Asteroids IV

1. INTRODUCTION The most important parameter governing the global extent of an impact is the mass ratio of the projectile to the target, g = M2/M1. In the case of a cratering event this ratio is small, and there is a well-defined geometric locus. Crater scaling then becomes a powerful tool (e.g., Housen et al., 1983) that allows simple analytical approaches to be applied to determine whether an impact “goes global” — for instance, whether the surface is shaken everywhere to the escape velocity , or whether the target is shattered or melted. At the other extreme, as M2 → M1, there is no impact locus , so the mechanics and dynamics are complex (Asphaug, 2010). Crater scaling does not apply, even though the impact physics are fundamentally the same. By definition, these similar-sized collisions (SSCs) are global events. Unlike most cratering impacts, they involve substantial downrange or even escaping motion of the projectile M2, depending on the impact velocity vimp and the impact angle q. Impact velocity is the next most important parameter, because of its dynamical and thermodynamical consequences. In order for an asteroid to be eroded in a cratering impact, for example, one projectile mass of material must be ejected to vej > vesc, where vej is the ejecta velocity and vesc is the escape velocity described below. The ejection velocity in turn scales with vimp, so that a cratering projectile has to strike at a few times vesc in a competent rocky target if it is to cause net escape of material, and an order of magnitude faster to cause net mass loss from a highly porous target (Housen and Holsapple, 2011). This implies a very different impact evolution depending on porosity. Impact velocity also represents a specific collisional kinetic energy Q = 1 2(M1v2 1 + M2v2 2 )/(M1 + M2) where v1 Q* S, then shattering occurs, breaking the solid bonds of the asteroid into pieces no larger than M1/2. If gravitationally bound (ejected at Q* D > Q* S, to break any solid bonds and also to overcome internal friction (see below), and to exceed the gravitational binding energy, thereby dispersing the fragments to vej > vesc. For massive bodies, intermediate energy collisions Q* D > Q > Q* S can lead to complicated (altered and reassembled) geologies. These are idealizations because impact energy is not deposited uniformly inside a target. Much of this chapter is to study how this deposition occurs, and what it does. The impact angle q is especially important in this regard, especially for similar colliding masses, since only a limited amount of angular momentum can be accreted in a collision , and because objects of comparable diameter tend to suffer grazing collisions more often than not. And finally, two asteroids of masses M1 and M2 cannot be thought of as colliding in isolation, even if one ignores all the other asteroids and planets: Both bodies orbit the Sun and their 661 Asphaug E., Collins G., and Jutzi M. (2015) Global-scale impacts. In Asteroids IV (P. Michel et al., eds.), pp. 661–677. Univ. of Arizona, Tucson, DOI: 10.2458/azu_uapress_9780816532131-ch034. Global-Scale Impacts Erik Asphaug Arizona State University Gareth Collins Imperial College, London Martin Jutzi University of Bern Global-scale impacts modify the physical or thermal state of a substantial fraction of a target asteroid. Specific effects include accretion, family formation, reshaping, mixing and layering, shock and frictional heating, fragmentation, material compaction, dilatation, stripping of mantle and crust, and seismic degradation. Deciphering the complicated record of global-scale impacts in asteroids and meteorites will lead us to understand the original planet-forming process and its resultant populations, and their evolution in time as collisions became faster and fewer. We provide a brief overview of these ideas, and an introduction to models. 662   Asteroids IV fragments continue orbiting on intersecting orbits, so their interaction extends long after the original collision. 1.1. Mass Effects Generally speaking, impacts slower than vesc cause accretion , and impacts faster than vesc cause erosion, with the specific boundary depending on the impact angle q. This is effectively the case for cratering impacts and for similarsized collisions, so we consider the governing parameter vimp/vesc. But vimp can be no slower than vesc, the impact velocity of two spheres falling from infinity with initial relative velocity vrel = 0 v G M M R R esc = + ( ) + ( ) 2 1 2 1 2 (1) where R1 and R2 are the corresponding radii. As a rule of thumb, vesc = Rkm, in meters per second, where...