Abstract In this work, we develop simplified surface temperature models for spherical bodies with insignificant atmospheres, able to produce a latitude/longitude temperature map that includes seasonality effects. We start from the commonly employed depth‐dependent model by Spencer et al. (1989, https://doi.org/10.1016/0019‐1035(89)90182‐6 ) based on the dimensionless one‐dimensional heat‐diffusion equation. We include internal heating in the model and then remove the depth dependence by either specifying shape functions or via a lumped‐parameter approach. We obtain three different zero‐dimensional models where the surface temperature at a point is described by a single ordinary differential equation (ODE). The accuracy of the approximation is investigated for fast and slow rotating spherical bodies with or without internal heating. We also propose a linearized version of the ODE, and obtain its analytical solution. Overall, this linearized solution loses some accuracy with respect to the non‐linear ODE models, but remains accurate for rapidly rotating bodies. Considering that the surface temperature of slowly rotating bodies is already well known analytically (i.e., of the hour angle), our results add an analytical solution for fast‐rotating bodies. The simplified models proposed in this work are computationally cheaper than traditional depth‐dependent models.
Boccelli et al. (Sun,) studied this question.