Conductive cooling of spherical bodies with emphasis on the Earth

To explore planetary evolution, we provide conductive cooling profiles that account for planet size, phonon diffusivity and various internal heating scenarios. Our new analytical solution for simple cooling of spheres reveals that heat is removed from only Earth's outermost ~1000 km over geological time. Numerical models with decaying heat production show that any upward concentration of radionuclides causes high temperatures at shallow depths, forcing interior temperatures to increase with time while producing a thermal gradient that forbids lower mantle convection. Hence, differentiation drives upper mantle magmatism and tectonics, leaving a quiescent but hot deep interior, while slowly melting the core.