Doubly synchronous binary asteroid mass parameter observability

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. We can also 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 behaviors of these doubly synchronous systems and to provide observational requirements for their mass parameters.