The Stability of Tidal Equilibrium for Hierarchical Star-Planet-Moon Systems
arXiv:1607.08170 · doi:10.1093/mnras/stw1883
Abstract
Motivated by the current search for exomoons, this paper considers the stability of tidal equilibrium for hierarchical three-body systems containing a star, a planet, and a moon. In this treatment, the energy and angular momentum budgets include contributions from the planetary orbit, lunar orbit, stellar spin, planetary spin, and lunar spin. The goal is to determine the optimized energy state of the system subject to the constraint of constant angular momentum. Due to the lack of a closed form solution for the full three-body problem, however, we must use use an approximate description of the orbits. We first consider the Keplerian limit and find that the critical energy states are saddle points, rather than minima, so that these hierarchical systems have no stable tidal equilibrium states. We then generalize the calculation so that the lunar orbit is described by a time-averaged version of the circular restricted three-body problem. In this latter case, the critical energy state is a shallow minimum, so that a tidal equilibrium state exists. In both cases, however, the lunar orbit for the critical point lies outside the boundary (roughly half the Hill radius) where (previous) numerical simulations indicate dynamical instability. These results suggest that star-planet-moon systems have no viable long-term stable states analogous to those found for two-body systems.
arXiv comment17 pages, 4 figures, accepted to MNRAS
References in corpus (19)
- Planetary Candidates Observed by Kepler, III: Analysis of the First 16 Months of Data
- Characteristics of planetary candidates observed by Kepler, II: Analysis of the first four months of data
- DHP Framework: Digital Health Passports Using Blockchain -- Use case on international tourism during the COVID-19 pandemic
- On detecting terrestrial planets with timing of giant planet transits
- Architecture and Dynamics of Kepler's Candidate Multiple Transiting Planet Systems
- Transit timing effects due to an exomoon
- Tidal Evolution of Close-in Planets
- Stellar Rotation Periods of the Kepler Objects of Interest: A Dearth of Close-in Planets around Fast Rotators
- Stability of Satellites Around Close-in Extrasolar Giant Planets
- Rotation Periods, Variability Properties and Ages for Kepler Exoplanet Candidate Host Stars
- Falling Transiting Extrasolar Giant Planets
- Formation, Habitability, and Detection of Extrasolar Moons
- Magnetic and Gravitational Disk-Star Interactions: An Interdependence of PMS Stellar Rotation Rates and Spin-Orbit Misalignments
- On the detectability of habitable exomoons with Kepler-class photometry
- Resonant Removal of Exomoons During Planetary Migration
- Stability criteria for hierarchical triple systems
- Stability of Satellites in Closely Packed Planetary Systems
- Limits on the Orbits and Masses of Moons around Currently-Known Transiting Exoplanets
- On the Stability of Extrasolar Planetary Systems and other Closely Orbiting Pairs
Cited by in corpus (10)
- Energy Optimization in Extrasolar Planetary Systems: The Transition from Peas-in-a-Pod to Runaway Growth
- Exomoon Habitability and Tidal Evolution in Low-Mass Star Systems
- Exoplanets Torqued by the Combined Tides of a Moon and Parent Star
- Pairwise Tidal Equilibrium States and the Architecture of Extrasolar Planetary Systems
- Impact of Tides on the Potential for Exoplanets to Host Exomoons
- Giant Outer Transiting Exoplanet Mass (GOT 'EM) Survey. II. Discovery of a Failed Hot Jupiter on a 2.7 Year, Highly Eccentric Orbit
- The ominous fate of exomoons around hot Jupiters in the high-eccentricity migration scenario
- Energy Optimization in Binary Star Systems: Explanation for Equal Mass Members in Close Orbits
- Probing Planets with Exomoons: The Cases of Kepler-1708 b and Kepler-1625 b
- Special cases : moons, rings, comets, trojans