# Figure of the Earth

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## figure of the earth

[′fig·yər əv__th__ē ′ərth]

## 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 (*see*EARTH 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