A user-friendly package and workflow for generating effective homogeneous rheologies for the study of the long-term orbital evolution of multilayered planetary bodies
This tool addresses the need for reproducible and accessible rheological modeling in planetary science, making it easier to incorporate physical tidal dissipation into orbital studies without solving complex layered problems repeatedly.
The authors developed an open-source Wolfram Language package that automates the creation of effective homogeneous rheologies for multilayered planetary bodies, enabling easier simulation of long-term orbital evolution by applying it to a five-layer lunar model to produce a reduced representation with fewer relaxation elements.
We present a user-friendly, open-source Wolfram Language package that automates the construction of an effective homogeneous generalized Voigt rheology for a spherically symmetric, incompressible layered body with Maxwell solid layers. It provides a practical bridge between layered interior models and time-domain simulations of tidal evolution. The package combines three components: (i) a forward computation of the degree-2 tidal Love number based on the propagator-matrix formulation for incompressible stratified viscoelastic bodies; (ii) numerical identification of the secular relaxation poles and residues of the layered model; and (iii) inversion of the resulting response into the compliance of an equivalent homogeneous generalized Voigt body. The implementation is based on the equivalence established for multilayer Maxwell bodies and includes an optional dominant-mode selection procedure for obtaining reduced rheological models over a prescribed frequency range. The package returns the parameters of the equivalent homogeneous model, including elastic, gravitational, viscous, and Voigt-element contributions, in a format suitable for downstream numerical applications. As a case study, we apply the package to a five-layer lunar interior model and obtain its equivalent generalized Voigt representation, together with a reduced model that preserves the tidal response over the frequency interval relevant for orbital evolution while using fewer relaxation elements. This package makes the reduction from stratified viscoelastic interiors to effective homogeneous rheologies reproducible and accessible. It allows physical tidal dissipation models to be used in long-term orbital and spin-evolution studies without having to repeatedly solve the full layered boundary-value problem.