Forming Binary Near-Earth Asteroids From Tidal Disruptions

of the satellite in question. For an asteroid of density 2.0 g cm −3 , the Roche limit wouldbe ∼ 3.45 R ⊕ about Earth.In an attempt to extend this limit to solid bodies, Jeffreys (1947) considered internalstrength. He applied his solution to asteroids breaking up around the Earth and Jupiter, aswell as the formation of the rings of Saturn from objects with the consistency of ice. Hiscalculations estimated high internal strengths, and therefore determined that tidal forces,which increase with size, could only be effective on objects with a diameter roughly> 200 km. After the discovery of Comet Ikeya-Seki in 1965, Opik (1966) consideredmodels of tidal disruption for the sun grazing family of comets, and included self-gravity.Opik (1966) suggested that Ikeya-Seki may have had a rubble-pile structure and evenmade qualitative arguments about the effect that the direction of the axis of rotation couldhave on a tidal disruption.In their study of self-gravitating, non-rotating viscous bodies during parabolic encounterswith planets Sridhar & Tremaine (1992) showed that small bodies can shed mass ordisrupt entirely. They determined a pericenter distance inside of which disruption or massloss would occurr disrupt < 1.69R p(ρpρ s) 1/3(1.5)which is smaller than the classical Roche limit. For non-viscous bodies that are heldtogether by self-gravity they determined that the bodies would behave approximately likethe viscous fluid.Richardson et al. (1998) used rubble pile models to simulate tidal disruption of Earth–crossing asteroids. These simulations explored a parameter space which included theasteroid’s hyperbolic encounter (periapse q and encounter velocity with Earth v ∞ ), spinperiod P and shape–orientation conditions. The outcomes were parametrized by the massstripped off during the disruption, or the distortion of the body.23