Evaluation of the heat, entropy, and rotational changes produced by gravitational segregation during core formation

Core formation by gravitational segregation allegedly released sufficient interior heat to melt the Earth. Analysis of the energetics, which compare gravitational potential energy (U_g) of a fictitious, homogeneous reference state to Earth’s current layered configuration, needs updating to correct errors and omissions, and to accommodate recent findings: (1) An erroneous positive sign was used for U_g while maintaining the reference value of 0 at infinity, which results in an incorrect sign for ΔU_g, which is crucial in determining whether a process is endothermic or exothermic. (2) The value of U_g for Earth’s initial state is uncertain. (3) Recent meteorite evidence indicates that core formation began before the Earth was full-sized, which severely limits ΔU_g. (4) Inhomogeneous accretion additionally reduced ΔU_g. (5) The potentially large effect of differential rotation between the core and the mantle was not accounted for. (6) Entropy changes associated with creating order were neglected. Accordingly, we revise values of U_g, evaluate uncertainties, and show that ΔU_g was converted substantially to configurational energy (TΔS). These considerations limit the large sources of primordial heat to impacts and radioactivity. Although these processes may play a role in core formation, their energies are independent of gravitational segregation, which produces order and rotational energy, not internal heat. Instead, gravitational segregation promotes planetary cooling mainly because it segregates lithophilic radioactive elements upward, increasing surface heat flux while shortening the distance over which radiogenic heat diffuses outwards.