What Would Happen If We Were About 1 pc Away from a Supermassive Black Hole?

We consider a hypothetical planet with the same mass $m$, radius $R$, angular momentum $\boldsymbol{S}$, oblateness $J_2$, semimajor axis $a$, eccentricity $e$, inclination $I$, and obliquity $\varepsilon$ of the Earth orbiting a main-sequence star with the same mass $M_\star$ and radius $R_\star$ of the Sun at a distance $r_\bullet \simeq 1\,\mathrm{parsec}\,\left(\mathrm{pc}\right)$ from a supermassive black hole in the center of the hosting galaxy with the same mass $M_\bullet$ of, say, $\mathrm{M87}^\ast$. We preliminarily investigate some dynamical consequences of its presence in the neighborhood of such a stellar system on the planet's possibility of sustaining complex life over time. 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 $P_\mathrm{b}$ and $P_\bullet$, of $e,\,I,\,\varepsilon$, which are the main quantities directly linked to the stellar insolation. We find that, for certain orbital configurations, the planet's perihelion distance $q=a\left(1-e\right)$ may greatly shrink and lead to, in some cases, an impact with the star. $I$ may also notably change, with variations even of the order of tens of degrees. On the other hand, $\varepsilon$ does not seem to be particularly affected, being shifted, at most, by $\simeq 0^\circ.02$ over 1 Myr. Our results strongly depend on the eccentricity $e_\bullet$ of the galactocentric motion.