GJ 581d is a potentially habitable super-Earth in the multiple system of exoplanets orbiting a nearby M dwarf .
We explore this planet ’ s long-term dynamics , with an emphasis on its probable final rotation states acquired via tidal interaction with the host .
The published radial velocities for the star are re-analysed with a benchmark planet detection algorithm , to confirm that there is no evidence for the recently proposed two additional planets ( f and g ) .
Limiting the scope to the four originally detected planets , we assess the dynamical stability of the system and find bounded chaos in the orbital motion .
For the planet d , the characteristic Lyapunov time is 38 yr .
Long-term numerical integration reveals that the system of four planets is stable , with the eccentricity of the planet d changing quasi-periodically in a tight range around 0.27 , and with its semimajor axis varying only a little .
The spin-orbit interaction of GJ 581d with its host star is dominated by the tides exerted by the star on the planet .
We model this interaction , assuming a terrestrial composition of the mantle .
Besides the triaxiality-caused torque and the secular part of the tidal torque , which are conventionally included into the equation of motion , we also include the tidal torques ’ oscillating components .
It turns out that , dependent on the mantle temperature , the planet gets trapped into the 2:1 or an even higher spin-orbit resonance .
It is very improbable that the planet could have reached the 1:1 resonance .
This enhances the possibility of the planet being suitable for sustained life