Open AccessOn the Stability of a Spherical Gravitating Compressible Liquid Planet without Spin
Author(s) -
Longman I. M.
Publication year - 1975
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1975.tb05883.x
Subject(s) - hydrostatic equilibrium , compressibility , physics , inner core , classical mechanics , stability (learning theory) , planet , thermodynamic equilibrium , mechanics , thermodynamics , geophysics , astrophysics , quantum mechanics , machine learning , computer science
During the past ten years or so there has been considerable discussion in the literature regarding the author's 1963 contention that (neglecting temperature effects and spin) the Earth's liquid core cannot be stable unless the Adams‐Williamson condition relating density distribution and compressibility holds there. The present paper throws light on this question by showing mathematically that a sphere of gravitating compressible liquid cannot be internally stable unless this condition is fulfilled. Physical reasons for the necessity of this condition, which implies that particles of the liquid are in neutral equilibrium, are also discussed. By internal stability is meant stability of the density distribution while the spherical shape is maintained. The question of shape stability is not treated here, since it may be assumed that the Earth's mantle is sufficiently rigid to keep the core essentially spherical. The liquid is assumed to be a perfect fluid, elastic, and in the discussion only small strains are considered from an equilibrium configuration of initial hydrostatic stress. Furthermore thermodynamic effects are neglected and there is no spin.