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Géodésie terrestre et géodésie par satellites

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Résumé

Après un rappel des notions fondamentales utilisées en géodésie terrestre et en géodésie spatiale, les auteurs décrivent les méthodes de construction d'un système géodésique, soit par la triangulation et le nivellement astro-géodésique, soit par l'observation des satellites sur fond d'étoiles.

Puis, on discute la détermination des trois constantes fondamentales relatives à la terre: rayon équatorial, constante géocentrique de la gravitation, et facteur d'ellipticité géopotentielle. Les diverses déterminations du champ de gravitation terrestre (par la dynamique des satellites, la gravimétrie ou par des méthodes mixtes incluant des déterminations de direction) sont décrites et comparées en utilisant en particulier les cartes générales du géoïde. Puis toutes les méthodes géométriques ou dynamiques sont comparées à l'aide de cartes locales du géoïde.

Abstract

In the first part of the paper some of the most important concepts used in terrestrial and satellite geodesy are defined and discussed.

  1. (A)

    The three reference surfaces: the topographic surface, the geoid and the reference ellipsoïd. The later is to be considered more as a convenient mathematical tool rather than a representation of the form of the earth.

  2. (B)

    Gravimetry: the reductions of the gravity measurements are an important step before getting the overall field force of the earth. Free-air reductions and isostatic hypotheses play an important role in the interpretation of results. A result of such a general discussion of gravity measurements is the international gravity formula.

  3. (C)

    Use of gravity measurements: this formula, g 0=978.049(1+0.0052884 sin2ϕ-0.0000059sin22ϕ plays in gravimetry the same part as the reference ellipsoid in geometrical geodesy.

    The relationship between this formula and the parameters describing the earth as the flattening, α, of the ellipsoid or the dynamical form factor for the earth (J 2) is given under the assumption that the ellipsoid is also an equipotential surface (Equations 6 to 9).

    The relations that exist between the external gravitational field and the terrestrial gravity represented by the gravity anomalies are presented, leading to the Bruns' formula (15), the fundamental equation of gravimetry (17) and its approximate solution by Stokes' formula (18). The later permits the computation of the height of the geoïd above the reference ellipsoid.

  4. (D)

    Systems of reference: the orientation in space and one with respect to another of the reference surfaces is one of the main problems of geodesy. Local and astronomical reference frames are defined and their motions, linked with the motion of the north pole on the earth, are described. The system of longitudes is also dependent upon the time determination and the relationship between Universal Time and the usual time scales.

The second part is devoted to geometrical geodesy, that is the measurement of distances and space directions between points on the earth's surface.

  1. (A)

    Geodetic systems: a geodetic system is characterised by its fundamental point and the dimensions, position and orientation of the reference ellipsoïd. The computation of the position of a point in such a system is made using geodetic coordinates and the deflection of the vertical which are defined. The relationship between the position of the centre of gravity of the Earth and the absolute deflection of the gravity at the fundamental point is given.

  2. (B)

    Terrestrial geodesy: the techniques of geodetic survey by triangulation are described. The final step to get a geodetic system is the general adjustment of the measures. The final altitudes are, however, not referred to the ellipsoïd, but to the geoid, and the position of the center of gravity is left unknown.

  3. (C)

    Main geodetic systems: Table I gives the characteristics of the six more important geodetic systems deduced from terrestrial geodesy.

  4. (D)

    Satellite geodesy: the principles of the method (a simultaneous photography of satellites from at least three stations) are given and the photographic techniques are discussed. The problem of synchronisation of the stations is particularly important. The most elegant solution is found in the use of flashing satellites. The precision obtained by various authors in local satellite triangulation is given. A relative precision of 1/150000 is currently obtained. When simultaneous observations are made only in two stations, Veis (1963) obtained the direction of the line of the two stations. He is also the first to have obtained a world triangulation net by this method (1967).

The measurements of distances (‘Secor’ or ‘Laser’) may improve greatly the geo metric satellite triangulation in the future.

In the third part, Dynamical geodesy is described.

  1. (A)

    External terrestrial potential: the general analytical form of the earth's potential is derived and the significance of the first terms in terms of the position and the orientation of the reference frame are given.

  2. (B)

    Fundamental constants for the earth: these are the equatorial radius a of the reference ellipsoïd, the geocentric gravitational constant, GM and the dynamical form factor J 2; their determination is fundamental in an overall knowledge of the shape of the earth.

    Different methods for obtaining GM are discussed: the absolute measurements of gravity together with a reference gravity formula; the use of the third Kepler's law on the moon together with the measurement of its distance; the orbit determination of distant satellites and lunar probes.

    Then various determinations of J 2 from the motion of close artificial satellites are given. Other methods now seem to have only a historical interest.

    Various methods for determining a are described: method of areas (Hayford), geodetic-gravimetric methods (Isotov or Fischer) and the dynamical method with satellites. However, the latter does not easily separate the determination of a and GM. The method of comparison astrogeodetic and dynamical geoids is also quoted.

    However, the best values of these parameters are to be obtained from a general discussion of determinations using various techniques as shown by Cook (1965d). In the opinion of the authors the best values are GM = 398601 km3/s2, J 2 = 1082.64 × 10-6 and a = 6378.160 km. The most uncertain is GM and the observation of distances of lunar orbiter might greatly improve it.

  3. (C)

    Determination of the earth's gravitational field: since the determination of zonal harmonics was throughly discussed lately by Kozai (1966), this section is mainly devoted to tesseral harmonics, when they can be separated from zonal as is the case in dynamical methods. One can distinguish four methods:

  1. (1)

    Two dynamical methods are presented and described: the method of Izsak (1964), which was used by Gaposchkin (1967) for the Standard Earth model, and the method of Kaula (1966b).

  2. (2)

    Mixed dynamical and geometrical satellite methods were used by Kaula (1966b) and by Köhnlein (1965). The comparison between these two kinds of method is summarised by Table IV.

  3. (3)

    The most complete synthesis of gravimetric observations is due to Kivioja (1963). But the results are biased by the fact that gravity anomalies have to be extrapolated over 60% of the earth's surface.

  4. (4)

    Kaula (1966c) made an attempt to use dynamical and gravimetric information simultaneously. This solution is compared with Gaposchkin (1967) and Kivioja (1963) solutions.

An external test of these results was performed by kaula (1966c). This test is described: it consists of the testing of dynamical methods by the knowledge of well-determined gravity anomalies. Following this test, the best solution for the external field is by Gaposchkin (1967).

  1. (D)

    The shape of the geoid: using Stokes' formula, Levallois (1967) derived the geoid from gravimetric measurements. It is compared to the best geoids derived from dynamical solutions which have large similarities (Figures 11–15).

  2. (E)

    The center of gravity: it can be reached by dynamical and mixed methods, through the positions of the stations or the fitting of an ellipsoid on the geoïd. It can also be obtained in the process of comparing an astrogeodetic geoid with a gravi-metric or dynamical geoid (Veis, 1965).

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  1. Bureau des Longitudes et Observatoire de Paris-Meudon, France

    J. Kovalevsky & F. Barlier

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Kovalevsky, J., Barlier, F. Géodésie terrestre et géodésie par satellites. Space Sci Rev 7, 69–134 (1967). https://doi.org/10.1007/BF00173116

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