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

King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia

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Received: 14 March 2026
Accepted: 30 April 2026

Abstract

Context. Tidal dissipation plays an important role in the long-term orbital evolution of planets and moons. For stratified viscoelastic bodies, evaluating the frequency-dependent tidal response during long-term dynamical integrations is computationally expensive, since it requires repeatedly solving the internal deformation problem. Therefore, orbital evolution codes benefit from effective homogeneous rheologies that approximate the dissipation of stratified interiors at low computational cost.

Aims. We present a user-friendly, open-source Wolfram Language package that constructs an effective homogeneous generalized Voigt rheology for a spherically symmetric, incompressible layered body with Maxwell solid layers. The package converts the tidal response of a layered interior model into the parameters required by time-domain simulations of tidal evolution.

Methods. 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.

Results. The package returns the parameters of the equivalent homogeneous model, including elastic, gravitational, viscous, and Voigt-element contributions, in a format that can be used by external tidal-evolution codes. 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.

Conclusions. The package provides a reproducible implementation of the reduction from stratified viscoelastic interiors to effective homogeneous rheologies. It allows tidal dissipation from layered models to be included in long-term orbital and spin-evolution calculations without solving the full layered boundary-value problem at each step.