The State of Deformation in Earthlike Self-Gravitating Objects by Wolfgang H. Müller & Wolf Weiss

Author:Wolfgang H. Müller & Wolf Weiss
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(2.2.19)

The third and fourth picture in Fig. 2.14 illustrate these relationships when evaluated in the equatorial plane of the Earth, , (positive values due to centrifugal acceleration), in the polar direction, , (negative values due to lateral contraction, i.e., the Poisson effect), and at 45, , using Earth data from Table 2.1 (with ) for physically reasonable ranges of Young’s moduli and Poisson’s ratios. Obviously, all values stay below the 1 % threshold and, hence, the message is that linear elasticity may be used to describe the centrifugal displacements and stresses even in the case of the Earth. The so-called flattening parameter, f, is defined by the ratio , a and c being the radial distances from the Earth’s center to the equator and to the pole, respectively. By using Eq. (2.2.19) we compute the flattening as follows:

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