The Hill stability of triple planets in the Solar system

The Hill stability of the nine known triple asteroid systems in the solar system has been investigated in a framework of the three body system. In this paper, the Sun and triple-asteroid system are treated as a four body system to analyze the influence of the Sun on the Hill stability of the triple subsystem. First, the relationship of the total energy and the angular momentum between the four body system and the triple subsystem is derived. It is found that the total energy of this 1-3 configuration four body system is the sum of the energy of the triple subsystem and the energy of a two-body system composed of the Sun and the mass center of the subsystem; so is the angular momentum. Then, the Hill stability of the triple subsystem is reinvestigated using a previous criterion in the four body problem (Gong and Liu in Mon. Not. R. Astron. Soc. 462: 547-553, 2016) and the results are compared to those in the three body problem. Among the nine known triple-asteroid systems, 1995 CC and 1999 TC are Hill stable for both models; the others are stable in the three body model while not stable in the four body model. In addition, the exploration of Pluto by New Horizons has attracted great attention in recent years, the Sun-Pluto-Charon-Hydra four body system is investigated in the paper, and it is found that the system is Hill stable.