Università Roma Tre

Earth in the Solar System
Titus-Bode Law. Terrestrial and gaseous planets. Notes on the formation of the solar system. Elements of chemistry of the solar system. Geochemical classification of the elements. Formation and differentiation of planets

The Earth as a Planet
Definition of planet. Kepler's laws. General features: liquid water, atmosphere, crustal dichotomy, magnetic field, internal dynamics.

Earth's mass, density and moment of inertia
The problem of estimating the average density of the Earth: historical notes (from Newton to Poynting). Cavendish's experiment in a modern way. Estimate of the mass of the Earth and planets - Average density of the Earth. Recalling the moment of inertia. Tensor of moments of inertia. Ellipsoid and spheroid. Moment of inertia of a solid sphere with constant density. Moments of inertia and models of planetary structures.

Earth's shape and gravity
The shape (figures) of the Earth .. Oblate ellipsoid and polar crushing. Earth shape and topography. Earth shape and variations of g. Acceleration and gravitational potential. Gravitational potential: Laplace equation. Gravitational potential in spherical coordinates. Gravitational potential of a solid sphere with constant density. General solution of the Laplace equation in spherical coordinates. Legendre polynomials. Spherical harmonics and Stokes coefficients. MacCullagh equation and moments of inertia. Ellipticity of the shape (figures) of the Earth. The acceleration ratio m (acceleration ratio). The geopotential. Relationship between J2, J4, m and f. Calculation of the inertia ratio for the Earth. Gravity on the reference spheroid. Geocentric and geographical latitude. Clairaut formula. Normal gravity. The geoid. Measurements of g. Absolute and relative measures. Corrections to the extent of g. Anomalies in open air and Bouguer. Non-uniqueness of the anomalies of g. Isostasy. Isostatic anomalies. Vertical movements of the crust. Isostatic compensation. Isostatic adjustments and coat viscosity. Satellite geoid measurements. Geoid ripples.

Tides and land rotation
Origin of the tides. Tidal potential. Components of the lunar tidal acceleration. Combination of lunar and solar tides. Terrestrial tides. Tidal friction and deceleration of terrestrial and lunar rotation. Euler nutation and Chandler swing. Solar-solar precession.

Notes on the properties of minerals and rocks
Crystalline structure of minerals. The rocks. Classification of rocks. Sedimentary, igneous and metamorphic rocks. Eutectics and solid solutions.

Terrestrial magnetism: History - from Petrus Peregrinus to Gauss.

The magnetism of the rocks
Physics of magnetism. Ampere equivalence principle. Review of atomic magnetic moments. Magnetic susceptibility. Magnetic properties of matter. Diamagnetism (classical theory). Paramagnetism (classical theory). Ferromagnetism. Ferrimagnetismo. Antiferromagnetism. Parasitic ferromagnetism. Magnetic minerals. Magnetism of the rocks. Titanomagnetites and magnetic series. Magnetization of rocks. Types of magnetization. Thermo-remaining magnetization (TRM). Remaining chemical magnetization (CRM). Remaining Debris Magnetization (DRM). Notes on Paleomagnetism.

Earth's magnetic field
The observables of the CMT. General characteristics of the CMT. Laplace equation and CMT potential. Gauss coefficients. CMT modeled with dipoles. The terrestrial dipolar field. CMT best fit - inclined eccentric dipole. Power spectrum of the CMT. Estimated depth of the source of the main field. Secular variation. External sources of the CMT. Earth core composition. CMT models. Bullard dynamo. Self-excited dynamo model. The magnetohydrodynamic approach. Magnetohydrodynamics equations. Hydrodynamic magneto models. Magnetic measurements. Precession magnetometer. Magnetic anomalies and corrections.

Terrestrial heat
Earth's energy budget. Heat transmission within the Earth: conduction, convection, radiation and advection. Internal heat sources. Original heat; radiogenic heat; other heat sources. Conduction equation (Fourier equation). Heat conduction equation in three dimensions. Thermal diffusion. Adjective term. Balance geotherm. Notes on the transport of heat in the oceanic and continental lithosphere. Time scale of the conductive heat flow. Adiabatic thermal gradient. Melting point gradient. Geothermal diagrams inside the Earth.

Internal structure of the Earth
Adams-Williamson equation. Density trend with depth. Unzipped density. The mineralogical phases of the coat. Compositional model of the Earth. Structure and asymmetries of the Earth's core. Profiles of v, rho, g and P within the Earth. Bullen model and Preliminary Reference Earth Model (PREM).

Stacey, F. D., and Davis, P. M. (2008) Physics of the Earth, Cambridge University Press.

Fowler, C. M. R. (2005). The Solid Earth, Cambridge University Press.