The Hill stability of low mass binaries in hierarchical triple systems

The Hill stability of the low mass binary system in the presence of a massive third body moving on a wider inclined orbit is investigated analytically. It is found that, in the case of the third body being on a nearly circular orbit, the region of Hill stability expands as the binary/third body mass ratio increases and the inclination (i) decreases. This i-dependence decreases very quickly with increasing eccentricity (e(2)) of the third body relative to the binary barycentre. In fact, if e(2) is not extremely small, the Hill stable region can be approximately expressed in a closed form by setting i = 90 degrees, and it contracts with increasing e(2) as e(2)(2) for sufficiently low mass binary. Our analytic results are then applied to the observed triple star systems and the Kuiper belt binaries.