The 3-dimensional architecture of the Upsilon Andromedae planetary system
Russell Deitrick, Rory Barnes, Barbara McArthur, Thomas R. Quinn,, Rodrigo Luger, Adrienne Antonsen, and G. Fritz Benedict

TL;DR
This study constructs the first full 3D, dynamically stable models of the Upsilon Andromedae planetary system consistent with observations, revealing the possible inclinations, masses, and orbital configurations of its three planets.
Contribution
It provides the first comprehensive 3D dynamical models of the system, integrating radial velocity and astrometric data to constrain planetary inclinations and stability.
Findings
Only 10 out of 1000 configurations are stable for 100 million years.
Planet b's orbit is near the invariable plane of c and d, with possible prograde or retrograde motion.
Planet b's radius is estimated at about 1.8 Jupiter radii, with eccentricity potentially causing radius inflation.
Abstract
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 3-dimensional configurations of planetary systems. We present, for the first time, full 3-dimensional, dynamically stable configurations for the 3 planets of the system consistent with all observational constraints. While the outer 2 planets, c and d, are inclined by about 30 degrees, the inner planet's orbital plane has not been detected. We use N-body simulations to search for stable 3-planet 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 about 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…
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