Dynamics in the Potential Field of the Triple Asteroid System 216 Kleopatra

Abstract

The triple asteroid system 216 Kleopatra in the main-belt is consisted of the primary 216 Kleopatra and two moonlets Alexhelios[S/2008(216) 1] as well as Cleoselene[S/2008(216) 2]. The primary is a contact binary asteroid which has highly irregular shape and looks like a dumb bell, its three-axes lengths are 217 km×94 km×81 km. Alexhelios is the outer moonlet, with the size of 8.9 km, while Cleoselene is the inner moonlet, with the size of 6.9 km. The dynamical behavior of the triple asteroid system 216 Kleopatra contain extremely abundant scientific connotation. This paper studies its dynamic mechanism and the motion law of a spacecraft in the potential field. The dynamical equation expressed in the body-fixed frame of the primary has been analyzed, and the dynamical equations as well as the Jacobi integral of the full three-body problem of the triple asteroid system have been presented. The irregular shape, the orbit and the attitude of these three minor bodies are all considered. A new kind of period-doubling bifurcation in the potential field of the primary of the triple asteroid system 216 Kleopatra has been found. The dynamical configuration of this triple asteroid system has been investigated, with considering the irregular gravitational force, the geometrical shape, and the interaction mechanism between these two moonlets. It is found that the irregular shape and the interaction mechanism between these two moonlets cause the orbital parameters of the two moonlets Alexhelios and Cleoselene vary obviously.

Keywords

triple asteroids / contact binary asteroids / gravitational full N-body problem / bifurcations / equilibrium point

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