Consistent tidal and rotational models for satellites in synchronous rotation

¹ Dipartimento di Ingegneria Industriale, Alma Mater Studiorum – Università di Bologna, 47121 Forlì (FC), Italy
² Centro Interdipartimentale di Ricerca Industriale Aerospaziale, Alma Mater Studiorum – Università di Bologna, 47121 Forlì (FC), Italy
³ LTE, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Université, Université de Lille 1, Paris, France

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Received: 28 November 2024
Accepted: 12 December 2025

Abstract

Tidal dissipation in natural satellites plays a crucial role in shaping their thermal state, internal structure, and evolution; for example, sustaining subsurface oceans in Europa and Enceladus and driving Io’s volcanic activity. The amount of dissipation can be inferred from secular orbital drift and gravity variations induces by tides, which can be measured through astrometric observations and spacecraft radiometric data. We examine a discrepancy in the literature regarding the semimajor axis evolution due to tides in synchronously rotating satellites, whereby predictions from the variation of orbital elements approach (using direct tidal accelerations) differ by nearly a factor of three from the classical energetic method. This discrepancy may introduce systematic biases in dissipation estimates of the same order. We identify the source of this inconsistency as the effect of tidal dissipation on the moon’s rotation, which induces an offset of the prime meridian. In classical synchronous rotation models, the prime meridian always points to the empty focus of the orbit, but once this offset is properly accounted for we recover an agreement with the energetic method. We then extend our analysis to include the main physical libration at the orbital period. Additionally, we compare the time-lag and complex Love number tidal models from an orbital evolution perspective, finding unexpected differences and proposing a formula to reconcile the two models. Finally, we observe that a nonzero static S_2,2 gravity coefficient of a moon, considering the classical synchronous rotation as mentioned above, produces a variation in energy and angular momentum, suggesting that it must be constrained with dissipation parameters to avoid biases.