Download PDF by Professor Antonio Marussi (auth.): Intrinsic Geodesy

By Professor Antonio Marussi (auth.)

The technological know-how of Geodesy has gone through far-reaching adjustments within the final part century. The effect of recent expertise, from electromag­ netic distance measurements to using man made satellites, has been nice, and continues to be mostly to be felt. those alterations have compelled the practitioners of the traditional paintings of Earth size to change their frame of mind in regards to the area that surrounds us, anything essentially more challenging than soaking up a brand new know-how. A key effect during this modem swap in geodetic pondering has been the paintings of Antonio Marussi, in his medical courses from 1947 onwards, via his scholars and collaborators on the Uni­ versity of Trieste, and within the sequence of symposia on 3-dimensional Geodesy which he organised along with his nice buddy and collaborator, Martin Hotine. His impression at the latter, stemming from their first assembly on the common meeting of the foreign organization of Geodesy in Oslo in 1948, was once awesome in itself, top because it did to the last word booklet of Hotine's Mathematical Geodesy in 1969.

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7. Discontinuities oj "If/, a, and Gradg As is known, the potential of gravity and its gradient are continuous on crossing a surface S of density discontinuity, but the homography ~ is not. In particular, denoting by n' the outward normal to the surface S which encloses, in its interior, masses of density 0, and denoting by "Ife the homography ~external to S, and by 11'; that internal, 11';- "Ife= [~= -4njoH(n',n'). 1) [~ to n we have [gradg] = (grad g)j-(grad g)e = 4njon' xn . n' . 2) This relationship allows us to find the jumps undergone by the gravimetric elements on crossing a surface, and the jumps in the curvature of the lines of force and their principal normals.

As we shall see, this is the direction of the isozenithal line. It has already been seen that, on the other hand, n is the null direction of K a. 7. Discontinuities oj "If/, a, and Gradg As is known, the potential of gravity and its gradient are continuous on crossing a surface S of density discontinuity, but the homography ~ is not. In particular, denoting by n' the outward normal to the surface S which encloses, in its interior, masses of density 0, and denoting by "Ife the homography ~external to S, and by 11'; that internal, 11';- "Ife= [~= -4njoH(n',n').

2) This relationship allows us to find the jumps undergone by the gravimetric elements on crossing a surface, and the jumps in the curvature of the lines of force and their principal normals. 3) g having denoted by n 1: the component along I of the versor n '. Nothing further will be said concerning discontinuities; but those who wish to study this question more deeply should tum to the important studies of Caldonazzo, who has examined the discontinuities of the third derivatives of the volumetric potential across an equipotential surface which separates elements of differing density, and of Manacorda, who has equally studied the behaviour, up to the third derivatives, of the potential of a single layer crossing the generating layer.

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