A Time-Dependent Framework for Planetary Habitability and the Role of Natural Satellites

This work presents a conceptual, time-dependent framework for planetary habitability, H(t), designed to characterize the persistence of habitable conditions over geological timescales rather than their instantaneous suitability. The framework formalizes habitability as a dimensionless comparative index integrating obliquity stability, tidal-orbital regulation, geophysical activity, and atmospheric loss within a multiplicative dynamical structure. A classification of satellite regimes is introduced and applied in a first-order comparative implementation to illustrate how different planet-satellite architectures map onto distinct temporal persistence patterns. The study is intended as a structurally testable framework that complements traditional habitability criteria and provides a foundation for future quantitative, numerical, and observational investigations.