Orbital Stability of Moons Around the TRAPPIST-1 Planets

TL;DR

The study investigates the orbital stability of potential moons around the seven TRAPPIST-1 planets using high-precision $N$-body simulations, incorporating the system's multi-resonant configuration. By simulating moons from the Roche limit up to the prograde stability boundary near $0.5\,R_H$ and accounting for perturbations from neighboring planets, the authors map the realistic outer satellite boundaries, finding consistent limits around $0.40$–$0.45\,R_H$ with modest contractions due to the full planetary ensemble (most pronounced for planets b and e). They further constrain long-term moon survival via tidal-decay arguments, adopting $k_{2p}=0.25$, $Q=100$, and an age of $7$ Gyr, which yield extremely small maximum moon masses on the order of $M_m \sim 10^{-10}$ to $10^{-7}$ $M_\oplus$, corresponding to diameters of roughly $80$–$280$ km. Taken together, the results imply TRAPPIST-1 is unlikely to host sizeable, long-lived exomoons, though tiny satellites could exist with negligible dynamical impact.

Abstract

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).

Figures (1)

• Figure 1: Final semi-major axes of satellites versus their initial orbital distance (in Hill radii) for each TRAPPIST-1 planet. Each panel compares stability outcomes under different perturbations: none, individual neighbouring planets, and the full multi-planet system. A drop to zero marks unstable orbits. The vertical dashed line indicates the empirical stability limit. In all cases, the full system shifts the stability boundary inward compared to isolated or single-perturber configurations.