The famous (and oldest) solution of Clairaut's equation or Legendre-Laplace law of density was used for the parameterization of the hydrostatic/adiabatic Earth's radial density distribution in the two standard forms continuous and piecewise radial cases. As a result, the set of recursive formulae were found for the solution of direct and inverse problems (on the ground of fundamental geodetic constants and seismic data simultaneously) the mentioned piecewise Legendre-Laplace density is in a good agreement with the PREM-density model.

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