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

TL;DR

This paper provides a mathematical proof confirming that tidal heating in a synchronously rotating body always exceeds that in a nonsynchronous state, regardless of orbital eccentricity, obliquity, or spin-orbit resonance.

Contribution

It offers a rigorous proof that tidal heating in synchronous rotation is always greater than in nonsynchronous states, extending previous numerical evidence to a general mathematical result.

Findings

Tidal heating in synchronous rotation exceeds nonsynchronous states.

The result holds for any orbital eccentricity and obliquity.

The proof applies to all spin-orbit resonances.

Abstract

In a recent paper, Wisdom (2007, Icarus, in press) 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.