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This work is dedicated to debias the Near-Earth Objects (NEO) population based on observations from the Asteroid Terrestrial-impact Last Alert System (ATLAS) telescopes. We have applied similar methods used to develop the recently released NEO model generator (NEOMOD), once debiasing the NEO population using data from Catalina Sky Survey (CSS) G96 telescope. ATLAS is composed of four different telescopes. We first analyzed observational data from each of all four telescopes separately and later combined them. Our results highlight main differences between CSS and ATLAS, e.g., sky coverage and survey power at debiasing the NEO population. ATLAS has a much larger sky coverage than CSS, allowing it to find bright NEOs that would be constantly "hiding" from CSS. Consequently, ATLAS is more powerful than CSS at debiasing the NEO population for H $\lesssim$ 19. With its intrinsically greater sensitivity and emphasis on observing near opposition, CSS excels in the debiasing of smaller objects. ATLAS, as an all sky survey designed to find imminent hazardous objects, necessarily spends a significant fraction of time looking at places on the sky where objects do not appear, reducing its power for debiasing the population of small objects. We estimate a NEO population completeness of $\approx$ 88%$^{+3\%}_{-2\%}$ for H $<$ 17.75 and $\approx$ 36%$^{+1\%}_{-1\%}$ for H $<$ 22.25. Those numbers are similar to previous estimates (within error bars for H $<$ 17.75) from CSS, yet, around 3% and 8% smaller at their face values, respectively. We also confirm previous finding that the $\nu_6$ secular resonance is the main source of small and faint NEOs at H = 28, whereas the 3:1 mean motion resonance with Jupiter dominates for larger and brighter NEOs at H = 15., Comment: Accepted for publication in Icarus, 26 pages, 13 figures, 2 tables

Our previous model (NEOMOD2) for the orbital and absolute magnitude distribution of Near Earth Objects (NEOs) was calibrated on the Catalina Sky Survey observations between 2013 and 2022. Here we extend NEOMOD2 to include visible albedo information from the Wide-Field Infrared Survey Explorer. The debiased albedo distribution of NEOs can be approximated by the sum of two Rayleigh distributions with the scale parameters p_V,dark=0.03 and p_V,bright=0.17. We find evidence for smaller NEOs having (on average) higher albedos than larger NEOs; this is likely a consequence of the size-dependent sampling of different main belt sources. These inferences and the absolute magnitude distribution from NEOMOD2 are used to construct the debiased size distribution of NEOs. We estimate 830+/-60 NEOs with diameters D>1 km and 20,000+/-2,000 NEOs with D>140 m. The new model, NEOMOD3, is available via the NEOMOD Simulator -- an easy-to-operate code that can be used to generate user-defined samples (orbits, sizes and albedos) from the model., Comment: Icarus, in press

Catalina Sky Survey (CSS) is a major survey of Near-Earth Objects (NEOs). In a recent work, we used CSS observations from 2005-2012 to develop a new population model of NEOs (NEOMOD). CSS's G96 telescope was upgraded in 2016 and detected over 10,000 unique NEOs since then. Here we characterize the NEO detection efficiency of G96 and use G96's NEO detections from 2013-2022 to update NEOMOD. This resolves previous model inconsistencies related to the population of large NEOs. We estimate there are 936+/-29 NEOs with absolute magnitude H<17.75 (diameter D>1 km for the reference albedo p_V=0.14). The slope of the NEO size distribution for H=25-28 is found to be relatively shallow (cumulative index 2.6) and the number of H<28 NEOs (D>9 m) is determined to be (1.20+/-0.04)x10^7. Small NEOs have a different orbital distribution and higher impact probabilities than large NEOs. We estimate 0.034+/-0.002 impacts of H<28 NEOs on the Earth per year, which is near the low end of the impact flux range inferred from atmospheric bolide observations. Relative to a model where all NEOs are delivered directly from the main belt, the population of small NEOs detected by G96 shows an excess of low-eccentricity orbits with a=1--1.6 au that appears to increase with H. We suggest that the population of very small NEOs is boosted by tidal disruption of large NEOs during close encounters to the terrestrial planets. When the effect of tidal disruption is (approximately) accounted for in the model, we estimate 0.06+/-0.01 impacts of H<28 NEOs on the Earth per year, which is more in line with the bolide data., Comment: Icarus, in press. arXiv admin note: text overlap with arXiv:2306.09521

Near Earth Objects (NEOs) are a transient population of small bodies with orbits near or in the terrestrial planet region. They represent a mid-stage in the dynamical cycle of asteroids and comets, which starts with their removal from the respective source regions -- the main belt and trans-Neptunian scattered disk -- and ends as bodies impact planets, disintegrate near the Sun, or are ejected from the Solar System. Here we develop a new orbital model of NEOs by numerically integrating asteroid orbits from main belt sources and calibrating the results on observations of the Catalina Sky Survey. The results imply a size-dependent sampling of the main belt with the $\nu_6$ and 3:1 resonances producing $\simeq 30$\% of NEOs with absolute magnitudes $H = 15$ and $\simeq 80$\% of NEOs with $H = 25$. Hence, the large and small NEOs have different orbital distributions. The inferred flux of $H<18$ bodies into the 3:1 resonance can be sustained only if the main-belt asteroids near the resonance drift toward the resonance at the maximal Yarkovsky rate ($\simeq 2 \times 10^{-4}$ au Myr$^{-1}$ for diameter $D=1$ km and semimajor axis $a=2.5$~au). This implies obliquities $\theta \simeq 0^\circ$ for $a<2.5$~au and $\theta \simeq 180^\circ$ for $a>2.5$~au, both in the immediate neighborhood of the resonance (the same applies to other resonances as well). We confirm the size-dependent disruption of asteroids near the Sun found in previous studies. An interested researcher can use the publicly available NEOMOD Simulator to generate user-defined samples of NEOs from our model., Comment: AJ

The June 2, 2018, impact of asteroid 2018 LA over Botswana is only the second asteroid detected in space prior to impacting over land. Here, we report on the successful recovery of meteorites. Additional astrometric data refine the approach orbit and define the spin period and shape of the asteroid. Video observations of the fireball constrain the asteroid's position in its orbit and were used to triangulate the location of the fireball's main flare over the Central Kalahari Game Reserve. 23 meteorites were recovered. A consortium study of eight of these classifies Motopi Pan as a HED polymict breccia derived from howardite, cumulate and basaltic eucrite, and diogenite lithologies. Before impact, 2018 LA was a solid rock of about 156 cm diameter with high bulk density about 2.85 g/cm3, a relatively low albedo pV about 0.25, no significant opposition effect on the asteroid brightness, and an impact kinetic energy of about 0.2 kt. The orbit of 2018 LA is consistent with an origin at Vesta (or its Vestoids) and delivery into an Earth-impacting orbit via the nu_6 resonance. The impact that ejected 2018 LA in an orbit towards Earth occurred 22.8 +/- 3.8 Ma ago. Zircons record a concordant U-Pb age of 4563 +/- 11 Ma and a consistent 207Pb/206Pb age of 4563 +/- 6 Ma. A much younger Pb-Pb phosphate resetting age of 4234 +/- 41 Ma was found. From this impact chronology, we discuss what is the possible source crater of Motopi Pan and the age of Vesta's Veneneia impact basin., Comment: Meteoritics & Planetary Science (2021)

This paper reports the first OH 18-cm line observation of the first detected interstellar object 1I/2017 U1 (`Oumuamua) using the Green Bank Telescope. We have observed the OH lines at 1665.402 MHz, 1667.359, and 1720.53 MHz frequencies with a spectral resolution of 357 Hz (approximately 0.06 km-s^{-1}). At the time of the observation, `Oumuamua was at topocentric distance and velocity of 1.07 au and 63.4 km-s^{-1}, respectively, or at heliocentric distance and velocity of 1.8 au and 39 km-s^{-1}, respectively. Based on a detailed data reduction and an analogy-based inversion, our final results confirm the asteroidal origin of `Oumuamua (as discussed in Meech et al., 2017) with an upper bound of OH production of Q[OH] < 0.17 x 10^{28} s^{-1}., Comment: accepted for publication in Astronomical Journal, 7 pages, 1 figure, 1 table

Near-Earth asteroid 2014 AA entered the Earth's atmosphere on 2014 January 2, only 21 hours after being discovered by the Catalina Sky Survey. In this paper we compute the trajectory of 2014 AA by combining the available optical astrometry, seven ground-based observations over 69 minutes, and the International Monitoring system detection of the atmospheric impact infrasonic airwaves in a least-squares orbit estimation filter. The combination of these two sources of observations results in a tremendous improvement in the orbit uncertainties. The impact time is 3:05 UT with a 1-sigma uncertainty of 6 min, while the impact location corresponds to a west longitude of 44.7 deg and a latitude of 13.1 deg with a 1-sigma uncertainty of 140 km. The minimum impact energy estimated from the infrasound data and the impact velocity result in an estimated minimum mass of 22.6 t. By propagating the trajectory of 2014 AA backwards we find that the only window for finding precovery observations is for the three days before its discovery.

We report on observations of near-Earth asteroid 2011 MD with the Spitzer Space Telescope. We have spent 19.9 h of observing time with channel 2 (4.5 {\mu}m) of the Infrared Array Camera and detected the target within the 2{\sigma} positional uncertainty ellipse. Using an asteroid thermophysical model and a model of nongravitational forces acting upon the object we constrain the physical properties of 2011 MD, based on the measured flux density and available astrometry data. We estimate 2011 MD to be 6 (+4/-2) m in diameter with a geometric albedo of 0.3 (+0.4/-0.2) (uncertainties are 1{\sigma}). We find the asteroid's most probable bulk density to be 1.1 (+0.7/-0.5) g cm^{-3}, which implies a total mass of (50-350) t and a macroporosity of >=65%, assuming a material bulk density typical of non-primitive meteorite materials. A high degree of macroporosity suggests 2011 MD to be a rubble-pile asteroid, the rotation of which is more likely to be retrograde than prograde., Comment: 20 pages, 4 figures

Comet C/2013 A1 (siding Spring) will experience a high velocity encounter with Mars on October 19, 2014 at a distance of 135,000 km +- 5000 km from the planet center. We present a comprehensive analysis of the trajectory of both the comet nucleus and the dust tail. The nucleus of C/2013 A1 cannot impact on Mars even in the case of unexpectedly large nongravitational perturbations. Furthermore, we compute the required ejection velocities for the dust grains of the tail to reach Mars as a function of particle radius and density and heliocentric distance of the ejection. A comparison between our results and the most current modeling of the ejection velocities suggests that impacts are possible only for millimeter to centimeter size particles released more than 13 au from the Sun. However, this level of cometary activity that far from the Sun is considered extremely unlikely. The arrival time of these particles spans a 20-minute time interval centered at October 19, 2014 at 20:09 TDB, i.e., around the time that Mars crosses the orbital plane of C/2013 A1. Ejection velocities larger than currently estimated by a factor >2 would allow impacts for smaller particles ejected as close as 3 au from the Sun. These particles would reach Mars from 43 to 130 min after the nominal close approach epoch of the purely gravitational trajectory of the nucleus.

The target asteroid of the OSIRIS-REx asteroid sample return mission, (101955) Bennu (formerly 1999 RQ$_{36}$), is a half-kilometer near-Earth asteroid with an extraordinarily well constrained orbit. An extensive data set of optical astrometry from 1999--2013 and high-quality radar delay measurements to Bennu in 1999, 2005, and 2011 reveal the action of the Yarkovsky effect, with a mean semimajor axis drift rate $da/dt = (-19.0 \pm 0.1)\times 10^{-4}$ au/Myr or $284\pm 1.5\;\rm{m/yr}$. The accuracy of this result depends critically on the fidelity of the observational and dynamical model. As an example, neglecting the relativistic perturbations of the Earth during close approaches affects the orbit with $3\sigma$ significance in $da/dt$. The orbital deviations from purely gravitational dynamics allow us to deduce the acceleration of the Yarkovsky effect, while the known physical characterization of Bennu allows us to independently model the force due to thermal emissions. The combination of these two analyses yields a bulk density of $\rho = 1260\pm70\,\rm{kg/m^3}$, which indicates a macroporosity in the range $40\pm10$% for the bulk densities of likely analog meteorites, suggesting a rubble-pile internal structure. The associated mass estimate is $(7.8\pm0.9)\times 10^{10}\, \rm{kg}$ and $GM = 5.2\pm0.6\,\rm{m^3/s^2}$. Bennu's Earth close approaches are deterministic over the interval 1654--2135, beyond which the predictions are statistical in nature. In particular, the 2135 close approach is likely within the lunar distance and leads to strong scattering and therefore numerous potential impacts in subsequent years, from 2175--2196. The highest individual impact probability is $9.5\times 10^{-5}$ in 2196, and the cumulative impact probability is $3.7\times 10^{-4}$, leading to a cumulative Palermo Scale of -1.70.

We assess the risk of an Earth impact for asteroid (99942) Apophis by means of a statistical analysis accounting for the uncertainty of both the orbital solution and the Yarkovsky effect. We select those observations with either rigorous uncertainty information provided by the observer or a high established accuracy. For the Yarkovsky effect we perform a Monte Carlo simulation that fully accounts for the uncertainty in the physical characterization, especially for the unknown spin orientation. By mapping the uncertainty information onto the 2029 b-plane and identifying the keyholes corresponding to subsequent impacts we assess the impact risk for future encounters. In particular, we find an impact probability greater than 10^-6 for an impact in 2068. We analyze the stability of the impact probability with respect to the assumptions on Apophis' physical characterization and consider the possible effect of the early 2013 radar apparition.

We describe the physical and orbital properties of C/2011 W3. After surviving perihelion, the comet underwent major changes (permanent loss of nuclear condensation, formation of spine tail). The process of disintegration culminated with an outburst on December 17.6 (T+1.6 d) and this delayed response is inconsistent with the rubble pile model. Probable cause was thermal stress from the heat pulse into the nucleus after perihelion, which could also produce fragmentation of sungrazers far from the Sun. The spine tail was a synchronic feature, made up of dust released at <30 m/s. Since the nucleus would have been located on the synchrone, we computed the astrometric positions of the missing nucleus as the coordinates of the points of intersection of the spine tail's axis with lines of forced orbital-period variation, derived from orbital solutions based on preperihelion astrometry from the ground. The resulting osculating orbital period was 698+/-2 years, which proves that C/2011 W3 is the first major member of the predicted new, 21st-century cluster of bright Kreutz-system sungrazers. The spine tail's tip contained dust 1-2 mm in diameter. The bizarre appearance of the dust tail in images taken hours after perihelion with coronagraphs on SOHO and STEREO is readily understood. The disconnection of the comet's head from the preperihelion tail and the apparent activity attenuation near perihelion are both caused by sublimation of all dust at heliocentric distances smaller than ~1.8 solar radii. The tail's brightness is strongly affected by forward scattering of sunlight by dust. The longest-imaged grains had a radiation-pressure parameter beta ~ 0.6, probably submicron-sized silicate grains. The place of C/2011 W3 within the hierarchy of the Kreutz system and its genealogy via a 14th century parent suggest that it is indirectly related to the celebrated sungrazer X/1106 C1., Comment: Submitted to Astrophysical Journal; 35 pages, 18 figures, 8 tables

The Asteroid Threat Assessment Project (ATAP), a part of NASAs Planetary Defense Coordination Office (PDCO) has the responsibility to appraise the range of surface damage by potential asteroid impacts on land or water. If a threat is realized, the project will provide appraisals to officials empowered to make decisions on potential mitigation actions. This paper describes a scenario for assessment of surface damage when characterization of an asteroid had been accomplished by a rendezvous mission that would be conducted by the international planetary defense community. It is shown that the combination of data from ground and in-situ measurements on an asteroid provides knowledge that can be used to pin-point its impact location and predict the level of devastation it would cause. The hypothetical asteroid 2017 PDC with a size of 160 to 290 m in diameter to be discussed at the PDC 2017 meeting is used as an example. In order of importance for appraising potential damage, information required is: (1) where will the surface impact occur? (2) What is the mass, shape and size of the asteroid and what is its entry state (speed and entry angle) at the 100 km atmospheric pierce point? And (3) is the asteroid a monolith or a rubble pile? If it is a rubble pile, what is its sub and interior structure? Item (1) is of first order importance to determine levels of devastation (loss of life and infrastructure damage) because it varies strongly on the impact location. Items (2) and (3) are used as input for ATAPs simulations to define the level of surface hazards: winds, overpressure, thermal exposure; all created by the deposition of energy during the objects atmospheric flight, andor cratering. Topics presented in this paper include: (i) The devastation predicted by 2017 PDCs impact based on initial observations using ATAPs risk assessment capability, (ii) How information corresponding to items (1) to (3) could be obtained from a rendezvous mission, and (iii) How information from a rendezvous mission could be used, along with that from ground observations and data from the literature, could provide input for an new risk analysis capability that is emerging from ATAPs research. It is concluded that this approach would result in appraisal with the least uncertainty possible (herein called the best-case) using simulation capabilities that are currently available or will be in the future.

Mission Description and Objectives: NASA's Asteroid Redirect Mission (ARM) consists of two mission segments: 1) the Asteroid Redirect Robotic Mission (ARRM), a robotic mission to visit a large (greater than approximately 100 meters diameter) near-Earth asteroid (NEA), collect a multi-ton boulder from its surface along with regolith samples, and return the asteroidal material to a stable orbit around the Moon; and 2) the Asteroid Redirect Crewed Mission (ARCM), in which astronauts will explore and investigate the boulder and return to Earth with samples. The ARRM is currently planned to launch at the end of 2021 and the ARCM is scheduled for late 2026.

The National Aeronautics and Space Administration (NASA) is developing the Asteroid Redirect Mission (ARM) as a capability demonstration for future human exploration, including use of high-power solar electric propulsion, which allows for the efficient movement of large masses through deep space. The ARM will also demonstrate the capability to conduct proximity operations with natural space objects and crewed operations beyond the security of quick Earth return. The Asteroid Redirect Robotic Mission (ARRM), currently in formulation, will visit a large near-Earth asteroid (NEA), collect a multi-ton boulder from its surface, conduct a demonstration of a slow push planetary defense technique, and redirect the multi-ton boulder into a stable orbit around the Moon. Once returned to cislunar space in the mid-2020s, astronauts aboard an Orion spacecraft will dock with the robotic vehicle to explore the boulder and return samples to Earth. The ARM is part of NASA's plan to advance technologies, capabilities, and spaceflight experience needed for a human mission to the Martian system in the 2030s. The ARM and subsequent availability of the asteroidal material in cis-lunar space, provide significant opportunities to advance our knowledge of small bodies in the synergistic areas of science, planetary defense, and in-situ resource utilization (ISRU). NASA established the Formulation Assessment and Support Team (FAST), comprised of scientists, engineers, and technologists, which supported ARRM mission requirements formulation, answered specific questions concerning potential target asteroid physical properties, and produced a publically available report. The ARM Investigation Team is being organized to support ARM implementation and execution. NASA is also open to collaboration with its international partners and welcomes further discussions. An overview of the ARM robotic and crewed segments, including mission requirements, NEA targets, and mission operations, and a discussion of potential opportunities for participation with the ARM will be provided.

The National Aeronautics and Space Administration (NASA) is developing the Asteroid Redirect Mission (ARM) as a capability demonstration for future human exploration, including use of high-power solar electric propulsion, which allows for the efficient movement of large masses through deep space. The ARM will also demonstrate the capability to conduct proximity operations with natural space objects and crewed operations beyond the security of quick Earth return. The Asteroid Redirect Robotic Mission (ARRM), currently in formulation, will visit a large near-Earth asteroid (NEA), collect a multi-ton boulder from its surface, conduct a demonstration of a slow push planetary defense technique, and redirect the multi-ton boulder into a stable orbit around the Moon. Once returned to cislunar space in the mid-2020s, astronauts aboard an Orion spacecraft will dock with the robotic vehicle to explore the boulder and return samples to Earth. The ARM is part of NASA's plan to advance technologies, capabilities, and spaceflight experience needed for a human mission to the Martian system in the 2030s. The ARM and subsequent availability of the asteroidal material in cis-lunar space, provide significant opportunities to advance our knowledge of small bodies in the synergistic areas of science, planetary defense, and in-situ resource utilization (ISRU). The current reference target for the ARM is NEA (341843) 2008 EV5, which may have been the primary body of a former binary system (Busch et al., 2011; Tardivel et al., 2016). The ARRM will perform several close proximity operations to investigate the NEA and map its surface. A detailed investigation of this object may allow a better understanding of binary NEA physical characteristics and the possible outcomes for their evolution. An overview of the ARM robotic and crewed segments, including mission operations, and a discussion of potential opportunities for participation with the ARM will be provided in this presentation.

To achieve its long-term goal of sending humans to Mars, the National Aeronautics and Space Administration (NASA) plans to proceed in a series of incrementally more complex human spaceflight missions. Today, human flight experience extends only to Low-Earth Orbit (LEO), and should problems arise during a mission, the crew can return to Earth in a matter of minutes to hours. The next logical step for human spaceflight is to gain flight experience in the vicinity of the Moon. These cis-lunar missions provide a "proving ground" for the testing of systems and operations while still accommodating an emergency return path to the Earth that would last only several days. Cis-lunar mission experience will be essential for more ambitious human missions beyond the Earth- Moon system, which will require weeks, months, or even years of transit time.

The population of near-Earth asteroids (NEAs) that may be accessible for human space flight missions is defined by the Near-Earth Object Human Space Flight Accessible Targets Study (NHATS). The NHATS is an automated system designed to monitor the accessibility of, and particular mission opportunities offered by, the NEA population. This is analogous to systems that automatically monitor the impact risk posed to Earth by the NEA population. The NHATS system identifies NEAs that are potentially accessible for future round-trip human space flight missions and provides rapid notification to asteroid observers so that crucial follow-up observations can be obtained following discovery of accessible NEAs. The NHATS was developed in 2010 and was automated by early 2012. NHATS data are provided via an interactive web-site, and daily NHATS notification emails are transmitted to a mailing list; both resources are available to the public.

Over the past several years, much attention has been focused on the human exploration of near-Earth asteroids (NEAs). Two independent NASA studies examined the feasibility of sending piloted missions to NEAs [1, 2], and in 2009, the Augustine Commission identified NEAs as high profile destinations for human exploration missions beyond the Earth-Moon system [3]. More recently the current U.S. presidential administration directed NASA to include NEAs as destinations for future human exploration with the goal of sending astronauts to a NEA in the mid to late 2020s. This directive became part of the official National Space Policy of the United States of America as of June 28, 2010 [4]. Detailed planning for such deep space exploration missions and identifying potential NEAs as targets for human spaceflight requires selecting objects from the ever growing list of newly discovered NEAs. Hence NASA developed and implemented the Near-Earth Object (NEO) Human Space Flight (HSF) Accessible Target Study (NHATS), which identifies potential candidate objects on the basis of defined dynamical trajectory performance constraints.

Newly found asteroid 2003 YN107 is the first and only known current quasi-satellite (QS) of the Earth. Asteroid 2002 AA29 is in a horseshoe orbit (HS) but has periods of QS behavior. Both asteroids closely follow Earth s orbit. 2002 AA29 has inclination i is approximately 11 degrees while for 2003 YN107 i<5 degrees, making the most Earth-like orbit known. 2003 YN107, 2002 AA29, and other Earth-resonant objects in less Earthlike orbits, form an important new class of co-orbital bodies with interesting dynamics and are the best targets for sample return missions to asteroids.

Automated detection of potentially hazardous near-earth object encounters will be described.

We report initial results of daily delay/Doppler observations of Toutatis with the Goldstone 8510-MHz (3.5-cm) radar during November 25 - December 3, 1996. Using the physical model of Toutatis derived form 1992 radar observations (Hudson and Ostro 1995, Science 270, 84-86) to analyze the new data, we obtain refined estimates of the asteroid's orbit, spin state, and surface properties.

Comprehensive analysis of discrete events of secondary fragmentation leads to a conceptually new understanding of the process of disintegration of comet Shoemaker-Levy 9. We submit that the jovian tidal forces inflicted extensive cracks throughout the interior of the original nucleus but did not split it apart. The initial disruption was apparently accomplished by stresses exerted on the cracked object by its fast rotation during the early post-perijove period of time. We argue that this disruption was in fact a rapid sequence of episodes during July 1992 that gave birth to the 12 on-train, or primary, fragments: A, C, D, E, G, H, K, L, Q (later Q(sub 1)), R, S, and W. The discrete events of secondary fragmentation, which gave birth to the off-train fragments, are understood in this scenario as stochastic manifestations of the continuing process of progressive disintegration. Of the 13 off-train fragments considered, nine were secondary--B, F, G(sub 2), M, N, P (later P(sub 2) or P(sub 2a)), Q(sub 2), U, and V--and four tertiary (J, P(sub 1), P(sub 2b), and T). The separation parameters of 11 off-train fragments were determined. The vectorial distribution of separation velocities of these fragments shows a strong concentration toward a great circle, unquestionably an effect of the approximately conserved angular momentum of the progenitor comet since the time of its initial disruption. Also apparent is their clumping (except for P(sub 1)) to a segment along the great circle, implying that the fragments were consistently released from one side of their parents, thus explaining for the first time why the off-train fragments preferentially appeared on one side of the nuclear train. In order to obtain a consistent solution, our model requires that the points of separation be on the antisolar side of the parent fragments, where thermal stresses are likely to enhance the effect of rotation. The episodes of secondary fragmentation are found to have nine months after the close encounter with Jupiter in early July 1992, and the separation velocities ranged between 0.36 and 1.7 m/s. The spin-axis position is determined to have been nearly in the jovicentric orbit plane, which rules out the Asphaug-Benz-Solem strengthless aggregate model as a plausible breakup hypothesis. Since the separation velocities are rotational in nature, they cannot substantially exceed the critical limit for centrifugal breakup and offer an estimate for the original nuclear dimensions. The comet's nucleus is found to have been approximately 10 km in diameter and spinning rapidly. With the exception of P(sub 1) and apparently also P(sub 2) and F, no nongravitational deceleration was detected in the motions of the off-train fragments. Serious doubts are cast on continuing appreciable activity of any of these fragments. Indeed, when it was necessary to introduce a deceleration into the equations of motion, the effect appears to have been due to the action of solar radiation pressure on the centroid of centimeter-sized particulates in the disintegrating condensations.

Of the ~100 numbered Earth crossing asteriods (ECAs), none is predicted to impact the Earth within the next 200 years. It is more difficult to make definitive predictions for unnumberted ECAs because their orbits are not accurately known.