Abstract
The stability limit of coplanar hierarchical triple systems is numerically studied. Systems we investigated consist of two equal mass bodies initially on a circular orbit and third body with various masses, which at the maximum are equal to the mass of the binary. In order to estimate the stability limit, we use an empirically-found fact that the system is quasi-periodic if the initial eccentricity of the outer binary is less than some critical value, otherwise the third body eventually escapes. We make an analytical expression for the stability limit in terms of the ratio of the orbital radii and find that the expression improves the previous criteria. The resultant expression also suggests that the ratio of the orbital radii rapidly approaches to a certain value (e.g. \(\sim \)2, in an initially circular outer binary) as the mass of the third-body tends to zero.
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Saito, M.M., Tanikawa, K. & Orlov, V.V. Disintegration process of hierarchical triple systems II: non-small mass third body orbiting equal-mass binary. Celest Mech Dyn Astr 116, 1–10 (2013). https://doi.org/10.1007/s10569-013-9474-y
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DOI: https://doi.org/10.1007/s10569-013-9474-y