Orbital Stability of Moons Around the TRAPPIST-1 Planets

We investigate the dynamical stability of potential satellites orbiting the seven planets of the \texttt{TRAPPIST-1} system using a suite of $N$-body simulations. For each planet, we show that moons can remain stable from the Roche limit out to near the theoretical prograde stability boundary at roughly $0.5$ Hill Radii. We quantify how perturbations from neighbouring planets modify these stability limits. Although the overall effect of individual perturbers is generally weak, the combined gravitational influence of the full multi-planet configuration produces a modest contraction of the outer stable radius, notably for \texttt{TRAPPIST-1 b} and \texttt{TRAPPIST-1 e}. For each of the seven planets, the outer stability limit for satellites is at 40-45\% of the Hill radius, consistent with previous work. Using simple long-term tidal decay calculations, we show that the most massive satellites that could survive over Gyr timescales are $10^{-(7-9)} M_\oplus$ (with higher possible masses for the outer planets).