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An intriguing question in the context of dynamics arises: Could a moonpossess a moon itself? Such a configuration does not exist in the Solar System,although this may be possible in theory. Kollmeier et al. (2019) determined thecritical size of a satellite necessary to host a long-lived sub-satellite, orsubmoon. However, the orbital constraints for these submoons to exist are stillundetermined. Domingos et al. (2006) indicated that moons are stable out to afraction of the host planet Hill radius $R_{H,p}$, which in turn depends on theeccentricity of its host's orbit. Motivated by this, we simulate a system ofexomoons and submoons for $10^5$ planetary orbits, while considering manyinitial orbital phases to obtain the critical semimajor axis in terms of$R_{H,p}$ or the hosts satellite's Hill radius $R_{H,sat}$, respectively. Wefind that, assuming circular coplanar orbits, the stability limit for exomoonsis 0.40 $R_{H,p}$ and for a submoon is 0.33 $R_{H,sat}$. Additionally, wediscuss the observational feasibility of detecting these sub-satellites throughphotometric, radial velocity, or direct imaging observations using theNeptunes-sized exomoon candidates Kepler 1625b-I (Teachey et al. 2018) andidentify how stability can shape the identification of future candidates.

Orbital Stability of Exomoons and Submoons with Applications to Kepler 1625b-I