Dynamics of rotationally fissioned asteroids: Source of observed small asteroid systems

We present a model of near-Earth asteroid (NEA) rotational fission and ensuing dynamics that describes the creation of synchronous binaries and all other observed NEA systems including: doubly synchronous binaries, high-e binaries, ternary systems, and contact binaries. Our model only presupposes the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect, “rubble pile” asteroid geophysics, and gravitational interactions. The YORP effect torques a “rubble pile” asteroid until the asteroid reaches its fission spin limit and the components enter orbit about each other (Scheeres, D.J. [2007]. Icarus 189, 370-385). Non-spherical gravitational potentials couple the spin states to the orbit state and chaotically drive the system towards the observed asteroid classes along two evolutionary tracks primarily distinguished by mass ratio. Related to this is a new binary process termed secondary fission - the secondary asteroid of the binary system is rotationally accelerated via gravitational torques until it fissions, thus creating a chaotic ternary system. The initially chaotic binary can be stabilized to create a synchronous binary by components of the fissioned secondary asteroid impacting the primary asteroid, solar gravitational perturbations, and mutual body tides. These results emphasize the importance of the initial component size distribution and configuration within the parent asteroid. NEAs may go through multiple binary cycles and many YORP-induced rotational fissions during their approximately 10 Myr lifetime in the inner Solar System. Rotational fission and the ensuing dynamics are responsible for all NEA systems including the most commonly observed synchronous binaries.     

Rotational fission of contact binary asteroids

The energetics and dynamics of contact binary asteroids as they approach and pass the rotational fission limit is studied. We presume that the asteroids are subject to an external torque, such as from the YORP effect, that increases their angular momentum. Furthermore, we assume the asteroids can be described by a fairly minimal model comprised of a sphere and ellipsoid resting on each other. The minimum energy configurations for contact binary asteroids at different levels of angular momentum are computed and discussed. We find distinct transitions between different configurations as the angular momentum of the system is increased. These indicate that rapidly rotating contact binary asteroids may seek out clearly different relative configurations than slowly rotating systems. We find a single end state of the systems prior to rotational fission, and distinct dynamical outcomes as a function of mass distribution and shape when the rotational fission limit is exceeded. Our theoretical results agree qualitatively with observed properties of near-Earth asteroids, and can be used to help explain the spin-rate barrier, contact binaries, and the observed morphology of most NEO binaries.     

A survey of small fast rotating asteroids among the near-Earth asteroid population

A survey of 62 small near-Earth asteroids was conducted to determine the rotation state of these objects and to search for rapid rotation. Since results for 9 of the asteroids were previously published (Pravec, P., Hergenrother, C.W., Whiteley, R.J., Šarounová, L., Kušnirák, P., Wolf, M. [2000]. Icarus 147, 477-486; Pravec, P. et al. [2005] Icarus 173, 108-131; Whiteley, R.J., Tholen, D.J., Hergenrother, C.W. [2002a]. Icarus 157, 139-154; Hergenrother, C.W., Whiteley, R.J., Christensen, E.J. [2009]. Minor Planet Bull. 36, 16-18.), this paper will present results for the remaining 53 objects. Rotation periods significantly less than 2 h are indicative of intrinsic strength in the asteroids, while periods longer than 2 h are typically associated with gravitationally bound aggregates. Asteroids with absolute magnitude (H) values ranging from 20.4 to 27.4 were characterized. The slowest rotator with a definite period is 2004 BW₁₈ with a period of 8.3 h, while 2000 DO₈ and 2000 WH₁₀ are the fastest with periods of 1.3 min. A minimum of two-thirds of asteroids with H > 20 are fast rotating and have periods significantly faster than 2.0 h. The percentage of rapid rotators increases with decreasing size and a minimum of 79% of H ? 24 objects are rapid rotators. Slowly-rotating objects, some with periods as long as 10-20 h, make up a small though significant fraction of the small asteroid population. There are three fast rotators with relatively large possible diameters (D): 2001 OE₈₄ with 470 ? D ? 820 m (Pravec, P., Kušnirák, P., Šarounová, L., Harris, A.W., Binzel, R.P., Rivkin, A.S. [2002b]. Large coherent Asteroid 2001 OE84. In: Warmbein, B. (Eds.), Proceedings of Asteroids, Comets, Meteors - ACM 2002. Springer, Berlin, pp. 743-745), 2001 FE₉₀ with 265 ? D ? 594 m (Hicks, M., Lawrence, K., Rhoades, H., Somers, J., McAuley, A., Barajas, T. [2009]. The Astronomer’s Telegrams, # 2116), and 2001 VF₂ with a possible D of 145 ? D ? 665 m. Using the diameters derived from nominal absolute magnitudes and albedos, the remainder of the fast rotating population is completely consistent with D ? 200 m. Even when taking into account the largest possible uncertainties in the determination of diameters, the remainder must all have D ? 400 m. With the exceptions of 2001 OE₈₄, this result agrees with previous upper diameter limits for fast rotators in Pravec and Harris (Pravec, P., Harris, A.W. [2000]. Icarus 148, 589-593) and Whiteley et al. (Whiteley, R.J, Tholen, D.J., Hergenrother, C.W. [2002a]. Icarus 157, 139-154.     

Modeling of lightcurves of binary asteroids

We present a numerical method for inverting long-period components of lightcurves of asynchronous binary asteroids. Data of five near-Earth binary asteroids, (175706) 1996 FG₃, (65803) Didymos, (66391) 1999 KW₄, (185851) 2000 DP₁₀₇ and (66063) 1998 RO₁, for two of them from more than one apparition, were inverted. Their mutual orbits' poles and Keplerian elements, size ratios, and ellipsoidal shape axial ratios were estimated via this inversion. The pole solutions and size ratios for 1999 KW₄ and 2000 DP₁₀₇ are in a good agreement with independent estimates from radar measurements. We show that uncertainties of estimates of bulk densities of binary systems can be large, especially when observed on short arcs.     

Photometry and models of eight near-Earth asteroids

We present new observations and models of the shapes and rotational states of the eight near-Earth Asteroids (1580) Betulia, (1627) Ivar, (1980) Tezcatlipoca, (2100) Ra-Shalom, (3199) Nefertiti, (3908) Nyx, (4957) Brucemurray, and (5587) 1990 SB. We also outline some of their solar phase curves, corrected to common reference geometry with the models. Some of the targets may feature sizable global nonconvexities, but the observable solar phase angles were not sufficiently high for confirming these. None is likely to have a very densely cratered surface. We discuss the role of the intermediate topographic scale range in photometry, and surmise that this scale range is less important than large or small scale lengths.     

Photometry of Aten asteroids—More than a handful of binaries

Photometric observations were conducted on eight Aten near-Earth asteroids, with the goal of building physical models for the objects (85989) 1999 JD₆, (86450) 2000 CK₃₃, (86667) 2000 FO₁₀, (137170) 1999 HF₁, 1999 MN, 2000 PJ₅, 2002 JC and 2003 NZ₆. The results show rotation periods from 2.3 to almost 26 h. Some objects exhibit amplitudes higher than one magnitude on their lightcurves (1999 JD₆, 2000 CK₃₃ and 2003 NZ₆). Phase curve values (β, H^′, see below) were derived for four Atens and H-G values were found for two. Five Atens were classified by using their B-V and V-R color indices. This taxonomy was compared with the phase coefficient-albedo correlation defined by Belskaya and Shevchenko [Belskaya, I.N., Shevchenko, V.G., 2000. Icarus 147, 94-105]. Color variations during rotation and phase angle change were searched for. Our study demonstrates the high variety among Atens. Five out of the eight Atens are binaries or possible binaries, a significantly higher fraction than the expected 15% [Bottke, W.F., Melosh, H.J., 1996. Nature 281, 51-53]. The lightcurve of 2000 PJ₅ exhibits a binary character with a probable highly eccentric orbital rotation of the secondary component. The different periods of the known binary 1999 HF₁'s are easily detected. Other Atens have lightcurve with features such as high amplitude, V-shaped minima and U-shaped maxima that can be interpreted as a binary asteroid with a synchronous rotation (2003 NZ₆, 2000 CK₃₃ and perhaps also 1999 JD₆). The very red colors of 2000 CK₃₃ suggest a unique surface composition for this near-Earth object.     

Equilibrium figures of inhomogeneous synchronous binary asteroids

The present paper deals with the application of the classical theory of equilibrium figures of two rotating liquid masses to the case where bodies exhibit a radially stratified internal density distribution so that they can be considered as inhomogeneous bodies. The derived ellipsoidal shape solutions are applied to five real systems of equal-sized synchronous asteroids. Furthermore, internal inhomogeneity puts strong constraints on the surface grain density. A satisfactory model fit is achieved with internal densities of asteroids steadily increasing outwards. In particular, from such an approach we derived grain densities of the considered systems in agreement with their mineralogical composition inferred from reflectance spectroscopy. According to this new approach, 4492 Debussy, presently of unknown spectral type, is predicted to appear as a C-type object with a grain density on the order of 2 g/cm³.     

Shapes and rotational properties of thirty asteroids from photometric data

We have analyzed photometric lightcurves of 30 asteroids, and present here the obtained shapes, rotational periods and pole directions. We also present new photometric observations of five asteroids. The shape models indicate the existence of many features of varying degrees of irregularity. Even large main-belt asteroids display such features, so the resulting poles and periods are more consistent than those obtained by simple ellipsoid-like models. In some cases the new rotational parameters are rather different from those obtained previously, and in a few cases there were no proper previous estimates at all.     

Albedo and size determination of potentially hazardous asteroids: (99942) Apophis

The near-Earth object (99942) Apophis will make an extremely close approach to the Earth in 2029, and currently has approximately a one-in-45,000 chance of impacting our planet in 2036 (JPL Sentry, November 2006). Computation of the orbital evolution of this object is limited by insufficient knowledge of physical properties required to determine the role played by non-gravitational effects. Using polarimetric observations, we have obtained the first reliable determination of the albedo of Apophis, obtaining 0.33±0.08. We also derive an updated estimate of the asteroid's absolute magnitude: H=19.7±0.4. Using this albedo and H, we find that Apophis has a diameter of 270±60 m, slightly smaller than preliminary estimates based upon an assumed albedo. Our observations demonstrate the feasibility of polarimetric observations aimed at obtaining albedos and sizes of small, potentially hazardous asteroids.     

Thermal inertia of near-Earth asteroids and implications for the magnitude of the Yarkovsky effect

Thermal inertia determines the temperature distribution over the surface of an asteroid and therefore governs the magnitude the Yarkovsky effect. The latter causes gradual drifting of the orbits of km-sized asteroids and plays an important role in the delivery of near-Earth asteroids (NEAs) from the main belt and in the dynamical spreading of asteroid families. At present, very little is known about the thermal inertia of asteroids in the km size range. Here we show that the average thermal inertia of a sample of NEAs in the km-size range is . Furthermore, we identify a trend of increasing thermal inertia with decreasing asteroid diameter, D. This indicates that the dependence of the drift rate of the orbital semimajor axis on the size of asteroids due to the Yarkovsky effect is a more complex function than the generally adopted D⁻¹ dependence, and that the size distribution of objects injected by Yarkovsky-driven orbital mobility into the NEA source regions is less skewed to smaller sizes than generally assumed. We discuss how this fact may help to explain the small difference in the slope of the size distribution of km-sized NEAs and main-belt asteroids.     

Orbital evolution of small binary asteroids

About 15% of both near-Earth and main-belt asteroids with diameters below 10 km are now known to be binary. These small asteroid binaries are relatively uniform and typically contain a fast-spinning, flattened primary and a synchronously rotating, elongated secondary that is 20-40% as large (in diameter) as the primary. The principal formation mechanism for these binaries is now thought to be YORP (Yarkovsky-O’Keefe-Radzievskii-Paddack) effect induced spin-up of the primary followed by mass loss and accretion of the secondary from the released material. It has previously been suggested (?uk, M. [2007]. Astrophys. J. 659, L57-L60) that the present population of small binary asteroids is in a steady state between production through YORP and destruction through binary YORP (BYORP), which should increase or decrease secondary’s orbit, depending on the satellite’s shape. However, BYORP-driven evolution has not been directly modeled until now. Here we construct a simple numerical model of the binary’s orbital as well the secondary’s rotational dynamics which includes BYORP and selected terms representing main solar perturbations. We find that many secondaries should be vulnerable to chaotic rotation even for relatively low-eccentricity mutual orbits. We also find that the precession of the mutual orbit for typical small binary asteroids might be dominated by the perturbations from the prolate and librating secondary, rather than the oblate primary. When we evolve the mutual orbit by BYORP we find that the indirect effects on the binary’s eccentricity (through the coupling between the orbit and the secondary’s spin) dominate over direct ones caused by the BYORP acceleration. In particular, outward evolution causes eccentricity to increase and eventually triggers chaotic rotation of the secondary. We conclude that the most likely outcome will be reestablishing of the synchronous lock with a “flipped” secondary which would then evolve back in. For inward evolution we find an initial decrease of eccentricity and secondary’s librations, to be followed by later increase. We think that it is likely that various forms of dissipation we did not model may damp the secondary’s librations close to the primary, allowing for further inward evolution and a possible merger. We conclude that a merger or a tidal disruption of the secondary are the most likely outcomes of the BYORP evolution. Dissociation into heliocentric pairs by BYORP alone should be very difficult, and satellite loss might be restricted to the minority of systems containing more than one satellite at the time.     

Radar and optical observations and physical modeling of triple near-Earth Asteroid (136617) 1994 CC

We report radar, photometric, and spectroscopic observations of near-Earth Asteroid (136617) 1994 CC. The radar measurements were obtained at Goldstone (8560 MHz, 3.5 cm) and Arecibo (2380 MHz, 12.6 cm) on 9 days following the asteroid’s approach within 0.0168 AU on June 10, 2009. 1994 CC was also observed with the Panchromatic Robotic Optical Monitoring and Polarimetry Telescopes (PROMPT) on May 21 and June 1-3. Visible-wavelength spectroscopy was obtained with the 5-m Hale telescope at Palomar on August 25. Delay-Doppler radar images reveal that 1994 CC is a triple system; along with (153591) 2001 SN263, this is only the second confirmed triple in the near-Earth population. Photometry obtained with PROMPT yields a rotation period for the primary P = 2.38860 ± 0.00009 h and a lightcurve amplitude of ∼0.1 mag suggesting a shape with low elongation. Hale telescope spectroscopy indicates that 1994 CC is an Sq-class object. Delay-Doppler radar images and shape modeling reveal that the primary has an effective diameter of 0.62 ± 0.06 km, low pole-on elongation, few obvious surface features, and a prominent equatorial ridge and sloped hemispheres that closely resemble those seen on the primary of binary near-Earth Asteroid (66391) 1999 KW4. Detailed orbit fitting reported separately by Fang et al. (Fang, J., Margot, J.-L., Brozovic, M., Nolan, M.C., Benner, L.A.M., Taylor, P.A. [2011]. Astron. J. 141, 154-168) gives a mass of the primary of 2.6 × 10¹¹ kg that, coupled with the effective diameter, yields a bulk density of 2.1 ± 0.6 g cm⁻³. The images constrain the diameters of the inner and outer satellites to be 113 ± 30 m and 80 ± 30 m, respectively. The inner satellite has a semimajor axis of ∼1.7 km (∼5.5 primary radii), an orbital period of ∼30 h, and its Doppler dispersion suggests relatively slow rotation, 26 ± 12 h, consistent with spin-orbit lock. The outer satellite has an orbital period of ∼9 days and a rotation period of 14 ± 7 h, establishing that the rotation is not spin-orbit locked. Among all binary and triple systems observed by radar, at least 25% (7/28) have a satellite that rotates more rapidly than its orbital period. This suggests that asynchronous configurations with P_rotation < P_orbital are relatively common among multiple systems in the near-Earth population. 1994 CC’s outer satellite has an observed maximum separation from the primary of ∼5.7 km (∼18.4 primary radii) that is the largest separation relative to primary radius seen to date among all 36 known binary and triple NEA systems. 1994 CC, (153591) 2001 SN263, and 1998 ST27 are the only triple and binary systems known with satellite separations >10 primary radii, suggesting either a detection bias, or that such widely-separated satellites are relatively uncommon in NEA multiple systems.     

New determination of the size and bulk density of the binary Asteroid 22 Kalliope from observations of mutual eclipses

In 2007, the M-type binary Asteroid 22 Kalliope reached one of its annual equinoxes. As a consequence, the orbit plane of its small moon, Linus, was aligned closely to the Sun's line of sight, giving rise to a mutual eclipse season. A dedicated international campaign of photometric observations, based on amateur-professional collaboration, was organized and coordinated by the IMCCE in order to catch several of these events. The set of the compiled observations is released in this work. We developed a relevant model of these events, including a topographic shape model of Kalliope refined in the present work, the orbit solution of Linus as well as the photometric effect of the shadow of one component falling on the other. By fitting this model to the only two full recorded events, we derived a new estimation of the equivalent diameter of Kalliope of 166.2±2.8 km, 8% smaller than its IRAS diameter. As to the diameter of Linus, considered as purely spherical, it is estimated to 28±2 km. This substantial “shortening” of Kalliope, gives a bulk density of 3.35±0.33 g/cm³, significantly higher than past determinations but more consistent with its taxonomic type. Some constraints can be inferred on the composition.     

Binary asteroid systems: Tidal end states and estimates of material properties

The locations of the fully despun, double synchronous end states of tidal evolution, where the rotation rates of both the primary and secondary components in a binary system synchronize with the mean motion about the center of mass, are derived for spherical components. For a given amount of scaled angular momentum J/J′, the tidal end states are over-plotted on a tidal evolution diagram in terms of mass ratio of the system and the component separation (semimajor axis in units of primary radii). Fully synchronous orbits may not exist for every combination of mass ratio and angular momentum; for example, equal-mass binary systems require J/J′ > 0.44. When fully synchronous orbits exist for prograde systems, tidal evolution naturally expands the orbit to the stable outer synchronous solution. The location of the unstable inner synchronous orbit is typically within two primary radii and often within the radius of the primary itself. With the exception of nearly equal-mass binaries, binary asteroid systems are in the midst of lengthy tidal evolutions, far from their fully synchronous tidal end states. Of those systems with unequal-mass components, few have even reached the stability limit that splits the fully synchronous orbit curves into unstable inner and stable outer solutions.Calculations of material strength based on limiting the tidal evolution time to the age of the Solar System indicate that binary asteroids in the main belt with 100-km-scale primary components are consistent with being made of monolithic or fractured rock as expected for binaries likely formed from sub-catastrophic impacts in the early Solar System. To tidally evolve in their dynamical lifetime, near-Earth binaries with km-scale primaries or smaller created via a spin-up mechanism must be much weaker mechanically than their main-belt counterparts even if formed in the main belt prior to injection into the near-Earth region. Small main-belt binaries, those having primary components less than 10 km in diameter, could bridge the gap between the large main-belt binaries and the near-Earth binaries, as, depending on the age of the systems, small main-belt binaries could either be as strong as the large main-belt binaries or as weak as the near-Earth binaries. The inherent uncertainty in the age of a binary system is the leading source of error in calculation of material properties, capable of affecting the product of rigidity μ and tidal dissipation function Q by orders of magnitude. Several other issues affecting the calculation of μQ are considered, though these typically affect the calculation by no more than a factor of two. We also find indirect evidence within all three groups of binary asteroids that the semimajor axis of the mutual orbit in a binary system may evolve via another mechanism (or mechanisms) in addition to tides with the binary YORP effect being a likely candidate.     

Angular momentum of binary asteroids: Implications for their possible origin

We describe in this work a thorough study of the physical and orbital characteristics of extensively observed main-belt and trojan binaries, mainly taken from the LAOSA (Large Adaptive Optics Survey of Asteroids [Marchis, F., Baek, M., Berthier, J., Descamps, P., Hestroffer, D., Kaasalainen, M., Vachier, F., 2006c. In: Workshop on Spacecraft Reconnaissance of Asteroid and Comet Interiors. Abstract #3042]) database, along with a selection of bifurcated objects. Dimensionless quantities, such as the specific angular momentum and the scaled primary spin rate, are computed and discussed for each system. They suggest that these asteroidal systems might be the outcome of rotational fission or mass shedding of a parent body presumably subjected to an external torque. One of the most striking features of separated binaries composed of a large primary (Rp>100 km) with a much smaller secondary (Rs<20 km) is that they all have total angular momentum of ∼0.27. This value is quite close to the Maclaurin-Jacobi bifurcation (0.308) of a spinning fluid body. Alternatively, contact binaries and tidally locked double asteroids, made of components of similar size, have an angular momentum larger than 0.48. They compare successfully with the fission equilibrium sequence of a rotating fluid mass. In conclusion, we find that total angular momentum is a useful proxy to assess the internal structure of such systems.     

Spin axis evolution of two interacting bodies

We consider the solid-solid interactions in the two body problem. The relative equilibria have been previously studied analytically and general motions were numerically analyzed using some expansion of the gravitational potential up to the second order, but only when there are no direct interactions between the orientation of the bodies. Here we expand the potential up to the fourth order and we show that the secular problem obtained after averaging over fast angles, as for the precession model of Boué and Laskar [Boué, G., Laskar, J., 2006. Icarus 185, 312-330], is integrable, but not trivially. We describe the general features of the motions and we provide explicit analytical approximations for the solutions. We demonstrate that the general solution of the secular system can be decomposed as a uniform precession around the total angular momentum and a periodic symmetric orbit in the precessing frame. More generally, we show that for a general n-body system of rigid bodies in gravitational interaction, the regular quasiperiodic solutions can be decomposed into a uniform precession around the total angular momentum, and a quasiperiodic motion with one frequency less in the precessing frame.     

Rotational lightcurves of asteroids belonging to families

Complete lightcurves of 17 asteroids belonging to the Themis, Eos, and Maria families have been obtained, as well as single-night photometric observations of eight objects belonging to the same families. Using also data previously available in the literature, we perform a preliminary statistical analysis aimed at detecting possible correlations between rotational periods, overall lightcurve amplitudes, and objetcs' sizes. No evident correlation was found, with the possible exception of a weak anticorrelation between size and spin period. The implications of this possible anticorrelation are discussed.     

The orbit and size distribution of small Solar System objects orbiting the Sun interior to the Earth's orbit

We present the first observational measurement of the orbit and size distribution of small Solar System objects whose orbits are wholly interior to the Earth's (Inner Earth Objects, IEOs, with aphelion <0.983 AU). We show that we are able to model the detections of near-Earth objects (NEO) by the Catalina Sky Survey (CSS) using a detailed parameterization of the CSS survey cadence and detection efficiencies as implemented within the Jedicke et al. [Jedicke, R., Morbidelli, A., Spahr, T., Petit, J.M., Bottke, W.F., 2003. Icarus 161, 17-33] survey simulator and utilizing the Bottke et al. [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J.-M., Levison, H.F., Michel, P., Metcalfe, T.S., 2002. Icarus 156, 399-433] model of the NEO population's size and orbit distribution. We then show that the CSS detections of 4 IEOs are consistent with the Bottke et al. [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J.-M., Levison, H.F., Michel, P., Metcalfe, T.S., 2002. Icarus 156, 399-433] IEO model. Observational selection effects for the IEOs discovered by the CSS were then determined using the survey simulator in order to calculate the corrected number and H distribution of the IEOs. The actual number of IEOs with H<18 (21) is 36±26 (530±240) and the slope of the H magnitude distribution (∝¹⁰αH) for the IEOs is . The slope is consistent with previous measurements for the NEO population of αNEO=0.35±0.02 [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J.-M., Levison, H.F., Michel, P., Metcalfe, T.S., 2002. Icarus 156, 399-433] and αNEO=0.39±0.013 [Stuart, J.S., Binzel, R.P., 2004. Icarus 170, 295-311]. Based on the agreement between the predicted and observed IEO orbit and absolute magnitude distributions there is no indication of any non-gravitational effects (e.g. Yarkovsky, tidal disruption) affecting the known IEO population.     

Physical investigation of the potentially hazardous Asteroid (144898) 2004 VD17

In this paper we present the observational campaign carried out at ESO NTT and VLT in April and May 2006 to investigate the nature and the structure of the near-Earth object (144898) 2004 VD17. In spite of a great quantity of dynamical information, according to which it will have a close approach with the Earth in the next century, the physical properties of this asteroid are largely unknown. We performed visible and near-infrared photometry and spectroscopy, as well as polarimetric observations. Polarimetric and spectroscopic data allowed us to classify 2004 VD17 as an E-type asteroid. A good agreement was also found with the spectrum of the aubrite meteorite Mayo Belwa. On the basis of the polarimetric albedo (pv=0.45) and of photometric data, we estimated a diameter of about 320 m and a rotational period of about 2 h. The analysis of the results obtained by our complete survey have shown that (144898) 2004 VD17 is a peculiar NEO, since it is close to the breakup limits for fast rotator asteroids, as defined by Pravec and Harris [Pravec, P., Harris, A.W., 2000. Icarus 148, 12-20]. These results suggest that a more robust structure must be expected, as a fractured monolith or a rubble pile in a “strength regime” [Holsapple, K.A., 2002. Speed limits of rubble pile asteroids: Even fast rotators can be rubble piles. In: Workshop on Scientific Requirements for Mitigation of Hazardous Comets and Asteroids, Washington, September, 2002].     

The main belt as a source of near-Earth asteroids

We investigate the flux of main-belt asteroid fragments into resonant orbits converting them into near-Earth asteroids (NEAs), and the variability of this flux due to chance interasteroidal collisions. A numerical model is used, based on collisional physics consistent with the results of laboratory impact experiments. The assumed main-belt asteroid size distribution is derived from that of known asteroids extrapolated down to sizes of 40 cm, modified in such a way to yield a quasi-stationary fragment production rate over times 100 Myr. The results show that the asteroid belt can supply a few hundred km-sized NEAs per year, well enough to sustain the current population of such bodies. On the other hand, if our collisional physics is correct, the number of existing 10-km objects implies that these objects either have very long-lived orbits, or must come from a different source (i.e., comets). Our model predicts that the fragments supplied from the asteroid belt have initially a power-law size distribution somewhat steeper than the observed one, suggesting preferential removal of small objects. The component of the NEA population with dynamical lifetimes shorter than or of the order of 1 Myr can vary by a factor reaching up to a few tens, due to single large-scale collisions in the main belt; these fluctuations are enhanced for smaller bodies and faster evolutionary time scales. As a consequence, the Earth's cratering rate can also change by about an order of magnitude over the 0.1 to 1 Myr time scales. Despite these sporadic spikes, when averaged over times of 10 Myr or longer the fluctuations are unlikely to exceed a factor two.