A user-friendly package and workflow for generating effective homogeneous rheologies for the study of the long-term orbital evolution of multilayered planetary bodies

TL;DR

This paper introduces an open-source Wolfram Language package that simplifies converting layered planetary interior models into effective homogeneous rheologies for long-term orbital evolution simulations.

Contribution

It provides a practical, automated tool for deriving equivalent homogeneous rheologies from layered models, facilitating tidal evolution studies without complex boundary-value problem solving.

Findings

Successfully applied to a lunar interior model

Produces reduced models preserving tidal response over key frequencies

Enables efficient long-term orbital evolution simulations

Abstract

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.