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We have used an improved model of the orbit and absolute magnitude distribution of Near Earth Objects (NEOs) to simulate the performance of asteroid surveys. Our results support general conclusions of previous studies using preliminary Near Earth Asteroid (NEA) orbit and magnitude distributions and suggest that meeting the Spaceguard Goal of 90% completion for Near Earth Objects (NEOs) greater than 1 km diameter by 2008 is impossible given contemporary surveying capabilities. The NEO model was derived from NEO detections by the Spacewatch Project. For this paper we developed a simulator for the Catalina Sky Survey (CSS) for which we had a complete pointing history and NEO detection efficiency. The good match between the output of the simulator and the actual CSS performance gives confidence that both the NEO model and simulator are correct. Then, in order to determine if existing surveys can meet the Spaceguard Goal, we developed a simulator to mimic the LINEAR survey, for which detailed performance characteristics were unavailable. This simulator serendipitously provided an estimate for the currently undiscovered population of NEOs upon which we base all our estimates of time to 90% completion. We also developed a set of idealized NEO surveys in order to constrain the best possible survey performance in contrast to more realistic systems. A 100% efficient, all-sky, every night survey, subject only to the constraints of detection above a specified air mass and when the Sun is 18[degrees] below the horizon provides a benchmark from which to examine the effect of imposing more restrictions and the efficacy of some simple survey strategies. Such a survey must have a limiting V-magnitude of 20.1 [+ or -] 0.2 to meet the Spaceguard Goal. More realistic surveys, limited by latitude, the galaxy, minimum rates of NEO motion, etc., require fainter limiting magnitudes to reach the same completion. Our most realistic simulations, which have been normalized to the performance of the LINEAR detector system's operation in the period 1999-2000, indicate that it would take them another 33 [+ or -] 5 years to reach 90% completeness for the larger asteroids ([greater than or equal to] 1 km diameter). They would need to immediately increase the limiting magnitude to about 24 in order to meet the Spaceguard Goal. The simulations suggest that there may be little need for distributing survey telescopes in longitude and latitude as long as there is sufficient sky coverage from a telescope or network of telescopes which may be geographically close. An idealized space-based survey, especially from a satellite orbit much interior to Earth, would offer an advantage over their terrestrial counterparts. We do not consider a cost-benefit analysis for any of the simulations but suspect that a local-area network of telescopes capable of covering much of the sky in a month to V ~ 21.5 may be administratively, financially, and scientifically the best compromise tot reaching 90% completion of NEOs larger than 1 km diameter. Keyword: Asteroids

The orbital and absolute magnitude distribution of the near-Earth objects (NEOs) is difficult to compute, partly because only a modest fraction of the entire NEO population has been discovered so far, but also because the known NEOs are biased by complicated observational selection effects. To circumvent these problems, we created a model NEO population which was fit to known NEOs discovered or accidentally rediscovered by Spacewatch. Our method was to numerically integrate thousands of test particles from five source regions that we believe provide most NEOs to the inner Solar System. Four of these source regions are in or adjacent to the main asteroid belt, while the fifth one is associated with the transneptunian disk. The nearly isotropic comets, which include the Halley-type comets and the long-period comets, were not included in our model. Test bodies from our source regions that passed into the NEO region (perihelia q < 1.3 AU and aphelia Q [greater than or equal to] 0.983 AU) were tracked until they were eliminated by striking the Sun or a planet or were ejected out of the inner Solar System. These integrations were used to create five residence time probability distributions in semimajor axis, eccentricity, and inclination space (one for each source). These distributions show where NEOs from a given source are statistically most likely to be located. Combining these five residence time probability distributions with an NEO absolute magnitude distribution computed from previous work and a probability function representing the observational biases associated with the Spacewatch NEO survey, we produced an NEO model population that could be fit to 138 NEOs discovered or accidentally rediscovered by Spacewatch. By testing a range of possible source combinations, a best-fit NEO model was computed which (i) provided the debiased orbital and absolute magnitude distributions for the NEO population and (ii) indicated the relative importance of each NEO source region. Our best-fit model is consistent with 960 [+ or -] 120 NEOs having H < 18 and a < 7.4 AU. Approximately 44% (as of December 2000) have been found so far. The limits on this estimate are conditional, since our model does not include nearly isotropic comets. Nearly isotropic comets are generally restricted to a Tisserand parameter (with respect to Jupiter) of T < 2, such that few are believed to have a < 7.4 AU. Our computed NEO orbital distribution, which is valid for bodies as faint as H < 22, indicates that the Amor, Apollo, and Aten populations contain 32 [+ or -] 1%, 62 [+ or -] 1%, and 6 [+ or -] 1% of the NEO population, respectively. We estimate that the population of objects completely inside Earth's orbit (IEOs) arising from our source regions is 2% the size of the NEO population. This value does not include the putative Vulcanoid population located inside Mercury's orbit. Overall, our model predicts that ~61% of the NEO population comes from the inner main belt (a < 2.5 AU), ~24% comes from the central main belt (2.5 < a < 2.8 AU), ~8% comes from the outer main belt (a > 2.8 AU), and ~6% comes from the Jupiter-family comet region (2 < T >[??] 3). The steady-state population in each NEO source region, as well as the influx rates needed to replenish each region, were calculated as a by-product of our method. The population of extinct comets in the Jupiter-family comet region was also computed. Key Words: asteroids; asteroid dynamics; orbits.

In this paper, we use N-body integrations to study the effect that planetary embryos spread between ~0.5 and 4 AU would have on primordial asteroids. The most promising model for the formation of the terrestrial planets assumes the presence of such embryos at the time of formation of Jupiter. At the end of their runaway growth phase, the embryos are on quasi-circular orbits, with masses comparable to that of the Moon or Mars. Due to gravitational interactions among them, and with the growing Jupiter, their orbits begin to cross each other, and they collide, forming bigger bodies. A general outcome of this model is that a few planets form in a stable configuration in the terrestrial planet region, while the asteroid belt is cleared of embryos. Due to combined gravitational perturbations from Jupiter and the embryos, the primordial asteroids are dynamically excited. Most of the asteroids are ejected from the system in a very short time, the dynamical lifetime being on the order of 1 My. A few asteroids (less than 1%) survive, mostly in the region 2.8-3.3 AU, and their eccentricity and inclination distribution qualitatively resembles the observed one. The surviving asteroids have undergone changes in semimajor axis of several tenths of an AU, which could explain the observed radial mixing of asteroid taxonomic types. When the distribution of massive embryos is truncated at 3 AU, we obtain too many asteroids in the outer part of the belt, especially too many Hildas. This suggests that the formation of Jupiter did not prohibit the formation of large embryos in the outer belt and Jupiter did not accrete them while it was still growing. Key Words: asteroids, origin; Solar System, planetary embryos.

We study the dynamical excitation that large planetesimals, scattered either by Neptune or Jupiter, could have provided to the primordial Edgeworth-Kuiper belt and the asteroid belt. Using both a refined Monte Carlo approach and direct numerical integration, we show that the Monte Carlo method is useful only to give qualitative insight into the resulting excitation, but cannot be trusted from a quantitative viewpoint. According to our direct integrations, Neptune-scattered planetesimals of mass from a few tenths to one Earth mass could have ejected most of the bodies from the primordial Edgeworth-Kuiper belt, thus explaining the large mass deficiency of the present belt up to about 50 AU. The remaining bodies are left on orbits with eccentricity and inclination comparable to those observed. This dynamical excitation is not restricted to the inner part of the belt but may extend to 100 AU. We also show that Pluto has too small a mass to destabilize the motion of other bodies in the 2:3 mean motion resonance with Neptune. The same mechanism involving Jupiter-scattered planetesimals of about one Earth mass can excite the outer asteroid belt, hence depleting it of most of its primordial mass. However, this fails to excite the inner belt. In the case where the planetesimals are isolated by mutual gravitational perturbations on long-lived main-belt-like orbits, safe from encounters with Jupiter, the resulting asteroid belt is very similar to the currently observed one, in terms of mass deficiency, excitation in eccentricity and inclination, and radial mixing. Pallas-like bodies are also obtained. However, the decoupling of planetesimals from Jupiter on well-behaved orbits is rather improbable (2% of our simulations), and the resulting asteroid belt is very critically dependent on the mass of the scattered planetesimals and their residence time in the belt. Key Words: asteroids; Kuiper belt objects; origin, solar system; planetesimals.

The existence of Dactyl, the small satellite of asteroid 243 Ida, presents an intriguing paradox: if exposed to the same projectile bombardment as Ida, it should have been disrupted long ago. To solve this paradox, it has been proposed that either Ida (and the entire Koronis family) is relatively young ([approximately equal to] 100 Myr) or Dactyl has reaccreted many times from its own debris after having been disrupted. Here we propose a third alternative, that is that Dactyl is much younger than Ida and it was formed by rotational bursting of a precursor fragment ejected from Ida after an impact. We discuss some recent experimental results showing that sizable fragments from shattered targets do undergo rotational bursting and are fissioned after traveling over a length of several target diameters; the relative speed between the fission remnants is comparable to the initial ejection velocity. Then we have performed a number of numerical integrations of the orbits of fictitious particles resulting from an assumed rotational bursting event in the gravitational field of Ida; the results show that, depending on the initial conditions, up to several percent of the particles get trapped into stable satellite-like orbits resembling that of Dactyl. We conclude that this mechanism may have formed Dactyl in the last [approximately equal to]10% of Ida's lifetime, either after an energetic cratering impact or (more probably) after a collision which shattered Ida without dispersing most of its fragments 'to infinity.'

Dactyl was discovered in solid state imaging (SSI) data on February 17,1994, during the long playback of approach images from the Galileo spacecraft's encounter with the asteroid 243 Ida. Forty-seven images of the Ida-Dactyl pair were obtained. A detailed search for other satellites was made. No confirmed detections were made, all other candidate features being consistent with radiation hits. We deduce a manifold of osculating two-body orbits that approximate Dactyl's motion over the observed orbital arc depending on the assumed mass of Ida. At the time of Galileo's encounter, Dactyl was found to be 85 km from the center of Ida, moving at [approximately]6 m [center dot] [sec.sup.-1] in the same direction as Ida's retrograde spin. The inclination of its orbit is [approximately]172 [degrees] in Ida's equatorial system (IAU definition). It was not possible to obtain a definitive orbit or measure of Ida's mass from the observed motion even though supplemental techniques (search for Dactyl's shadow on Ida, changes in angular diameter and brightness, and attempts to determine the spin of Dactyl) were explored. The influence of Ida's irregular gravitational field and solar perturbations on two-body motion are evaluated and found to be undetectable in the observed orbital arc. These effects may, however, strongly influence the motion over orbital time scales. Limits to the value of Ida's gravitation parameter, GM, are derived. A robust lower limit, GM > 0.0023 [km.sup.3] [center dot] [sec.sup.-2], is obtained by requiring Dactyl's orbit to be bound. Hubble Space Telescope observations, which show no evidence of Dactyl on a hyperbolic orbit, excludes values of GM in the range 0.00216 < GM < 0.0023 [km.sup.3] [center dot] [sec.sup.-2]. An upper limit, GM < 0.0031 [km.sup.3] [center dot] [sec.sup.-2], deduced by requiring that the orbital motion has a long lifetime in a realistic approximation to Ida's gravitational field, is illustrated with numerical calculations. Ida's mass is therefore constrained to the range 4.2 [+ or -] 0.6 x [10.sup.19] g, which, together with a volume of 16,100 [+ or -] 1900 [km.sup.3] (Thomas P. C., M. J. S. Belton, B. Carcich, C. R. Chapman, M. E. Davies, R. Sullivan, and J. Veverka 1996. Icarus 120, 20-32.) yields a bulk density of 2.6 [+ or -] 0.5 g [center dot] [cm.sup.-3] (Belton, M. J. S., C. R. Chapman, P. C. Thomas, M. E. Davies, R. Greenberg, K. Klaasen, D. Byrnes, L. D'Amario, S. Synnott, T. V. Johnson, A. McEwen, W. Merline, D. R. Davis, J-M. Petit, A. Storrs, J. Veverka, and B. Zellner 1995. Nature 374, 785-788.).

Galileo images of Asteroid 243 Ida and its satellite Dactyl show surfaces which are dominantly shaped by impact cratering. A number of observations suggest that ejecta from hypervelocity impacts on Ida can be distributed far and wide across the Ida system, following trajectories substantially affected by the low gravity, nonspherical shape, and rapid rotation of the asteroid. We explore the processes of reaccretion and escape of ejecta on Ida and Dactyl using three-dimensional numerical simulations which allow us to compare the theoretical effects of orbital dynamics with observations of surface morphology. The effects of rotation, launch location, and initial launch speed are first examined for the case of an ideal triaxial ellipsoid with Ida's approximate shape and density. Ejecta launched at low speeds (V [much greater than] [V.sub.esc]) reimpact near the source craters, forming well-defined ejecta blankets which are asymmetric in morphology between leading and trailing rotational surfaces. The net effect of cratering at low ejecta launch velocities is to produce a thick regolith which is evenly distributed across the surface of the asteroid. In contrast, no clearly defined ejecta blankets are formed when ejecta is launched at higher initial velocities (V [similar to] [V.sub.esc]). Most of the ejecta escapes, while that which is retained is preferentially derived from the rotational trailing surfaces. These particles spend a significant time in temporary orbit around the asteroid, in comparison to the asteroid's rotation period, and tend to be swept up onto rotational leading surfaces upon reimpact. The net effect of impact cratering with high ejecta launch velocities is to produce a thinner and less uniform soil cover, with concentrations on the asteroids' rotational leading surfaces. Using a realistic model for the shape of Ida (P. Thomas, J. Veverka, B. Carcich, M. J. S. Belton, R. Sullivan, and M. Davies 1996, Icarus 120, 000-000), we find that an extensive color/albedo unit which dominates the northern and western hemispheres of the asteroid can be explained as the result of reaccretion of impact ejecta from the large and evidently recent crater 'Azzurra.' Initial ejection speeds required to match the color observations are on the order of a few meters per second, consistent with models (e.g., M. C. Nolan, E. Asphaug, H. J. Melosh, and R. Greenberg 1996, Icarus, submitted; E. Asphaug, J. Moore, D. Morrison, W. Benz, and R. Sullivan 1996, Icarus 120, 158-184) that multikilometer craters on Ida form in the gravity-dominated regime and are net producers of locally retained regolith. Azzurra ejecta launched in the direction of rotation at speeds near 10 m/sec are lofted over the asteroid and swept up onto the rotational leading surface on the opposite side. The landing locations of these particles closely match the distribution of large ejecta blocks observed in high resolution images of Ida (P. Lee, J. Veverka, P. Thomas, P. Helfstein, M. J. S. Belton, C. Chapman, R. Greeley, R. Pappalardo, R. Sullivan, and J. W. Head 1996, Icarus 120, 87-105). Ida's shape and rotation allow escape of ejecta launched at speeds far below the escape velocity of a nonrotating sphere of Ida's volume and presumed density. While little ejecta from Ida is captured by Dactyl, about half of the mass ejected from Dactyl at speeds of up to 20 m/sec eventually falls on Ida. Particles launched at speeds just barely exceeding Dactyl's escape velocity can enter relatively long-term orbit around Ida, but few are ultimately reaccreted by the satellite. Because of its low gravity, erosion of Dactyl would take place on exceedingly short time scales if unconsolidated materials compose the satellite and crater formation is in the gravity regime. If Dactyl is a solid rock, then its shape has evolved from a presumably irregular initial fragment to its present remarkably rounded figure by collision with a population of impactors too small to be detected by counting visible craters. As the smallest solar system object yet imaged by a spacecraft, the morphology of Dactyl is an important clue to the asteroid population at the smallest sizes.

The history of Ida is constrained by its membership in the Koronis family, its satellite Dactyl, the record of impacts left on its surface, and other dynamical, morphological, and spectral properties. Models of crater production and comparably effective erasure processes, combined with the current size-frequency distribution of craters, suggest that the age of the surface is either about 50 myr or >1 byr. The younger age may be inconsistent with the degraded appearance of many craters, while the older age conflicts with the collisional life expectancy of Dactyl. Consideration of Dactyl's evolution may resolve this issue as well as shed light on the formation of Dactyl, the density of Ida, and possible source regions for Ida and Dactyl within the Koronis parent body.