Open AccessVariational methods to calculate the hydrostatic structure of rotating planets
Author(s) -
Abad S.,
Pacheco A.F.,
Sañudo J.
Publication year - 1995
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1995.tb06848.x
Subject(s) - flattening , planet , hydrostatic equilibrium , polynomial , physics , classical mechanics , calculus of variations , gravitation , variational method , energy minimization , mathematics , mathematical analysis , astrophysics , quantum mechanics , astronomy
SUMMARY Two variational strategies to calculate the internal flattening induced in the structure of slowly rotating hydrostatic planets are discussed. In the first procedure, the minimization of energy fixes the physical coefficients of a polynomial that describes the dependence of the flattening on depth. In the second, the planet is assumed to be divided into thin equidensity shells, and the condition of minimum energy leads to an algebraic method that can compete with the usual one based on Clairaut's equation. These methods are applied to the Earth. The differences between them and other previous variational strategies are discussed.