We have undertaken a thorough dynamical investigation of five extrasolar planetary systems using extensive numerical experiments on the supercomputer of the Max Planck Institute for Gravitational Physics ( Albert Einstein Institute ) .
This work was performed as part of the Helmholtz Institute for Supercomputational Physics Summer School on “ Chaos and Stability in Planetary Systems ” ( 2003 ) .
The systems Gl 777 A , HD 72659 , Gl 614 , 47 Uma and HD 4208 were examined concerning the question of whether they could host terrestrial like planets in their habitable zones ( =HZ ) .

First we investigated the mean motion resonances between fictitious terrestrial planets and the existing gas giants in these five extrasolar systems .
Then a fine grid of initial conditions for a potential terrestrial planet within the HZ was chosen for each system , from which the stability of orbits was then assessed by direct integrations over a time interval of 1 million years .
For each of the five systems the 2-dimensional grid of initial conditions contained 80 eccentricity points for the Jovian planet and up to 160 semimajor axis points for the fictitious planet .
The computations were carried out using a Lie-series integration method with an adaptive step size control .
This integration method achieves machine precision accuracy in a highly efficient and robust way , requiring no special adjustments when the orbits have large eccentricities .

The stability of orbits was examined with a determination of the Rényi entropy , estimated from recurrence plots , and with a more straight forward method based on the maximum eccentricity achieved by the planet over the 1 million year integration .
Additionally , the eccentricity is an indication of the habitability of a terrestrial planet in the HZ ; any value of e > 0.2 produces a significant temperature difference on a planet ’ s surface between apoapse and periapse .
The results for possible stable orbits for terrestrial planets in habitable zones for the five systems are summarized as follows : for Gl 777 A nearly the entire HZ is stable , for 47 Uma , HD 72659 and HD 4208 terrestrial planets can survive for a sufficiently long time , while for Gl 614 our results exclude terrestrial planets moving in stable orbits within the HZ .

Studies such as this one are of primary interest to future space missions dedicated to finding habitable terrestrial planets in other stellar systems .
Assessing the likelihood of other habitable planets , and more generally the possibility of other life , is the central question of astrobiology today .
Our investigation indicates that , from the dynamical point of view , habitable terrestrial planets seem to be quite compatible with many of the currently discovered extrasolar systems .