We consider a hypothetic planet with the same mass m, radius R, angular momentum S, oblateness J 2 , semimajor axis a, eccentricity e, inclination I, and obliquity ε of the Earth orbiting a main sequence star with the same mass M ⋆ and radius R ⋆ of the Sun at a distance r • ≃ 1 parsec pc from a supermassive black hole in the center of the hosting galaxy with the same mass M • of, say, M87 * . We preliminarily investigate some dynamical consequences of its presence in the neighbourhood of such a stellar system on the planet's possibility of sustaining complex life over the eons. In particular, we obtain general analytic expressions for the long-term rates of change, doubly averaged over both the planetary and the galactocentric orbital periods P b and P • , of e, I, ε, which are the main quantities directly linked to the stellar insolation. We find that, for certain orbital configurations, the planet's perihelion distance q = a (1 − e) may greatly shrink leading, in some cases, even to an impact with the star. Also I may notably change, with variations of the order even of tens of degrees. On the other hand, ε does not seem to be particularly affected, being shifted, at most, by ≃ 0.02 deg over a Myr. Our results strongly depend the eccentricity e • of the galactocentric motion. keywords gravitation − celestial mechanics − (galaxies:) quasars: supermassive black holes − planetary systems − extraterrestrial intelligence