The hydrostatic equilibrium figure of the Earth: an iterative approach

Details The hydrostatic equilibrium figure of the Earth: an iterative approach The hydrostatic equilibrium figure of the Earth: an iterative approach

Apr 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989pepi...54..180a&link_type=abstract

Physics of the Earth and Planetary Interiors, Volume 54, Issue 1-2, p. 180-192.

Physics

2

Scientific paper

The computation of the hydrostatic equilibrium of the Earth in which the gravitational and rotational potentials are considered may be performed by an iterative technique. The equilibrium surfaces can be sought directly as a function of the planet's radius r, without making use of the Clairaut equation, by refining the solution step by step until the desired accuracy is obtained.
In this paper we apply this technique using the density model provided by the Preliminary Reference Earth Model (PREM). The solution obtained yields a flattening at the external surface e-1 = 299.890 and the first zonal coefficients of the hydrostatic gravitational field as J2 = -1072.947 × 10-6 and J4 = 2.954 × 10-6 (in each shell the sum of the gravitational and rotational potentials is constant to eight decimal places). This confirms the discrepancy between the theoretical and the observed quantities.
This discrepancy may be attributed to a set of causes such as non-uniform density distribution, permanent tidal deformation, change in the distribution of the mass during the last deglaciation and the higher former spin rate of the Earth. However, it must also be emphasized that this discrepancy may be attributed to the parameters used in the computation, such as the gravitational constant G (known to only four decimal places), or to the density model used. The angular velocity ω is known with sufficient accuracy.

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