Simulation and analysis of the dynamics of binary near-Earth Asteroid (66391) 1999 KW4

Near-Earth Asteroid (66391) 1999 KW4 was the subject of the recently published first extensive radar imaging, shape and mutual orbit modeling, and physical and dynamical characterization of a binary asteroid. In this paper we present in detail our numerical simulation of KW4 behind that work. Our propagations of the system with some variation in estimated parameters cover the set of KW4's possible current dynamical states consistent with the body models and other information obtained directly from the observations. We also apply our implementation of this simulation capability to address some of the dynamical mechanisms by which KW4 may be moved into the more energetically excited of those possible current states, particularly solar gravity interaction. Through comparison of the results with certain features of the observation data, we conclude that the actual KW4 system is not in the most energetically relaxed configuration but must be moderately excited. The system occupies a generalized Cassini state 2 which is different from that considered in most previously published treatments of Cassini states in that it involves co-precession of the primary's spin frame and the mutual orbit rather than co-precession of a satellite's spin frame and that satellite's orbit about the primary. We present a simple analytical theory describing the system's dynamics, which should be applicable to any other binary systems, of which KW4 is representative, in which a massive, roughly oblate primary is spinning rapidly relative to the rate of its mutual orbit with an on-average synchronous, elongated secondary. We examine separately both the effect of the larger binary component's oblateness, and the effect of the smaller component's roughly triaxial ellipsoid shape. The simple analytical formulae obtained agree with full-detail numerical simulation results, and can be used for remote estimation of binary mass properties from observed system motion.