accumulation of observations, the idea of the convex shape of the Earth gradually arose. Objects lurking behind the horizon, the rays of the rising sun, illuminating first the peaks and then the bases of the mountains, and other facts have led to the need to admit that the Earth has the shape of a shield convex upward or a flat-convex dome. We find similar ideas among the ancient Babylonians, Hindus and some other cultural peoples of the ancient East.
The shape and size of the Earth. According to modern cosmogonic concepts, the Earth was formed about 4.6-4.7 billion years ago from a protoplanetary cloud captured by the gravity of the Sun. The formation of the first, most ancient of the studied rocks took 100-200 million years.
Its orbit lies between the orbits of Venus and Mars. It moves around the Sun at an average speed of 29.765 km / s in an elliptical, close to circular orbit (eccentricity 0.0167). The average distance from the Sun is 149.6 million km. At perihelion it decreases to 147 million km, and at aphelion it increases to 152 million km. The period of one revolution in orbit is 365.24 solar days. The rotation of the Earth around its own axis occurs with an average angular velocity of 7.3 · 10-5 rad / s, which approximately corresponds to a period of 23 hours 56 minutes 4.1 seconds. The linear velocity of the Earth's surface at the equator is about 465 m / s. The axis of rotation is inclined to the plane of the ecliptic at an angle of 66 ° 33? 22 ??. This tilt and the annual rotation of the Earth around the Sun determine the change of seasons, which is extremely important for the Earth's climate, and its rotation around the axis - the change of day and night. There are also small irregular variations in the length of the day.
In general, the shape of the Earth is close to an ellipsoid, flattened at the poles and stretched in the equatorial zone. In our country, the term "Krasovsky ellipsoid" is adopted. The average radius of the Earth is 6371 km, polar - 6356 km, equatorial - 6378 km. Earth mass 5.976 10 24kg, average density 5518 kg / m 3... The surface area of the Earth is 510.2 million km2 .
In fact, the level surface of the Earth does not coincide with the surface of the ellipsoid. Geoid is a conventional name for the true figure of the Earth, proposed in 1873 by the German scientist I. Listing (geoid - earthlike). A geoid is a geometrically complex surface of equal values of the gravity potential, coinciding with the undisturbed surface of the World Ocean and continued under the continents. It is close to an ellipsoid with a compression of 1: 298.2. Due to the daily rotation of the Earth, there are only fixed points on the earth's surface - the geographic poles are the points of intersection of the imaginary earth's axis with the earth's surface. The position of the geographic poles changes with a period of 434 days with an amplitude of 0.36 ??. In addition, there are also small seasonal movements.
In relation to the poles, the equator is determined, parallels and meridians are drawn. The equator is a line on a globe or map that is equidistant from the poles. Its length is 40,076 km. Parallels are lines parallel to the equator. These are circles of a mental section of the Earth with planes perpendicular to its axis. The latitude is determined by the parallels - the distance in degrees from the equator to any point. She changes from 90 º s.sh. up to 90 º south latitude Meridians are lines that connect the poles. These are circles formed by the intersection of the globe by planes passing through the earth's axis. The meridians determine the geographic longitude - the distance in degrees from the initial meridian to any point. Longitudes are western and eastern and vary from 0 to 180 °.
The idea of the shape and size of the Earth was created gradually, based on observations, measurements and calculations.
Already in the 7th century BC. ancient Greek scientists suggested that the earth was spherical. In the 4th century BC. Aristotle collected the already available evidence of the sphericity of the Earth, supplemented and substantiated them (the round shadow of the Earth during eclipses, a change in the appearance of a stellar appearance, etc.). Eratosthenes of Cyrene in the 2nd century BC determined the close to the real length of the great circle (40,000 km) and one degree of the meridian (110.6 m - real 111.2 m).
Traveling around the world only confirmed the evidence for sphericity. With the advent of accurate methods for measuring distances and angles (triangulation) in 1669-70. French scientist Jean Picard accurately measured the length of the meridian and came to the conclusion that the Earth is not a perfect ball with a radius of 6371.7 km. The French astronomer Richet, having made experiments with a pendulum, came to similar conclusions.
Newton formulated the law on the obligatory deviation of the figure of a rotating body from the ball. Simultaneously with Christian Huygens, he determined the polar compression of the Earth.
2. Study of the shape and size of the Earth at the present stage
Teaching about the Earth as a ball. As knowledge expanded, more accurate material began to accumulate on the change in the length of the midday shadow at different latitudes of the Earth. History has not preserved us with exact information about when and where the idea of the sphericity of the Earth first appeared. But there is reason to think that they originated among the Babylonians, and then moved to ancient Greece.
So, for example, the Greek thinker Parmenides already definitely spoke of the Earth as a ball. In the works of the famous Greek philosopher Aristotle, a number of very convincing proofs of the spherical shape of the Earth are given.
Aristotle's pupil Dicaearchus had already attempted to measure the Earth, taking as a base two points located on the same meridian. According to Dicaearchus, the circumference of the Earth has about 300 thousand stages. 2, i.e. about 47 thousand km. In any case, this value is not so far from the actual size.
Information about the measurement of the meridian, produced by the Alexandrian scientist Eratosthenes, is much more complete. Eratosthenes knew that in the city of Siena, located south of Alexandria, the sun once a year, on June 22, that is, on the day of the summer solstice, illuminates the bottom of the deepest wells at noon.
In other words, on this day at noon in Siena, the sun is at its zenith, and vertically standing objects do not give shadows. At the same time in Alexandria, objects give shade. Using a tall, upright post and its shadow, Eratosthenes calculated that in Alexandria on June 22 at noon, the sun's ray and the vertical form an angle. It is easy to see that this angle is equal to the central angle of the AOC. Knowing the length of the arc of the angle we marked (it is the distance between Siena and Alexandria), Eratosthenes calculated the circumference of the globe. The distance between Siena and Alexandria is 5 thousand Egyptian stages, so the circumference of the Earth is thousand stages.
After a very long break, the first measurement of a degree in order to determine the size of the globe was made by the French scientist Fresnel in 1528. Taking the distance from Amiens to Paris (measuring it by the number of revolutions of the wheel of the carriage) and determining astronomically the difference in latitudes, he obtained the dimensions of the Earth, quite close to modern.
The earth is like an ellipsoid. (Figure 2) Until the half of the 17th century. The earth was considered a regular ball, but then facts were noticed that made one doubt the correctness of this idea.
Figure 2
Thus, the astronomical clock, transported in 1672 from Paris to Cayenne (Guiana), began to lag every day. To get the correct time reading, the clock pendulum had to be shortened. Further observations made elsewhere showed that the swinging speed of the pendulum decreases as it moves from the poles to the equator. Initially, they tried to explain this phenomenon by the centrifugal force of the Earth's rotation. However, more accurate calculations showed that such changes would require an increase in the Earth's rotation speed by 17 times. The only possibility remained to assume that the decrease in the force of gravity from the poles to the equator depends on the polar compression of the Earth.
The conclusion about the polar compression of the Earth met with a number of objections. The controversy that erupted around these questions forced the French Academy to equip two expeditions to measure the length of a degree in polar and equatorial latitudes. Both expeditions, working completely independently (one in Peru in 1735 and the other in Lapland in 1736), gave the following results: the length of a degree in Lapland is 57,437 toises, the length of a degree in Peru is 56,753 toises. Consequently, the equatorial degree turned out to be shorter than the polar one by 648 tuise. From this it was possible to draw a completely definite conclusion about the polar compression of the Earth. Later, these conclusions were confirmed by other even more accurate measurements. The polar radius of the Earth turned out to be 21.4 km shorter than the equatorial one.
Earth as a geoid. Continuing in the XIX century. Degree measurements and measurements of gravity at various points showed that the shape of the Earth is more complex than it was supposed. For example, the stress of gravity on many oceanic islands turned out to be much greater than on the continents. Based on these facts, it was necessary to admit that the water level in the oceans is not the same, the shape of the Earth in many cases deviates from the shape of an ellipsoid of revolution. Further measurements showed that the Earth in its shape, although it approaches the ellipsoid of rotation, has a more complex shape inherent only in it, which is called the geoid 3... This individual shape of the Earth has not yet been adequately studied. It is known that the surfaces of the theoretically calculated ellipsoid and geoid do not coincide, but this discrepancy does not exceed 100 m.In practice, for geodesy and cartography, such a deviation from the shape of the ellipsoid does not play a role, and therefore geodesists in all their calculations proceed from the fact that the Earth has the shape of an ellipsoid rotation.
Dimensions of the Earth. In the Soviet Union, the dimensions of the globe, calculated by the Soviet scientists F.N. Krasovsky and A.A. Izotov, are currently accepted. They are characterized by the following data.
Shrinking the Earth
Surface of the Earth S = 510 million km2 .
The water surface of the Earth Sb = 71% of the entire surface of the Earth.
Land surface Sc = 29% of the entire surface of the Earth.
The volume of the Earth is V = 1083 billion km3 .
Earth mass m = 6X10 21tons, of which about 7% is water.
The arc length of 1 ° at different geographic latitudes is different:
To calculate the dimensions of the terrestrial ellipsoid, FN Krasovsky drew on extensive materials on the degree measurements not only of the Soviet Union, but also of Western Europe and the USA. In addition, for the first time, the results of measurements of the force of gravity were used to calculate the dimensions of the Earth. The dimensions of the ellipsoid derived in this way correspond more to the figure of the Earth in its continental part than all previously obtained ones. Therefore, on April 7, 1946, the Council of Ministers of the USSR adopted a resolution according to which all geodetic work should be carried out on the basis of the F. N. Krasovsky ellipsoid.
Geographic significance of the shape and size of the Earth. The spherical shape of the Earth causes an uneven distribution of heat on the earth's surface. The sun's rays fall on the convex surface of the ball at different angles. In the equatorial zone, they fall vertically or almost vertically, and with distance from the equator, the angle of incidence of sunlight on the earth's surface decreases. In this regard, the heating of the Earth at the same moment from the equator to the poles decreases, which leads to a change in climates, to a change in natural conditions at different latitudes.
It is hardly necessary to write much about the shape of the Earth. It is clear to everyone that the Earth is a ball, slightly flattened at the poles, that is, the so-called ellipsoid. However, the correct, modern idea of the shape and size of the Earth was not achieved immediately and was achieved at times in a difficult struggle between science and religion.
The Greek poet Homer (IX-VIII centuries BC) depicted the Earth in the form of a circle, captured from all sides by the Ocean River, "which rolls its mighty waters along the rim of a rich shield"; such an image of the Earth was engraved, allegedly, on the shield of the mythical hero Achilles. The philosopher Thales (VI century BC) believed that the Earth is a sphere, and his student Anaximander depicted the Earth in the form of a cylinder. Other philosophers and scientists of ancient Greece imagined the Earth in the form of a cube, then in the form of a boat, etc .; the disciples of Xenophon and Anaximenes believed that the Earth is a very high mountain. Greek mythology contains a legend about how Zeus, wanting to determine the size of the Earth, released two eagles simultaneously, one to the west, the other to the east: they met in the city of Delphi; it was called "the discovery of the earth by the flight of two eagles."
Over the course of a number of centuries, through the jungle of scholasticism and the religion of the Middle Ages, truth has made its way.
Quite recently, in 1862, the German scientist P. Ioseliani, determining the "depth of the earth's thickness", received 4536.8 km, which is 11/2 times less than the actual value. It’s hard to believe, but back in 1876 in St. Petersburg a brochure was published entitled: “The Earth is motionless, a popular lecture, proving that the globe does not revolve either about the axis or about the Sun. Chitan in Berlin, by Dr. Shepfer. Translated from German by N. Solovyov. Edition 2, revised. " We will not dwell on such misconceptions, and we will not touch on the history of the issue. Consider the information that is more significant for us in this case.
In 1841, the German astronomer F. Bessel, using degree measurements, calculated the radius of the Earth and its contraction at the poles, that is, he received figures characterizing the main elements of the earth's ellipsoid. The result was so accurate that these numbers were used in various geodetic studies, in cartography, etc. for 100 years.
3. Methods for studying the figure of the Earth
3.1 Gravimetric method
Gravimetry is a branch of the science of measuring quantities characterizing the Earth's gravitational field<#"59" src="doc_zip6.jpg" />
where G is the gravitational constant, mu is the unit mass, dm is the mass element, R are the radius vectors of the measurement point, r is the radius vector of the mass element, w is the angular velocity of the Earth's rotation; the integral is taken over all masses.
The potential of gravity, respectively, is determined by the ratio:
where - latitude of the measuring point.
Gravimetry includes the theory of leveling heights, processing of astronomical and geodetic networks in connection with variations in the Earth's gravitational field.
The unit of measurement in gravimetry is Gal (1 cm / s2), named after the Italian scientist Galileo Galilei.
Determinations of the force of gravity are made by the relative method, by measuring with the help of gravimeters and pendulum devices the difference in the force of gravity in the studied and reference points. The network of gravimetric reference points throughout the Earth is ultimately connected with the point in Potsdam (Germany), where the absolute value of the acceleration of gravity was determined by the revolving pendulums at the beginning of the 20th century (981,274 mgl; see Gal). Absolute definitions of gravity are difficult and less accurate than relative measurements. New absolute measurements made at more than 10 points of the Earth show that the reduced value of the acceleration of gravity in Potsdam is exceeded, apparently, by 13-14 mgl. After the completion of these works, the transition to a new gravimetric system will be carried out. However, in many problems of gravimetry, this error is not significant, since to solve them, not the absolute values themselves are used, but their differences. Most accurately, the absolute value of the force of gravity is determined from experiments with the free fall of bodies in a vacuum chamber. The relative determinations of the force of gravity are made by pendulum instruments with an accuracy of several hundredths of a millimeter. Gravimeters provide a slightly higher measurement accuracy than pendulum instruments, are portable and easy to use. There is special gravimetric equipment for measuring gravity from moving objects (submarines and surface ships, aircraft). The devices continuously record the change in the acceleration of gravity along the path of the ship or aircraft. Such measurements are associated with the difficulty of excluding from the readings of instruments the influence of disturbing accelerations and tilts of the instrument base caused by rolling. There are special gravimeters for measurements at the bottom of shallow water basins, in boreholes. The second derivatives of the gravity potential are measured using gravity variometers.
The main range of problems of gravimetry is solved by studying the stationary spatial gravitational field. To study the elastic properties of the Earth, the variations in the force of gravity over time are continuously recorded. Due to the fact that the Earth is inhomogeneous in density and has an irregular shape, its external gravitational field is characterized by a complex structure. To solve various problems, it is convenient to consider the gravitational field as consisting of two parts: the main one - called normal, which varies with the latitude of the place according to a simple law, and anomalous - small in magnitude, but complex in distribution, due to inhomogeneities in the density of rocks in the upper layers of the Earth. The normal gravitational field corresponds to some idealized model of the Earth, simple in shape and internal structure (an ellipsoid or a spheroid close to it). The difference between the observed gravity and normal gravity, calculated using one or another formula for the distribution of normal gravity and reduced by appropriate corrections to the accepted level of heights, is called the gravity anomaly. If this reduction takes into account only the normal vertical gravity gradient of 3086 evesh (i.e., assuming that there are no masses between the observation point and the reference level), then the anomalies obtained in this way are called free air anomalies. The anomalies calculated in this way are most often used in the study of the figure of the Earth. If the reduction also takes into account the attraction of a layer of masses considered to be homogeneous between the observation and reduction levels, then anomalies are obtained, called Bouguer anomalies. They reflect the heterogeneity in the density of the upper parts of the Earth and are used in solving geological exploration problems. In gravimetry, isostatic anomalies are also considered, which in a special way take into account the effect of masses between the earth's surface and the level of the surface at a depth at which the overlying masses exert the same pressure. In addition to these anomalies, a number of others are calculated (Preya, modified by Bouguer, etc.). Based on gravimetric measurements, gravimetric maps with isolines of gravity anomalies are constructed. Anomalies of the second derivatives of the gravity potential are determined similarly as the difference between the observed value (previously corrected for the terrain) and the normal value. Such anomalies are mainly used for mineral exploration.
In tasks involving the use of gravimetric measurements to study the shape of the Earth, it is usually the search for an ellipsoid that best represents the geometric shape and external gravitational field of the Earth.
3.2 Definition of a common terrestrial spheroid
Let us denote the major semiaxis of the spheroid (equatorial radius) by a, the minor (polar radius) by b; the ratio (a-b) / a is called the compression of the terrestrial spheroid ?. The value of a is influenced not only by the speed of rotation of the planet on its axis, but also by the nature (degree of homogeneity) of the internal structure of the planet. The most correct and accurate representation of the general figure of the Earth as a whole is an ellipsoid calculated by FN Krasovsky and his colleagues on the basis of new data obtained during the processing of degree measurements of the USSR, Western Europe and the USA. Consequently, the equatorial diameter of the Earth is 12756.5 km, the length of the Earth's axis is 12,713.7 km, and the polar radius is shorter than the equatorial one by only 21.4 km, and therefore the average polar compression is so negligible that the Earth's spheroid practically does not differ much from the correct one. ball. The magnitude of compression for planets such as Jupiter, Saturn and Uranus is much greater: it is equal to 1: 15.4, respectively; 1: 9.5 and 1: 14. Their greater compression is due to the presence of atmospheres of enormous extent and the fact that they rotate on their axes almost two and a half times faster than the Earth. The average radius of the Earth is considered to be the radius of the ball, the same volume as the earth's spheroid, namely 6371.110 km. It is calculated that the surface of the earth's spheroid is about 510 million square meters. km, and the volume is 1.083 X 1012 cubic meters. km. The circumference of the meridian is 40008.548 km. The work on calculating the new ellipsoid showed that the Earth is, in essence, a triaxial ellipsoid. This means that it has not only polar, but also equatorial compression, which, however, is only 1:30 000. Consequently, the earth's equator is not a circle, but an ellipse; the largest and smallest radii of the equator differ by 213 m. However, the adoption of a triaxial ellipsoid in geodetic work would greatly complicate this work and would not bring special practical benefits. Therefore, the figure of the Earth in geodesy and cartography is considered as a biaxial ellipsoid.
3.3 Space method
Space geodesy is a science that studies the use of the results of observations of artificial and natural satellites of the Earth for solving scientific and scientific-technical problems of geodesy. Observations are carried out both from the surface of the planet and directly on the satellites. Space geodesy has been widely developed since the launch of the first artificial Earth satellite.
One of the tasks of space geodesy is to study the shape of the Earth, Moon and planets using satellite measurements.
Since the launch of an artificial Earth satellite in 1958, new tasks have been set for geodesy, these are observations of artificial Earth satellites in orbit and the determination of the spatial coordinates of points on the Earth's surface, the creation of a geodetic reference network.
The influence of deviations of the real orbits of artificial earth satellites from those calculated by Kepler's formulas makes it possible to clarify the idea of the Earth's gravitational field and, ultimately, of its shape.
In conclusion, we present some considerations related to the prospects for the development of space geodesy. The fact is that at present, researchers have a fairly clear idea of how to use existing space facilities and methods to solve the main problems of geodesy and geodynamics. As before, the main task of geodesy is to determine the size, shape and gravitational field of the Earth. Work will continue to refine and develop large regional and global triangulation networks. In this work, an essential role is played by the establishment of a single general terrestrial coordinate system for high-precision measurements, and at the first stage - the determination of the relative position of the origins and orientation of the axes of various systems of geodetic coordinates.
The prevailing opinion that the origin of the common terrestrial coordinate system should be the center of mass of the Earth may change. The problem of determining the position of the center of mass in the Earth's body turned out to be much more complicated than previously assumed: in the exact formulation, we should talk about the center of mass of the Earth-Moon system. The creation of new equipment will make it possible to more accurately study such subtle geodynamic effects related specifically to the Earth-Moon system as the movement of the Earth's poles, variations in the Earth's rotation speed, and Earth tides.
The study of displacements of continental plates will continue, undoubtedly one of the projects of the global service for tracking the movement of continents will be carried out. The finest, at the limit of accuracy (several microGal), studies of variations in gravity will continue.
But the development of space methods in the near future will not be limited to their use within the Earth.
And although the prefix "geo" remains in the names of the scientific disciplines we are talking about, these methods have long become common for the study of the solar system as a whole.
The study of the gravitational field and the shape of the moon has been underway for a long time. There are even attempts to introduce the term "selenodezia" into scientific use (Selena is the ancient Greek name for the moon). It makes sense to talk about determining the gravitational fields of planets.
And if you look more seriously into the future of space methods, then you can imagine such a task. Is it possible to create within the solar system a unified approach to coordinate systems that would help to link them into a single hierarchical structure?
The fact is that when a spacecraft flies to distant planets, it seems to pass from a geocentric system to a heliocentric system, then, for example (if it flies around Mars), to an arecentric one, and it must have a connection with the coordinate systems of the satellites of Mars, etc.
And if we imagine the difference in the sizes (scales) of these coordinate systems, then it becomes unclear how to maintain uniform requirements for the relative accuracy of the coordinates being determined.
For the spacecraft itself, this problem is basically “removed” by the possibilities of correcting its motion, and for the planets and their natural satellites it is of significant importance. And since the development of the solar system has begun and continues, the task of establishing a uniform coordinate system structure for the solar system will undoubtedly be solved. )
