Doubly Synchronous Binary Asteroid Mass Parameter Observability

Abstract

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

45 pages, 11 figures. Accepted for publication in Icarus

References in corpus (4)

• Mean radius and shape of Pluto and Charon from New Horizons images
• Near-Earth Asteroid Satellite Spins Under Spin-Orbit Coupling
• Figure-Figure Interaction Between Bodies Having Arbitrary Shapes and Mass Distributions: A Power Series Expansion Approach
• Minimum Energy Configurations in the $N$-Body Problem and the Celestial Mechanics of Granular Systems

Cited by in corpus (12)

• Momentum Transfer from the DART Mission Kinetic Impact on Asteroid Dimorphos
• The Excited Spin State of Dimorphos Resulting from the DART Impact
• Predictions for the Dynamical States of the Didymos System before and after the Planned DART Impact
• The Dynamical State of the Didymos System Before and After the DART Impact
• Energy Dissipation in Synchronous Binary Asteroids
• Dynamical Evolution of the Didymos-Dimorphos Binary Asteroid as Rubble Piles following the DART Impact
• The Hera Radio Science Experiment at Didymos
• Rotation-induced granular motion on the secondary component of binary asteroids: Application to the DART impact on Dimorphos
• The accuracy of mutual potential approximations in simulations of binary asteroids
• A pair of Jovian Trojans at the L4 Lagrange point
• The spin-spin model and the capture into the double synchronous resonance
• Analytical theory of the spin-orbit state of a binary asteroid deflected by a kinetic impactor