Stable satellites around extrasolar giant planets

TLDR

The study investigates the stability of hypothetical satellites around extrasolar planets and derives analytical expressions for the critical semimajor axis beyond which they become unstable. The authors performed numerical simulations of the restricted elliptic three‑body problem and derived analytical expressions for the critical semimajor axis as a function of the planet’s and satellite’s eccentricities. The results show that prograde satellites remain stable up to aE≈0.4895(1−1.0305eP−0.2738esat) and retrograde satellites up to aE≈0.9309(1−1.0764eP−0.9812esat), indicating that habitable‑zone extrasolar planets could host Earth‑like satellites.

Abstract

In this work, we study the stability of hypothetical satellites of extrasolar planets. Through numerical simulations of the restricted elliptic three-body problem we found the borders of the stable regions around the secondary body. From the empirical results, we derived analytical expressions of the critical semimajor axis beyond which the satellites would not remain stable. The expressions are given as a function of the eccentricities of the planet, eP, and of the satellite, esat. In the case of prograde satellites, the critical semimajor axis, in the units of Hill's radius, is given by aE≈ 0.4895 (1.0000 − 1.0305eP− 0.2738esat). In the case of retrograde satellites, it is given by aE≈ 0.9309 (1.0000 − 1.0764eP− 0.9812esat). We also computed the satellite stability region (aE) for a set of extrasolar planets. The results indicate that extrasolar planets in the habitable zone could harbour the Earth-like satellites.