Study of the Sailboat stable region for binary systens.

Abstract

<p>The sailboat region was first identified by Giuliatti Winter, et al. (2010) exploring the Pluto-<br />Charon binary system, they identifed this unexpected stable region of S-type orbits around the dwarf<br />planet Pluto located at a = (0.5d, 0.7d) and e = (0.2, 0.9), where a and e are the initial values<br />of semi-major axis and eccentricity of particles, respectively and d is the separation of the binary.<br />The sailboat is associated with a family ”BD” of periodic orbits derived from the planar, circular,<br />restricted three-body problem. In this work, we analyzed through numerical simulations the structure<br />and stability of sailboat in hypothetical systems with different values of mass ratio and for several<br />orbital configurations.<br />To constrain the orbital parameters for sailboat regions, we numerically simulated several elliptic<br />three-body problem, exploring a large range of initial conditions. We adopt dimensionless systems<br />and the configuration for each simulation include a test particle in S-type orbit around the primary<br />body and gravitational disturbed by the secondary massive body. We set the central body as a point<br />of mass and a secondary with a mass equivalent to the mass ratio of the binary system (µ), with its<br />radius (r s ) defined as 10% of their Hill radius.<br />We created hypothetical systems with different mass ratio in the interval µ = [0.01, 0.30] in steps<br />∆µ = 0.01. The test particles were randomly distributed with semimajor axis in a = [0.45, 0.7],<br />considering 1 the distance between the two main bodies, the eccentricities varied from 0 to 0.99, and<br />initially the argument of the pericentre and inclination was set as 0º. We numerically integrated using<br />the REBOUND package and IAS15 integrator (Rein & Spiegel 2014) for 10 4 orbital periods of the<br />binary.<br />We analyzed the behaviour of the sailboat according to the eccentricity e of the secondary body,<br />looking for the maximum value for which the particles remain stable. A final set of simulations was<br />performed for different values of inclinations and argument of pericenter in order to determine the<br />extreme values for the stability.<br />Our results show the sailboat is robust and it exists for µ = [0.01,0.27] and for large intervals<br />of the argument of pericentre and inclination. This region of stability reaches its maximum size<br />with an argument of pericenter at 0 ◦ and 180 ◦ . The sailboat region also is present for values of<br />inclination > 60º and existing even retrogrades orbits in the systems with µ > 0.08.<br />The numerical results also showed that little changes in the eccentricity of the secondary body is<br />sufficient to vanish the sailboat region, for binaries system with µ > 0.12, the sailboat exists just for<br />values of e < 0.05.</p>