# Figure of the Earth

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## figure of the earth

[′fig·yər əvthē ′ərth]
(geodesy)
A precise geometric shape of the earth.

## Figure of the Earth

a conception or representation of the shape of the earth as a planet on the whole. This conception has changed during the historical development of knowledge and is defined by general agreement.

In antiquity, it was already recognized that the figure of the earth has the shape of a sphere. This was the first approximation in representing the earth’s figure. The problem of studying the figure of the earth was reduced to determining the radius of the globe (Eratosthenes, al-Biruni). I. Newton, proceeding from the law of universal gravitation he had discovered, hypothesized that as a consequence of the earth’s rotation about its axis and the mutual attraction of the masses composing the planet, the figure of the earth should be slightly oblate in the direction of the axis of rotation and should have a spheroidal shape similar to an ellipsoid of revolution (seeEARTH SPHEROID and EARTH ELLIPSOID). The results of arc and angle measurements in the first half of the 18th century confirmed the validity of both this hypothesis and the law of universal gravitation. The hypothesis that the figure of the earth has the shape of an ellipsoid of revolution was the second approximation in representations of the figure. In this approximation, the problem of studying the earth’s figure was reduced to determining the equatorial radius and oblateness of the earth.

The work of A. Clairaut on the theory of the equilibrium figures of a rotating fluid body extended Newton’s research and laid the foundations of the theory of the earth’s figure. The development of the theory of the figure of the earth in the 19th century by G. Stokes and other scientists led to introduction of the concept of a geoid. The identification of a geoid with the figure of the earth was the next approximation in representations of the earth’s figure. In the geoidal conception, the figure of the earth has a rather complex shape and depends on the earth’s internal structure.

M. S. Molodenskii’s theory of determining the figure of the earth in the contemporary understanding as the shape of the earth’s actual physical surface, which is formed by the undisturbed water surface on the seas and oceans and by the relief of the continents and islands, is totally free of any hypotheses whatsoever about the internal structure of the earth. Molodenskii introduced the quasi-geoid as an auxiliary surface whose strict mathematical determination made it possible to study the figure of the earth without relying on such hypotheses.

The goal of studying the figure of the earth consists in the determination of the true coordinates of points on the earth’s surface and the study of the earth’s external gravity field in a coordinate system common to the whole earth. This goal is the subject and the principal scientific problem of geodesy, which is solved on the basis of astronomical geodetic and gravimetric measurements and observations of the motion of artificial earth satellites. In practice, the shape of a geoid is replaced by the surface of an earth ellipsoid, since such a surface most closely resembles the figure of the earth. The Krasovskii ellipsoid is used for geodetic and cartographic work in the USSR.

### REFERENCES

Shimbirev, B. P. Teoriia figury Zemli. Moscow, 1975.
Izotov, A. A. Forma i razmery Zemli po sovremennym dannym. Moscow, 1950.
Molodenskii, M. S., V. F. Eremeev, and M. I. Iurkina. Metody izucheniia vneshnego gravitatsionnogo polia i figury Zemli. Moscow, 1960.
Clairaut, A. Teoriia figury Zemli, osnovannaia na nachalakh gidrostatiki. Moscow-Leningrad, 1947. (Translated from French.)
Picetti, P. Osnovy mekhanicheskoi teorii figury planet. Moscow-Leningrad, 1933. (Translated from Italian.)

A. A. IZOTOV and A. M. MIKISHA

References in periodicals archive ?
Chapter 4 'The Figure of the Earth and Coordinate Systems' chronologically follows how location has been mapped over the centuries.
The quest for the true figure of the Earth; ideas and expeditions in four centuries of geodesy.
Methods for Study of the External Gravitational Field and Figure of the Earth. TRUDY Ts NIIGAiK, 131, Geodezizdat, Moscow.
All of them change both the figure of the Earth and its orientation.
As it is being endeavoured in France to set up a new system of weights and measures derived from the length of a pendulum that oscillates in seconds at the latitude of 45[degrees], the King has judged it appropriate to take advantage of this opportunity to promote the progress of Geography and resolved that as the course of your voyage enables you to obtain information on this interesting point, you do so at convenient locations, so that it may be compared with that which has been verified in that Kingdom, and that knowledge concerning the actual figure of the Earth may be perfected by determining, if the southern hemisphere is more flattened, what may be this difference and others in the exterior shape of our globe, supposing its surface not to be as symmetrical as commonly imagined.
The Spanish naval officer and astronomer, Jose Mendoza y Rios, was already working closely with the French savants (having been sent to France and several other European countries as leader of a delegation of Spanish officers charged with obtaining information on advances in astronomy and navigation), and Valdez said in his letter to Malaspina that it was on his recommendation that it had been decided to add the task of measuring the figure of the earth to the expedition's mission.
According to the official letter to me from his Excellency the Minister of the Marine, by means of this Pendulum the experiments of the Gravity of Bodies at different Parallels of the Earth should be repeated as much as possible, not only for a Regulation of Measures which would depend on the consistent Observations which would in due course be verified in Europe exactly on the Parallel of 45[degrees], but also in order to carry on the investigations as to the true figure of the Earth in which there was suspected, not without basis, to be some variations from one Hemisphere to the other.
The experiments of gravitation, repeated in both hemispheres and at various latitudes, will conduce to important confirmation of the non-symmetrical figure of the earth, and will be the basis of a universal, verifiable measure, as constant as the laws on which it depends, that is intended to be established in Europe.
Methods for study of the external gravitational field and figure of the Earth, translated from Russian by the Israel program for scientific translations, Office of Technical Services, Department of Commerce, Washington, D.C.

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