Experiments on melting and phase transformations on iron in a laser-heated, diamond-anvil cell to a pressure of 150 gigapascals (approximately 1.5 million atmospheres) show that iron melts at the central core pressure of 363.85 gigapascals at 6350 +/- 350 kelvin. The central core temperature corresponding to the upper temperature of iron melting is 6150 kelvin. The pressure dependence of iron melting temperature is such that a simple model can be used to explain the inner solid core and the outer liquid core. The inner core is nearly isothermal (6150 kelvin at the center to 6130 kelvin at the inner core-outer core boundary), is made of hexagonal closest-packed iron, and is about 1 percent solid (MgSiO3 + MgO). By the inclusion of less than 2 percent of solid impurities with iron, the outer core densities along a thermal gradient (6130 kelvin at the base of the outer core and 4000 kelvin at the top) can be matched with the average seismic densities of the core.