The stability of evolving planetary orbits in an embedded cluster

An analysis is made of the survival of planetary systems due to the near passages of stars in the embedded stage of a stellar cluster. The planetary orbits are taken with initial parameters ( a , e ) = (1500 au, 0.9) and evolve in a resisting medium on a million‐year time‐scale to very close orbits, similar to those observed for exoplanets. During this process the embedded cluster becomes progressively less dense and, consequently, close passages of stars become less frequent. A precalculation computes detailed paths for planets with various initial orbital parameters, ( a , e ) perturbed by passing stars with various periastron distances, D . For each combination ( a , e , D ) computations are carried out for 900 different configurations, consisting of 150 random relative orientations of planet and passing‐star orbits together with six different initial times of periastron for the planet, uniformly distributed in time round the orbit. These results give a probability that for a particular ( a , e , D ) the planetary orbit will be disrupted. These results are then applied to the evolving orbits where they enable the total probability of disruption to be found for small time intervals, taking into account all possible parameters for the passing stars with their appropriate probabilities. The survival probability for a planetary orbit over the whole period of its evolution can thus be found. It is shown that the predicted survival rates of planets, under various conditions of the number density of stars and velocity dispersion in the cluster, are sufficient to explain the observed proportion of solar‐type stars with exoplanet systems.