  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.

Earth and Planetary Astrophysics