Applied Abstract Algebra by Joyner D., Kreminski R., Turisco J.

By Joyner D., Kreminski R., Turisco J.

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48 2 Linear Strain Theory Indeed, Eq. 20) is the result originally presented by Thomson and Tait [23], p. 432. , Young’s modulus and Poisson’s ratio, to use. On the other hand, if we believe that this simple Hookean model applies to terrestrial planets we may use it to determine their effective shear modulus or modulus of rigidity, μ ≡ G, if we use the experimentally observed data for the flattening. The is nearly constant for all possible values of ν. , ca. 1/7: factor 1+ν/2 7+5ν μ= 3mω02 . 21) If we evaluate this relation using Earth’s data we obtain a value of 50 GPa, which is smaller than the value for iron or steel (roughly 70 GPa), which is often quoted in context with planet Earth.

55) + O α3/2 , A = − 20 1+ν in other words, we end up with the old result from Eqs. 29), as it should be. 10 gives us a foretaste of what to expect if the gravitating mass becomes really large. Two curves are presented, the fully linear solution according to Eq. 29) in blue and the “extended” solution based on Eq. 53) in red. 1. , it is not small but in the range of more than 30 percent) the difference the two predictions for the normalized displacement are close together, and in the range of 2 %.

The contractive force is proportional to r , the stretching stress (compensation of the lateral contraction) is proportional to r 2 . Hence from some r onward the force is not strong enough for compression, resulting in a transition from the negative to the positive, in other words in the existence of a Love radius. In his later editions Love does no longer comment on the physical significance of his result. However, in the first edition [14] we find a clue: “The greatest extension4 has place at the surface, and is equal to”: rr x=1 = α ν .

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