A proof that tidal heating in a synchronous rotation is always larger than in an asymptotic nonsynchronous rotation state

Benjamin Levrard (1, 2, 3)

1 IMCCE - Institut de Mécanique Céleste et de Calcul des Ephémérides
2 ASD - Astronomie et systèmes dynamiques
3 CRAL - Centre de Recherche Astrophysique de Lyon

In a recent paper, Wisdom [Wisdom, J., 2008. Icarus, 193, 637-640] derived concise expressions for the rate of tidal dissipation in a synchronously rotating body for arbitrary orbital eccentricity and obliquity. He provided numerical evidence than the derived rate is always larger than in an asymptotic nonsynchronous rotation state at any obliquity and eccentricity. Here, I present a simple mathematical proof of this conclusion and show that this result still holds for any spin-orbit resonance.

Domaines: Astrophysique [astro-ph]

Benjamin Levrard. A proof that tidal heating in a synchronous rotation is always larger than in an asymptotic nonsynchronous rotation state. Icarus, 2008, 193, pp.641-643. ⟨10.1016/j.icarus.2007.10.003⟩. ⟨hal-03732496⟩