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R. Barnes, R. Greenberg (University of Arizona)
Planetary systems display a wide range of appearances, with apparently arbitrary values of semi-major axis, eccentricity, etc. We reduce the complexity of orbital configurations to a single value, \delta, which is a measure of how close, over secular timescales (~10,000 orbits), two consecutive planets come to each other. We measure this distance relative to the sum of the radii of their Hill spheres, sometimes referred to as mutual Hill radii (MHR). We determine the closest approach distance by numerically integrating the entire system on coplanar orbits, using minimum masses. For non-resonant systems, close approach occurs during apsidal alignment, either parallel or anti-parallel. For resonant pairs the distance at conjunction determines the closest approach distance. Previous analytic work found that planets on circular orbits were assuredly unstable if they came within 3.5 MHR (i.e. Gladman 1993; Chambers, Wetherill & Boss 1996). We find that most known pairs of jovian planets (including those in our solar system) come within 3.5 -- 7 MHR of each other. We also find that several systems are unstable (their closest approach distance is less than 3.5 MHR). These systems, if they are real, probably exist in an observationally permitted location somewhat different from the current best fit. In these cases, the planets' closest approach distance will most likely also be slightly larger than 3.5 MHR. Most pairs beyond 7 MHR probably experienced post-formation migration (i.e. tidal circularization, inward scattering of small bodies) which moved them further apart. This result is even more remarkable since we have used the minimum masses; most likely the systems are inclined to the line of sight, making the Hill spheres larger, and shrinking \delta. This dense packing may reflect a tendency for planets to form as close together as they can without being dynamically unstable. This result further implies there may be a large number of smaller, currently undetectable companions packed in orbits around stars with known planets.
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Bulletin of the American Astronomical Society, 37 #3
© 2004. The American Astronomical Soceity.