Stability of Relative Equilibria in the Full Two-Body Problem

The stability of relative equilibrium solutions for the interaction of two massive bodies is explored. We restrict ourselves to the interaction between an ellipsoid and a sphere, both with finite mass. The study of this problem has application to modeling the relative dynamics of binary asteroids, the motion of spacecraft about small bodies, and the dynamics of gravity gradient satellites. The relative equilibrium can be parameterized by a few constants, including the mass ratio of the two bodies, the shape of the ellipsoid, and the normalized distance between the two bodies. Planar stability is characterized over this range of parameter values. When restricted to motion in the symmetry plane, the dynamical problem can be reduced to a two-degrees of freedom Hamiltonian system, which allows for an efficient computation of stability characteristics of the relative equilibria. Future work will look at full stability of these relative equilibria.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73952/1/annals.1311.006.pd

Effect of Density Inhomogeneity on YORP: The case of Itokawa

The effect of density inhomogeneity on the YORP effect for a given shape model is investigated. A density inhomogeneity will cause an offset between the center of figure and the center of mass and a re-orientation of the principal axes away from those associated with the shape alone. Both of these effects can alter the predicted YORP rate of change in angular velocity and obliquity. We apply these corrections to the Itokawa shape model and find that its YORP angular velocity rate is sensitive to offsets between its center of mass and center of figure, with a shift on the order of 10 meters being able to change the sign of the YORP effect for that asteroid. Given the non-detection of YORP for Itokawa as of 2008, this can shed light on the density distribution within that body. The theory supports a shift of the asteroid center of mass towards Itokawa's neck region, where there is an accumulation of finer gravels. Detection of the YORP effect for Itokawa should provide some strong constraints on its density distribution. This theory could also be applied to asteroids visited by future spacecraft to constrain density inhomogeneities.Comment: 23 pages, 3 figure

Post-main-sequence debris from rotation-induced YORP break-up of small bodies II : multiple fissions, internal strengths and binary production

Over one quarter of white dwarfs contain observable metallic debris from the breakup of exo-asteroids. Understanding the physical and orbital history of this debris would enable us to self-consistently link planetary system formation and fate. One major debris reservoir is generated by YORP-induced rotational fission during the giant branch phases of stellar evolution, where the stellar luminosity can exceed the Sun’s by four orders of magnitude. Here, we determine the efficacy of the giant branch YORP effect for asteroids with nonzero internal strength, and model post-fission evolution by imposing simple analytic fragmentation prescriptions. We find that even the highest realistic internal strengths cannot prevent the widespread fragmentation of asteroids and the production of a debris field over 100 au in size. We compute the number of successive fission events as they occur in progressively smaller time intervals as the star ascends the giant branches, providing a way to generate size distributions of asteroid fragments. The results are highly insensitive to progenitor stellar mass. We also conclude that the ease with which giant branch YORP breakup can generate binary asteroid subsystems is strongly dependent on internal strength. Formed binary subsystems in turn could be short-lived due to the resulting luminosity-enhanced BYORP effect

Microscopic dynamics underlying the anomalous diffusion

The time dependent Tsallis statistical distribution describing anomalous diffusion is usually obtained in the literature as the solution of a non-linear Fokker-Planck (FP) equation [A.R. Plastino and A. Plastino, Physica A, 222, 347 (1995)]. The scope of the present paper is twofold. Firstly we show that this distribution can be obtained also as solution of the non-linear porous media equation. Secondly we prove that the time dependent Tsallis distribution can be obtained also as solution of a linear FP equation [G. Kaniadakis and P. Quarati, Physica A, 237, 229 (1997)] with coefficients depending on the velocity, that describes a generalized Brownian motion. This linear FP equation is shown to arise from a microscopic dynamics governed by a standard Langevin equation in presence of multiplicative noise.Comment: 4 pag. - no figures. To appear on Phys. Rev. E 62, September 200