Giant gaseous planets often reside on orbits in sufficient proximity to their host stars for the planetary quadrupole gravitational field to become non-negligible. In presence of an additional planetary companion, a precise characterization of the system's orbital state can yield meaningful constraints on the transiting planet's interior structure. However, such methods can require a very specific type of system. This paper explores the dynamic range of applicability of these methods and shows that interior structure calculations are possible for a wide array of orbital architectures. The HAT-P-13 system is used as a case study, and the implications of perturbations arising from a third distant companion on the feasibility of an interior calculation are discussed. We find that the method discussed here is likely to be useful in studying other planetary systems, allowing the possibility of an expanded survey of the interiors of exoplanets.

Accepted to ApJ