The determination of planetary structure in tidally relaxed inclined systems

The recent discovery of a transiting short-period planet on a slightly non-circular orbit with a massive highly eccentric companion orbiting the star HAT-P-13 offers the possibility of probing the structure of the short-period planet. The ability to do this relies on the system being in a quasi-equilibrium state in the sense that the eccentricities are constant on the usual secular time-scale (typically, a few thousand years), and decay on a time-scale which is much longer than the age of the system. Since the equilibrium eccentricity is effectively a function only of observable system parameters and the unknown Love number of the short-period planet, the latter can be determined with accurate measurements of the planet s eccentricity and radius.