Scheeres et al.: The Fate of Asteroid Ejecta 527 The Fate of Asteroid Ejecta D. J. Scheeres The University of Michigan D. D. Durda Southwest Research Institute P. E. Geissler University of Arizona The distribution of regolith on asteroid surfaces has only recently been measured directly by in situ observations from spacecraft. To the surprise of many researchers, most of the classical predictions for the distribution of asteroid impact ejecta have not rung true, with regoliths appear- ing to be geologically active at small scales on asteroid surfaces. This indicates that significant insight into geological processes on asteroids may be inferred by detailed studies of the distribu- tion of impact ejecta on asteroids. This chapter has been written to support these future investiga- tions, by trying to identify and clarify all the important elements for such a study, to point to the recent history of such studies, and to indicate the current gaps in our understanding. The chapter begins with a discussion of the initial conditions of ejecta fields generated from impacts on the asteroid surface. Then the relevant physical laws and forces affecting asteroid ejecta, in orbit and on the surface, are reviewed and the basic dynamical equations of motion for ejecta are stated. Some general results and constraints on the solutions to these equations are given, and a classification scheme for ejecta trajectories is given. Finally, recent studies of asteroid ejecta are reviewed, showing the application of these techniques to asteroid science. 1. INTRODUCTION and strings of secondaries. The importance of erasure mecha- nisms, such as seismic shaking (Greenberg et al., 1994) and Whether the debris ejected from impacts on asteroids electromagnetic forces (Lee, 1996), that compete with dy- escapes or reimpacts has important implications for the namical effects to shape the surfaces of asteroids has re- erosion of asteroids, retention and distribution of regolith, cently been emphasized by detailed studies of Eros by dispersal or reaccretion of fragments after catastrophic dis- NEAR Shoemaker. ruptions, and the formation of temporary satellites and per- Rapid advances are expected in our understanding of im- manent moons. Asteroids present complex dynamical envi- pact cratering on diverse objects through in situ experiments ronments because of their low gravitational accelerations, such as NASA’s Deep Impact mission to Comet Tempel 1, nonspherical shapes, complex geological makeup, and di- numerical simulation of ejecta trajectories that employ real- verse rotation states. Additionally, critical parameters related istic shape and gravity models and consider third-body and to the flux and size distribution of impactors and the result- nongravitational forces, and geological evidence from anal- ing initial ejecta fields are only poorly known. Thus the ysis of spacecraft data. The fundamental motivation for the physics and dynamics of regolith processes are complicated study of asteroid regoliths arises from the meteoritics com- and not fully understood. Finally, physical observations of munity and the interpretations of (primordial) asteroid rego- asteroids are only now approaching the resolution necessary liths as observed in the meteorite database. Future motiva- to seriously constrain and delineate between competing tion for ejecta studies will include the necessity of providing theories of the asteroid environment, making the study of a complete mechanical understanding of the asteroid envi- asteroid ejecta a timely endeavor. ronment. Ultimately, a detailed understanding of ejecta dy- Within the last decade we have obtained closeup pictures namics will be crucial to characterize the safety of the or- of asteroids Gaspra, Ida and Dactyl, Mathilde, and Eros to bital environment about asteroids for rendezvous missions, supplement earlier images of the martian moons. Radar and landed operations on asteroid surfaces, and other close- telescopic observations have revealed the shapes and rota- proximity operations. A key issue of concern for any surface tion states of many more objects. Morphological indications operation on an asteroid, such as sampling, will be the trajec- of regolith on these asteroids include blocks, landslides, tories of ejecta disturbed and lofted into orbit during rou- buried craters, and color variations. Observational tests of tine operations, as disturbed regolith may reimpact on the dynamical theories include nonuniform regolith, ejecta block surface with speeds on the order of the surface escape speed distributions and asymmetric crater ejecta blankets, rays, long after being dislodged (Scheeres and Asphaug, 1998). 527 528 Asteroids III The study of asteroid ejecta is intimately tied to the study of binary asteroid systems relative to the solar tide, jovian of impacts on asteroids [see the reviews by Asphaug et al. perturbations, and collisions in a series of papers, based on (2002) and Holsapple et al. (2002)], transient and long-term the earlier studies of the dynamics of the “Hill problem” orbital dynamics close to asteroids, and the study of natu- (Hénon, 1969). Hamilton and Burns (1991a,b) investigated ral and artificial asteroid satellites (Merline et al., 2002). the limits of stable motion about an asteroid, with a spe- Additionally, the dynamics of asteroid ejecta have many cial interest given to the safety of the planned Galileo flybys similarities to the dynamics of cometary ejecta. In general, of asteroids Gaspra and Ida. These papers, taken together, methods devised for the study of each area will have ap- provide a clear picture of the stability of asteroid binaries, plication to both areas. and place constraints on the stability of asteroid ejecta that Out of necessity, this chapter brings together several di- move relatively far from the asteroid. Such studies are still verse areas of asteroid and dynamical science. Ideally, this continuing, and additional progress in understanding the dy- chapter will serve as a starting point for future investiga- namics of trajectories far from an asteroid have been made tions into the dynamics of ejecta from the surfaces of small (Richter and Keller, 1995; Hamilton and Krivov, 1997). bodies. As such, we have injected many topics into the Chauvineau et al. (1993) and Scheeres (1994) initiated chapter, in some instances without detailed descriptions of the study of dynamics in the near-asteroid environment, the background theory or its development. Thus, to supple- studying the motion of particles and ejecta close to rotating ment the work described herein, we suggest that the follow- ellipsoids. These early studies showed that the near-asteroid ing textbooks be referenced: Melosh (1989) for an intro- orbital environment was fundamentally different from the duction to the basic principles and physics of impacts, environment found in the vicinity of a planet or larger satel- Murray and Dermott (1999) for an introduction to the or- lite. Studies along these lines have continued with the de- bital dynamics of natural bodies, and Szebehely (1967) for tailed analysis of specific asteroid shapes (Geissler et al., an introduction to advanced orbital dynamics theory. 1996; Petit et al., 1997; Scheeres et al., 1996, 1998a, 2000a) and the theoretical analysis of motion in generalized models 2. A BRIEF HISTORY of asteroid gravity fields (Scheeres, 1999). Now this area of study has its first precision set of data with the results of the The study of asteroid ejecta has been considered in the NEAR Shoemaker mission to asteroid 433 Eros (Yeomans books Asteroids and Asteroids II, distributed among chap- et al., 2000; Miller et al., 2001), the fruits of which are already ters on asteroid regoliths (Cintala et al., 1979; Housen et al., being published (Thomas et al., 2001, Robinson et al., 2001). 1979b; Veverka and Thomas, 1979; McKay et al., 1989) and asteroid satellites (van Flandern et al., 1979; Weidenschil- 3. EJECTA GENERATION ling et al., 1989). Yet the study of ejecta and satellite dy- namics about asteroids was only fully validated with the The study of asteroid regolith mechanics and the dynam- discovery of Dactyl in orbit about Ida (Belton et al., 1996). ics of impact ejecta fields must first concern itself with the In recent years the relevance of this topic has continued to mechanics of impact ejecta generation. Weidenschilling et grow, with the rapid rate at which asteroid satellites have al. (1989) noted that there are tight constraints on ejecta been discovered (see the chapter by Merline et al., 2002) speed before all ejecta immediately escape from the asteroid and recent realizations from the NEAR Shoemaker mission and into heliocentric space. Indeed, early estimates on rego- that the small-scale structure of asteroid surfaces are not lith depth (or lack thereof) on smaller asteroids predicted well understood (Veverka et al., 2001; Cheng et al., 2001). little, if any, retained regolith. This view of asteroid surfaces Initial studies of asteroid ejecta, and orbital dynamics has changed with recent observations of asteroids from space- about asteroids, assumed that their dynamical environment craft and radar. In the following we review some basic re- was analogous to, and directly scalable from, planetary sat- sults on the ejecta fields resulting from impact events, with ellite dynamics (van Flandern et al., 1979; Weidenschilling an emphasis on the implications of these models for the ini- et al., 1989). However, Weidenschilling et al. (1989) already tial conditions