  The full two-body problem (F2BP) is often used to model binary asteroid
systems, representing the bodies as two finite mass distributions whose
dynamics are influenced by their mutual gravity potential. The emergent
behavior of the F2BP is highly coupled translational and rotational mutual
motion of the mass distributions. A large fraction of characterized binary
asteroids appear to be at, or near, the doubly synchronous equilibrium, which
occurs when both bodies are tidally-locked and in a circular co-orbit. Stable
oscillations about this equilibrium can be shown, for the nonplanar system, to
be combinations of seven fundamental frequencies of the system and the mutual
orbit rate. The fundamental frequencies arise as the linear periods of center
manifolds identified about the equilibrium which are heavily influenced by each
body's mass parameters. We leverage these eight dynamical constraints to
investigate the observability of binary asteroid mass parameters via dynamical
observations. This is accomplished by deriving a relationship between the
fundamental frequencies and mass parameters for doubly synchronous systems.
This relationship allows us to show the sensitivity of the dynamics to changes
in the mass parameters, first for the planar dynamics, and then for the
nonplanar dynamics. In so doing we are able to predict the idealized estimation
covariance of the mass parameters based on observation quality and define
idealized observation accuracies for desired mass parameter certainties. We
apply these tools to 617 Patroclus, a doubly synchronous Trojan binary and
flyby target of the LUCY mission, as well as the Pluto and Charon system in
order to predict mutual behavior
