Energy-Driven Radius Evolution of Chthonian Planets: A Viscoelastic Maxwell Framework with Applications to Earth

Chthonian planets—dense rocky or metallic remnants of gas giants stripped of their gaseous envelopes—experience extreme internal pressures and energy densities, making their structural evolution fundamentally different from classical terrestrial planets. We aim to develop a physically grounded framework to describe energy-driven radius evolution in such bodies and to understand how internal properties control their structural changes. Using mass conservation, hydrostatic equilibrium, and the virial theorem, we link changes in internal energy to gravitational potential energy. A single-mode Maxwell viscoelastic model is applied to derive an analytically solvable law for quasi-static radius relaxation. Earth is used as a case study to estimate effective interior viscosities and energy transformations during hypothetical historical expansion. Ultra-compressed interiors resist rapid expansion, while structural adjustments or reductions in viscosity can transiently accelerate radius growth. The model quantifies the influence of internal energy reservoirs on radius evolution and highlights the characteristic viscoelastic timescale of global relaxation. This framework provides a transparent and falsifiable model connecting microphysical planetary properties to macroscopic radius evolution, offering predictive insights for both Earth and exoplanetary chthonian cores.