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# GEODESY: DEFINITION, CLASSIFICATION, PROBLEMS

Ex.1 Read aloud and memorize the following words:

geodesy – геодезія

ocean – океан

external – зовнішній

selenodesy – селенодезія

coordinate – координатний

curvature – кривизна, вигин

surveying – зйомка

series – серія, ряд

fluid – рідкий, текучий, рідина

assumption – припущення

equipotential – рівно потенційний

geoids – геоїд

exterior – зовнішній

ellipsoid – еліпсоїд

ascertain – пересвідчитися

variable – мінливий , змінний

Ex.2 Words and expressions for the text comprehension:

validity – обґрунтованість

earth’s surface – поверхня землі

space exploration - дослідження космосу

heavenly body – небесне тіло

planetary geodesy – планетна геодезія

reference surface – еталонна поверхня

estate cadastre – майновий кадастр

terrestrial body – земне тіло

marine geodesy – морська геодезія

artificial satellite – штучний супутник

ocean surface – поверхня океану

bounding surface – гранична поверхня

Ex.3 Read and translate the text:

According to the classical definition geodesy is the “science of the measurement and mapping of the earth’s surface”. This definition has to this day retained its validity; it includes the determination of the earth’s external gravity field as well as the surface of the ocean floor. With this definition, geodesy may be included in the geosciences, and also in the engineering sciences.

Triggered by the development of space exploration geodesy turned in collaboration with other sciences toward the determination of the surfaces of other heavenly bodies ( moon, other planets). The corresponding disciplines are called selenodesy and planetary geodesy.

Geodesy may be divided into the areas of global geodesy, geodetic surveying, and plane surveying. Global geodesy is responsible for the determination of the figure of the earth including the complete external gravity field. A geodetic survey defines the surface of a country by the coordinates of a sufficiently large number of control points . In this fundamental work, the overall curvature of the earth must be considered. In plane surveying ( topographic surveying, cadastral surveying, engineering surveying ), the details of the land surface are obtained; the horizontal plane is in general sufficient as a reference surface.

There is close interaction between global geodesy, geodetic surveying and plane surveying. The geodetic survey adopts the parameters determined by measurements of the earth, and its own results are available to those who measure the earth. The plane surveys, in turn, are generally tied to the control points of the geodetic surveys and serve then particularly in the development of national map series and in the formation of real estate cadastres.

The problem of geodesy is to determine the figure and the external gravity field of the earth and of other heavenly bodies as functions of time; as well as, to determine the mean earth ellipsoid from parameters observed on and exterior to the earth’s surface. This geodetic boundary-value problem incorporates a geometric ( figure of the earth ) and a physical ( gravity field ) formulation of the problem; both are closely related. By the figure of the earth we mean the physical and the mathematical surface of the earth.

The physical surface of the earth is the border between the solid or fluid masses and the atmosphere. Recently, the ocean floor has also been included in the formulation of the geodetic problem, being the bounding surface between the solid terrestrial body and the oceanic water masses. The extension of the problem to the oceans is designated marine geodesy. The irregular surface of the solid earth ( continents and ocean floor ) is incapable of being represented by a simple mathematical relation; it is therefore described point wise by the use of coordinates of the control points. On the other hand, the ocean surfaces ( 70 % of the earth’s surface ) possess a simpler principle of formulation. Under certain assumptions, they form a part of a level ( equipotential) surface (surface of constant gravity potential) of the earth’s gravity field. We may think of this surface as being extended under the continents and then identify it as the mathematical figure of the earth.

What we call the surface of the earth in the geometrical sense is nothing more than that surface which intersects everywhere the direction of gravity at right angles, and part of which coincides with the surface of the oceans.

The majority of the observed parameters used in geodesy refers to the earth’s external gravity field, whose study thereby becomes a concern of geodesy. The upper limit of space that is of interest is governed by the geodetic usage of artificial satellites and space probes, as well as the earth’s moon. The physical aspect of the problem of geodesy follows from the consideration of the earth’s surface and geoids as bounding surface in the earth’s gravity field. The external gravity field may be described by the countless level surfaces extending completely or partially exterior to the earth’s surface.

Reference systems with a defined metric and curvature are required for the computations in global geodesy and geodetic surveying. Because of its simple equation, a rotational ellipsoid flattened at the poles is better suited as a geodetic reference surface than the geoids, which is determined by the uneven distribution of the earth’s masses. Particular significance is given to the mean earth ellipsoid, which is the optimal ellipsoid approximating the geoids.

The body of the earth and its gravity field are subject to temporal variations of secular, periodic, and singular nature, which can occur globally, regionally, and locally. The geodetic measurement and evaluation techniques today have advanced to the extent that they can detect a part of this change. Should average conditions be ascertained, observations must be corrected for these changes. With the detection of a part of the variations, geodesy also contributes to the investigation of the dynamics of the terrestrial body . The figure of the earth and the external gravity field are accordingly conceived as time dependent variables.

The earth’s external gravity field – зовнішнє гравітаційне поле Землі

Triggered by the development of space exploration – під впливом інтенсивного розвитку космічних досліджень

Global geodesy – вища геодезія

Geodetic surveying – геодезична зйомка Plane surveying – інженерна геодезія

The overall curvature of the earth – загальна кривизна Землі

Topographic surveying, cadastral surveying, engineering surveying – топографічні, кадастрові, інженерні зйомки

The control points of the geodetic surveys – вихідні пункти геодезичної зйомки

Real estate – нерухоме майно

Geodetic boundary-value problem – геодезична гранична ( за значенням ) задача

It is therefore described point wise by the use of coordinates – тому вона описується за допомогою координат

The countless level surfaces – незлічені рівневі поверхні

The mean earth ellipsoid – середній еліпсоїд Землі

Ex.4 Give Ukrainian equivalents of the following words from the text:

classical, global, figure, coordinate, fundamental, detail, formation, function, mass, control, principle, sense, interest, limit, regionally, locally.

Ex.5 Give English equivalents of the following words and word-combinations:

гранична поверхня, океан, поверхня океану, рідкий, зовнішній, морська геодезія, крива, топографічні зйомки, інженерна геодезія, вища геодезія, гравітаційне поле Землі, припущення, штучний супутник, земне тіло.

Ex.6 Read and translate the following sentences paying attention to the tense forms of the verbs:

1. The formulation of the problem of geodesy first developed in the course of the nineteenth century. 2. The question of the figure of the Earth had already been raised in anti quity. 3. In the sixteenth and seventeenth ceturies, new observations and ideas from astronomy and physics decisively influenced the perception of the figure of the Earth and its position in space. 4. after the rotational ellipsoid had asserted itself as a model for the Earth, numerous measurements were conducted untill the middle of the nineteenth century to determine the dimension of the Earth ellipsoid. 5. Polar motion has been determined since 1899. 6. The terrestrial geodetic measurements with the exception of spatial distances are tied to the direction of the plumb line at the point of observation, and thereby, to the earth’s gravity field.

Ex.7 Comprehension questions:

1. What is the classical definition of geodesy? 2. What sciences may geodesy be included in ? 3. What is the object of modern geodesy? 4. What areas may geodesy be divided into ?5. Why is there close interaction between global geodesy, geodetic surveying and plane surveying? 6. What are the problems of geodesy? 7. What do the majority of the observed parameters used in geodesy refer to? 8. What can you say about the advance of the geodetic measurement and evaluation technique today?

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