# Browsing by Subject "stability analysis"

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Item Origin And Dynamics Of The Mutually Inclined Orbits Of Upsilon Andromedae C And D(2011-07) Barnes, Rory; Greenberg, Richard; Quinn, Thomas R.; McArthur, Barbara E.; Benedict, G. Fritz; McArthur, Barbara E.; Benedict, G. FritzShow more We evaluate the orbital evolution and several plausible origin scenarios for the mutually inclined orbits of upsilon And c and d. These two planets have orbital elements that oscillate with large amplitudes and lie close to the stability boundary. This configuration, and in particular the observed mutual inclination, demands an explanation. The planetary system may be influenced by a nearby low-mass star, upsilon And B, which could perturb the planetary orbits, but we find it cannot modify two coplanar orbits into the observed mutual inclination of 30 degrees. However, it could incite ejections or collisions between planetary companions that subsequently raise the mutual inclination to >30 degrees. Our simulated systems with large mutual inclinations tend to be further from the stability boundary than upsilon And, but we are able to produce similar systems. We conclude that scattering is a plausible mechanism to explain the observed orbits of upsilon And c and d, but we cannot determine whether the scattering was caused by instabilities among the planets themselves or by perturbations from upsilon And B. We also develop a procedure to quantitatively compare numerous properties of the observed system to our numerical models. Although we only implement this procedure to upsilon And, it may be applied to any exoplanetary system.Show more Item The Three-Dimensional Architecture Of The Upsilon Andromedae Planetary System(2015-01) Deitrick, Russell; Barnes, Rory; McArthur, Barbara; Quinn, Thomas R.; Luger, Rodrigo; Antonsen, Adrienne; Benedict, G. Fritz; McArthur, Barbara; Benedict, G. FritzShow more The upsilon Andromedae system is the first exoplanetary system to have the relative inclination of two planets' orbital planes directly measured, and therefore offers our first window into the three-dimensional configurations of planetary systems. We present, for the first time, full three-dimensional, dynamically stable configurations for the three planets of the system consistent with all observational constraints. While the outer two planets, c and d, are inclined by similar to 30 degrees the inner planet's orbital plane has not been detected. We use N-body simulations to search for stable threeplanet configurations that are consistent with the combined radial velocity and astrometric solution. We find that only 10 trials out of 1000 are robustly stable on 100 Myr timescales, or similar to 8 billion orbits of planet b. Planet b's orbit must lie near the invariable plane of planets c and d, but can be either prograde or retrograde. These solutions predict that b's mass is in the range of 2-9 M-Jup and has an inclination angle from the sky plane of less than 25 degrees Combined with brightness variations in the combined star/planet light curve ("phase curve"), our results imply that planet b's radius is similar to 1.8 R-jup, relatively large for a planet of its age. However, the eccentricity of b in several of our stable solutions reaches >0.1, generating upward of 10(19) W in the interior of the planet via tidal dissipation, possibly inflating the radius to an amount consistent with phase curve observations.Show more