Shock-wave (Hugoniot) data for initially porous and nonporous samples of iron are inverted to yield values of the Gr¿neisen parameter (&ggr;), adiabatic bulk modulus (Ks), and coefficient of thermal expansion (α) along the Hugoniot to pressures of about 150 GPa (1.5 Mbar). This represents the first reliable estimate of thermal properties (e.g.,α) to such high pressures based directly on experimental data. The values of &ggr; fit the conventional function &ggr;=&ggr;0(V/V0)n but with n significantly larger than 1, while extrapolation formulas suggested to date for α appear not to provide the best fit to the data. The present analysis yields values of &ggr; between about 1.4 and 1.0 (essentially temperature independent) and α between about 1.0 and 0.4¿10-5 K-1 throughout the earth's core, therefore implying that simple dynamical models of the core are quite viable. These results provide experimental confirmation of the Vaschenko-Zubarev/Irvine-Stacey (or 'free-volume') formulation for &ggr; of iron at high pressures, as well as support for Stacey's recent model of the thermal state of the core. The data on density, sound speed, and bulk modulus of iron are extrapolated and corrected to pressures and temperatures existing throughout the earth's core, and compared with current seismological information. This leads to the following conclusions: (1) both densities and bulk moduli in the outer core are less than those of Fe under equivalent conditions (by about 10 and 12%, respectively) but (2) their gradients tjrough the outer core are consistent with gross chemical homogeneity (i.e., uniform intermixing of Fe and a lighter, more compressible element or compound); (3) both densities and bulk moduli for the inner core are compatible with those of iron, suggesting that (4) the inner core-outer core boundary is likely to be a compositional as well as a phase boundary. Assuming that the outer core consists of Fe and a lighter element or compound, X, the constraints on density, bulk modulus and mass fration of X which must be simultaneously satisfied are given.