Orbital Stability and Precession Effects in the Kepler-89 System

Among the numerous discoveries resulting from the {\it Kepler} mission are a plethora of compact planetary systems that provide deep insights into planet formation theories. The architecture of such compact systems also produces unique opportunities to study orbital dynamics in compact environments and the subsequent evolution of orbital parameters. One of the compact {\it Kepler} systems is Kepler-89; a system for which the radial velocity follow-up observations place strong upper limits on the masses of the planets and their Keplerian orbital elements. The potential for non-circular orbits in this system make it a compelling system to study dynamical constraints on the measured orbital parameters. We present a dynamical analysis of the system that demonstrates the stability of the circular model and shows the eccentric model of the system is not stable. The analysis indicates that planets c and d, although close to the 2:1 secular resonance, do not permanently occupy the 2:1 resonance configuration. We explore regions of orbital parameter space to identify the upper bounds of orbital eccentricity for the planets. We further show how the dynamics in the compact system leads to significant periastron precession of the innermost planets. Finally, we quantify the effect of the periastron precession on the transit times of the planets compared with the cyclic variations expected from transit timing variations.