The dynamical evolution of terrestrial planets resembling Mercury in the vicinity of spin-orbit resonances is investigated using comprehensive harmonic expansions of the tidal torque taking into account the frequency-dependent quality factors and Love numbers .
The torque equations are integrated numerically with a small step in time , includng the oscillating triaxial torque components but neglecting the layered structure of the planet and assuming a zero obliquity .
We find that a Mercury-like planet with its current value of orbital eccentricity ( 0.2056 ) is always captured in the 3:2 resonance .
The probability of capture in the higher 2:1 resonance is approximately 0.23 .
These results are confirmed by a semi-analytical estimation of capture probabilities as functions of eccentricity for both prograde and retrograde evolution of spin rate .
As follows from analysis of equilibrium torques , entrapment in the 3:2 resonance is inevitable at eccentricities between 0.2 and 0.41 .
Considering the phase space parameters at the times of periastron , the range of spin rates and phase angles , for which an immediate resonance passage is triggered , is very narrow , and yet , a planet like Mercury rarely fails to align itself into this state of unstable equilibrium before it traverses the 2:1 resonance .