  Context: Numerous theoretical studies of the stellar dynamics of triple
systems have been carried out, but fewer purely empirical studies that have
addressed planetary orbits within these systems. Most of these empirical
studies have been for coplanar orbits and with a limited number of orbital
parameters. Aims: Our objective is to provide a more generalized empirical
mapping of the regions of planetary stability in triples by considering both
prograde and retrograde motion of planets and the outer star; investigating
highly inclined orbits of the outer star; extending the parameters used to all
relevant orbital elements of the triple's stars and expanding these elements
and mass ratios to wider ranges that will accommodate recent and possibly
future observational discoveries. Methods: Using N-body simulations, we
integrated numerically the various four-body configurations over the parameter
space, using a symplectic integrator designed specifically for the integration
of hierarchical multiple stellar systems. The triples were then reduced to
binaries and the integrations repeated to highlight the differences between
these two types of system. Results: This established the regions of secular
stability and resulted in 24 semi-empirical models describing the stability
bounds for planets in each type of triple orbital configuration. The results
were then compared with the observational extremes discovered to date to
identify regions that may contain undiscovered planets.
