Forming Binary Near-Earth Asteroids From Tidal Disruptions

etween ω pri and L bin ), with close to 90% of the binaries having an obliquity less than20 ◦ . The obliquity of the secondary has no such relation, being nearly flat between 0 ◦ and90 ◦ , and falling off from 90 ◦ to 180 ◦ (Fig. 2.7b). With many secondaries formed fromaccreting material in orbit around the primary, retaining an aligned spin axis appears tobe unlikely for a secondary.Shape of the primaryThe shape of the primary was measured along the body’s three principal axes, a, b, andc for the longest, intermediate and shortest axis length. Nearly all primaries are in aprincipal axis rotation state, rotating around the shortest axis. Thus the shape irregularitieswhich are associated with a rotational lightcurve are a result of a difference between thelong axis, a and the intermediate axis, b. If the intermediate axis, b, equals a or c, thebody is either oblate (b = a) or prolate (b = c). However, few bodies approach suchperfect classification, so for the sake of simplicity we define a shape indexI = (a − b)/(a − c)where I = 1 means prolate, and I = 0 oblate.The progenitor bodies were created to be simple prolate ellipsoids (b = c), with differentvalues of a/c for varying amounts of elongation. The resulting primaries, as shown inFigure 2.8a, have a distribution of a/c concentrated between 1.0 and 3.0. The progenitorelongations used in the simulation were only varied between 1.0 and 2.0, so elongationwas significantly enhanced during the binary-forming encounters.The distribution of a/b is a more valuable comparison to the shape derived via lightcurvestudies for bodies rotating around their shortest principal axis. This distribution has thesame peak as a/c, at 1.95, but a larger concentration of objects near 1.0 (Fig. 2.8b). Whenthe distribution is separated into bodies with I < 0.5 and > 0.5 (more oblate-like or42