  We explore the orbital dynamics of systems consisting of three planets, each
as massive as the Earth, on coplanar, initially circular, orbits about a star
of one solar mass. The initial semimajor axes of the planets are equally spaced
in terms of their mutual Hill radius, which is equivalent to a geometric
progression of orbital periods for small planets of equal mass. Our simulations
explore a wide range of spacings of the planets, and were integrated for
virtual times of up to 10 billion years or until the orbits of any pair of
planets crossed. We find the same general trend of system lifetimes increasing
exponentially with separation between orbits seen by previous studies of
systems of three or more planets. One focus of this paper is to go beyond the
rough trends found by previous numerical studies and quantitatively explore the
nature of the scatter in lifetimes and the destabilizing effects of mean motion
resonances. In contrast to previous results for five-planet systems, a
nontrivial fraction of three-planet systems survive at least several orders of
magnitude longer than most other systems with similar initial separation
between orbits, with some surviving $10^{10}$ years at much smaller orbital
separations than any found for five-planet systems. Substantial shifts in the
initial planetary longitudes cause a scatter of roughly a factor of two in
system lifetime, whereas the shift of one planet's initial position by 100
meters along its orbit results in smaller changes in the logarithm of the time
to orbit crossing, especially for systems with short lifetimes.
