A classical result of De Bruijn and Erdős shows that any given n points are either collinear or determine at least n distinct lines in the plane. Chen and Chvátal conjectured that a generalization of this result in all metric spaces, with appropriate definitions of lines, holds as well. In this note, we show that the Chen-Chvátal generalization holds for Asteroidal-Triple free graphs, where lin...

To characterize the dynamical stability of an asteroid orbit, the calculation of its Lyapunov-Time TL is a widely used mean in celestial mechanics. In the present work we investigated the effects of the used computer hardware and integration method on the outcome of such stability computations. We showed that for some asteroids the change of the employed numerical method can change the obtained...

We discuss the existence and the properties of a new type of mean motion resonance populated by a large number of asteroids, the resonant angle being deÐned as a linear combination (with integer coefficients) of the mean longitudes of asteroid, Jupiter, and Saturn. We call these resonances the threebody mean motion resonances. In the present paper, we show that the anomalous large oscillation o...

We studied impact processes by means of smoothed-particle hydrodynamics (SPH) simulations. The method was applied to modeling formation main-belt families during the cometary bombardment (either early or late, ${\sim}\,3.85\,{\rm Gy}$ ago). If asteroids were bombarded comets, as predicted Nice model, hundreds asteroid (catastrophic disruptions diameter $D \ge 100\,{\rm km}$ bodies) should have ...

Introduction: Ca-Fe and alkali-halide alteration of CAIs is often attributed to aqueous alteration by fluids circulating on asteroidal parent bodies after the various chondritic components have been assembled, although debate continues about the roles of asteroidal vs. nebular modification processes [1-7]. Here we report detailed observations of alteration products in a large Type B2 CAI, TS4 f...

We perform numerical simulations to study the secular orbital evolution and dynamical structure in the HD 69830 planetary system, using the best-fit orbital solutions by Lovis and coworkers. In the simulations, we show that a triplet Neptunian system is stable for at least 2 Gyr and that the stability would not be greatly influenced even if we varied the planetary masses. In addition, we employ...