Orbital evolution of asteroids with the effects of mutual gravitational attraction

The effects of the mutual gravitational attraction between asteroids were analyzed by two N-body calculations, in which N=4,516 (the Sun, the nine planets, and 4,506 asteroids). In one calculation the gravity of the asteroids was taken into account, and in the other it was ignored. These calculations were carried out for a time period of about 100 years. The largest difference in the positions of the asteroids between these two calculations is about 10^–3 AU. For the orbital elements of the semimajor axis, the eccentricity, and the inclination, the largest differences were 9 × 10^–6 AU, 4 × 10^–6, and 5 × 10^–4 degrees, respectively. It was found that the distribution of the differences of the semimajor axis between the two calculations is quite similar to the Cauchy distribution.     

A Specific Nongravitational Effect in the Asteroid Belt

The evolution of orbits of asteroids found in the IRAS and WISE albedo databases was calculated numerically from 2005 to 2016. It follows from the analysis of the obtained results that a certain nongravitational effect (NGE) currently affects the motion of a considerable fraction of main-belt asteroids with diameters up to 40 km. This conclusion agrees with the available data regarding the axial rotation of asteroids. The NGE manifests itself in an increase in the semimajor axes of orbits of low-albedo asteroids relative to the semimajor axes of orbits of high-albedo bodies. The NGE-induced rate of elongation of semimajor axes of asteroids with albedos р_v < 0.1 may be as high as (2–8) × 10^–8 AU/year. Errors in orbital elements of asteroids (unrelated to the accuracy of observational data used to determine these orbital elements) were found in one of the MPC catalogues for 2003 in the process of estimation of the accuracy of calculations.     

Asteroid sizes and albedos

The radiometric method of determining diameters of asteroids is reviewed, and a synthesis of radiometric and polarimetric measurements of the diameters and geometric albedos of a total of 187 asteroids is presented. All asteroids with diameters greater than 250 km are identified, and statistical studies can be carried out of the size distributions of different albedo classes down to 80-km diameter for the entire main asteroid belt (2.0–3.5 AU). The distribution of albedos is strongly bimodal, with mean albedos for the C and S groups of 0.035 and 0.15, respectively. The C asteroids outnumber the S at all sizes and all values of semi-major axis, increasing from a little over half the population inside 2.5 AU to more than 95% beyond 3.0 AU; for all objects with D > 70 km, the ratio C/(C+S) is 0.88 ± 0.04. More than half of all asteroids in this size range have a > 3.0 AU. The M asteroids constitute about 5% of the population for a < 3.0 AU, but no members of of this class have been identified in the outer belt. There are no significant differences between the distributions of C, S, and M asteroids for the largest asteroids (D > 200 km) and for those of intermediate size (200–270 km). The total mass in the belt, down to 70-km size, but excluding Ceres, is about 2 × 10²⁴ g. Evidence is presented that several large asteroids rotate in a prograde sense, and that a real difference existsbetween the bulk densities of Ceres and Vesta.     

Do stony meteorites come from comets?

The place of origin of stony meteorites can be determined from their trapped solar-wind gases. “Gas-rich” meteorites have only 10^?3?10^?4 the solar noble gas content and ?10^?2?10^?4 the surface exposure age of lunar soils. These differences suggest that the gas implantation took place between 1 and 8 AU from the Sun, in a region where the cratering rate was 10²?10³ times higher than at 1 AU. Both characteristics point to the asteroid belt. The predicted Ne²⁰ content a gas-rich meteorite formed at 2.5 AU is 1.2 × 10^?5 cc STP g^?1, compared to an observed mean for H-chondrites of 0.5 × 10^?5 cc STP g^?1. The observed prevalence of gas-rich meteorites (40–100% among carbonaceous chondrites, 2–33% among other classes) requires that the parent body remained long enough in the asteroid belt to develop a substantial regolith. This condition can be met by asteroids (～ 10% of mass converted to regolith.in 4.5 × 10⁹ yr), but not by short period comets (～0.04% converted in 10⁷ yr). It appears that a cometary origin can be ruled out for all stony meteorite clases that have gas-rich members. This includes carbonaceous chondrites.     

Evolution of comet orbits under the perturbing influence of the giant planets and nearby stars

The orbital evolution of 500 hypothetical comets during 10⁹ years is studied numerically. It is assumed that the birthplace of such comets was the region of Uranus and Neptune from where they were deflected into very elongated orbits by perturbations of these planets. Then, we adopted the following initial orbital elements: perihelion distances between 20 and 30 AU, inclinations to the ecliptic plane smaller than 20°, and semimajor axes from 5 × 10³ to 5 × 10⁴ AU. Gravitational perturbations by the four giant planets and by hypothetical stars passing at distances from the Sun smaller than 5 × 10⁵ AU are considered. During the simulation, somewhat more than 50% of the comets were lost from the solar system due to planetary or stellar perturbations. The survivors were removed from the planetary region and left as members of what is generally known as the cometary cloud. At the end of the studied period, the semimajor axes of the surviving comets tend to be concentrated in the interval 2 × 10⁴ < a < 3 × 10⁴ AU. The orbital planes of the comets with initial $\text{a ≧ 3 × 10}{}^4\text{AU}$ acquired a complete randomization while the others still maintain a slight predominance of direct orbits. In addition, comet orbits with final a < 6 × 10⁴AU preserve high eccentricities with an average value greater than 0.8 Most “new” comets from the sample entering the region interior to Jupiter's orbit had already registered earlier passages through the planetary region. By scaling up the rate of paritions of hypothetical new comets with the observed one, the number of members of the cometary cloud is estimated to be about 7 × 10¹⁰ and the conclusion is drawn that Uranus and Neptune had to remove a number of comets ten times greater.     

Orbital stability of systems of closely-spaced planets,II: configurations with coorbital planets

We numerically investigate the stability of systems of 1 \({{\rm M}_{\oplus}}\) planets orbiting a solar-mass star. The systems studied have either 2 or 42 planets per occupied semimajor axis, for a total of 6, 10, 126, or 210 planets, and the planets were started on coplanar, circular orbits with the semimajor axes of the innermost planets at 1 AU. For systems with two planets per occupied orbit, the longitudinal initial locations of planets on a given orbit were separated by either 60° (Trojan planets) or 180°. With 42 planets per semimajor axis, initial longitudes were uniformly spaced. The ratio of the semimajor axes of consecutive coorbital groups in each system was approximately uniform. The instability time for a system was taken to be the first time at which the orbits of two planets with different initial orbital distances crossed. Simulations spanned virtual times of up to 1 × 10⁸, 5 × 10⁵, and 2 × 10⁵ years for the 6- and 10-planet, 126-planet, and 210-planet systems, respectively. Our results show that, for a given class of system (e.g., five pairs of Trojan planets orbiting in the same direction), the relationship between orbit crossing times and planetary spacing is well fit by the functional form log(t _c /t ₀) = b β + c, where t _c is the crossing time, t ₀ = 1 year, β is the separation in initial orbital semimajor axis (in terms of the mutual Hill radii of the planets), and b and c are fitting constants. The same functional form was observed in the previous studies of single planets on nested orbits (Smith and Lissauer 2009). Pairs of Trojan planets are more stable than pairs initially separated by 180°. Systems with retrograde planets (i.e., some planets orbiting in the opposite sense from others) can be packed substantially more closely than can systems with all planets orbiting in the same sense. To have the same characteristic lifetime, systems with 2 or 42 planets per orbit typically need to have about 1.5 or 2 times the orbital separation as orbits occupied by single planets, respectively.     

Long-period comet flux in the planetary region: Dynamical evolution from the Oort cloud

This study analyzes the evolution of 2 × 10⁵ orbits with initial parameters corresponding to the orbits of comets of the Oort cloud under the action of planetary, galactic, and stellar perturbations over 2 × 10⁹ years. The dynamical evolution of comets of the outer (orbital semimajor axes a > 10⁴ AU) and inner (5 × 10³ < a (AU) < 10⁴) parts of the comet cloud is analyzed separately. The estimates of the flux of “new” and long-period comets for all perihelion distances q in the planetary region are reported. The flux of comets with a > 10⁴ AU in the interval 15 AU < q < 31 AU is several times higher than the flux of comets in the region q < 15 AU. We point out the increased concentration of the perihelia of orbits of comets from the outer cloud, which have passed several times through the planetary system, in the Saturn-Uranus region. The maxima in the distribution of the perihelia of the orbits of comets of the inner Oort cloud are located in the Uranus-Neptune region. “New” comets moving in orbits with a < 2 × 10⁴ AU and arriving at the outside of the planetary system (q > 25 AU) subsequently have a greater number of returns to the region q < 35 AU. The perihelia of the orbits of these comets gradually drift toward the interior of the Solar System and accumulate beyond the orbit of Saturn. The distribution of the perihelia of long-period comets beyond the orbit of Saturn exhibits a peak. We discuss the problem of replenishing the outer Oort cloud by comets from the inner part and their subsequent dynamical evolution. The annual rate of passages of comets of the inner cloud, which replenish the outer cloud, in the region q < 1 AU in orbits with a > 10⁴ AU (～ 5.0 × 10^?14 yr^?1) is one order of magnitude lower than the rate of passage of comets from the outer Oort cloud (～ 9.1 × 10^?13 yr^?1).     

The frequency and intensity of comet showers from the Oort cloud

We simulate the Oort comet cloud to study the rate and properties of new comets and the intensity and frequency of comet showers. An ensemble of ∼10⁶ comets is perturbed at random times by a population of main sequence stars and white dwarfs that is described by the Bahcall-Soneira Galaxy model. A cloning procedure allows us to model a large ensemble of comets efficiently, without wasting computer time following a large number of low eccentricity orbits. For comets at semimajor axis a = 20,000 AU, about every 100 myr a star with mass in the range 1M_⊙−2M_⊙ passes within ∼10,000 AU of the Sun and triggers a shower that enhances the flux of new comets by more than a factor of 10. The time-integrated flux is dominated by the showers for comets with semimajor axes less than ∼30,000 AU. For semimajor axes greater than ∼30,000 AU the comet loss rate is roughly constant and strong showers do not occur. In some of our simulations, comets are also perturbed by the Galactic tidal field. The inclusion of tidal effects increases the loss rate of comets with semimajor axes between 10,000 and 20,000 AU by about a factor of 4. Thus the Galactic tide, rather than individual stellar perturbations, is the dominant mechanism which drives the evolution of the Oort cloud.     

Where are the Uranus Trojans?

The area of stable motion for fictitious Trojan asteroids around Uranus’ equilateral equilibrium points is investigated with respect to the inclination of the asteroid’s orbit to determine the size of the regions and their shape. For this task we used the results of extensive numerical integrations of orbits for a grid of initial conditions around the points L ₄ and L ₅, and analyzed the stability of the individual orbits. Our basic dynamical model was the Outer Solar System (Jupiter, Saturn, Uranus and Neptune). We integrated the equations of motion of fictitious Trojans in the vicinity of the stable equilibrium points for selected orbits up to the age of the Solar system of 5 × 10⁹ years. One experiment has been undertaken for cuts through the Lagrange points for fixed values of the inclinations, while the semimajor axes were varied. The extension of the stable region with respect to the initial semimajor axis lies between 19.05 ≤ a ≤ 19.3 AU but depends on the initial inclination. In another run the inclination of the asteroids’ orbit was varied in the range 0° < i < 60° and the semimajor axes were fixed. It turned out that only four ‘windows’ of stable orbits survive: these are the orbits for the initial inclinations 0° < i < 7°, 9° < i < 13°, 31° < i < 36° and 38° < i < 50°. We postulate the existence of at least some Trojans around the Uranus Lagrange points for the stability window at small and also high inclinations.     

Origin and sustainability of the population of asteroids captured in the exterior resonance 1:2 with Mars

At present, approximately 1500 asteroids are known to evolve inside or sticked to the exterior 1:2 resonance with Mars at a ? 2.418 AU, being (142) Polana the largest member of this group. The effect of the forced secular modes superposed to the resonance gives rise to a complex dynamical evolution. Chaotic diffusion, collisions, close encounters with massive asteroids and mainly orbital migration due to the Yarkovsky effect generate continuous captures to and losses from the resonance, with a fraction of asteroids remaining captured over long time scales and generating a concentration in the semimajor axis distribution that exceeds by 20% the population of background asteroids. The Yarkovsky effect induces different dynamics according to the asteroid size, producing an excess of small asteroids inside the resonance. The evolution in the resonance generates a signature on the orbits, mainly in eccentricity, that depends on the time the asteroid remains captured inside the resonance and on the magnitude of the Yarkovsky effect. The greater the asteroids, the larger the time they remain captured in the resonance, allowing greater diffusion in eccentricity and inclination. The resonance generates a discontinuity and mixing in the space of proper elements producing misidentification of dynamical family members, mainly for Vesta and Nysa-Polana families. The half-life of resonant asteroids large enough for not being affected by the Yarkovsky effect is about 1 Gyr. From the point of view of taxonomic classes, the resonant population does not differ from the background population and the excess of small asteroids is confirmed.     

Implications from the motion of outer belt asteroids

A principal feature of the asteroidal distribution is the rapid truncation of its population outward from ～3.4 AU. This paper presents further evidence, based on the motion and distribution of certain minor planets with large semimajor axes, that this truncation cannot be strictly the result of gravitational perturbations of the major planets even acting over times of ～10⁹ years. The motion of other outer asteroids sets a probable upper limit of 0.081 on Jupiter's eccentricity.     

Solar flare track densities in interplanetary dust particles: The determination of an asteroidal versus cometary source of the zodiacal dust cloud

Dust particles that are larger than 1 μm, when injected into the Solar System from comets and asteroids, will spiral into the Sun due to the Poynting-Robertson effect. During the process of spiraling in, such dust particles accumulate solar flare tracks in their component minerals. The accumulated track density for a given dust grain is a function of the duration of its space exposure and its distance from the Sun. Using a computer model, it was determined that the expected track density distributions from grains produced by comets are very different from those produced by asteroids. Individual asteroids produce populations of particles that arrive at 1 AU with scaled track density distributions containing “spikes,” while comets supply particles with a flatter and wider distribution of track densities. Particles with track densities above 3 × 10⁷ (sϱA/v) tracks/cm² have probably been exposed to solar flare tracks prior to injection into the interplanetary medium and are therefore likely to be asteroidal. Particles with track densities below 0.7 × 10⁷(sϱA/v) tracks/cm² must be derived from comets or Earth-crossing asteroids. Earth-crossing asteroids are not responsible for all the dust collected at 1 AU since they cannot produce the large track densities observed in some of the interplanetary dust particles collected in the stratosphere. The track densities observed in the stratospheric dust fall within the predicted range, but there is at present an insufficient number of carefully determined densities to make strong statements about the sources of the present dust population.     

The photodissociation lifetimes of the OH and OD radicals in comets

The rates of photodissociation of the OH and OD molecules from absorption of solar radiation in he X²Π-A²Σ⁺ electronic transition are calculated to lie between 3.5 and 6.7 × 10^?6 sec^?1 for OH for heliocentric velocities between -60 and +60 km sec^?1 and to be about 4.7 × 10^?7 sec^?1 for OD at 1 AU from the Sun. The corresponding lifetimes, which are upper bounds to the actual lifetimes, are generally consistent with the observational cometary data.     

On the transport of bodies within and from the asteroid belt

Abstract— This paper explores two processes, sweeping secular resonance (Ward, 1981) and gas drag (Lecar and Franklin, 1997), at work during the dispersal of the solar nebula. we have two aims not previously considered for the two mechanisms: (1) to explain the likely depletion, by a factor of 1000 or so, of the rocky material in the inner belt (2.0 < a < 3.2 AU); (2) to introduce a means for providing—or contributing to—the dispersion in semimajor axis of the various asteroidal taxonomic classes. We suggest that large asteroids with birthplaces separated by an astronomical unit or more can be finally deposited, owing to drag, at the same semimajor axis. For example, we find that bodies with radii up to 100 km can be transferred by gas drag from the outer belt (a > 3.3 AU) well into the inner one, and that an object already in the inner belt as large or even larger than Vesta (r = 250 km)—thought to be the parent body of many meteorites—can be inwardly displaced by as much as an astronomical unit if the nebula dispersal times lie close to 10⁵ years. For such times, a large fraction of the inner belt's primordial mass can be ejected, with most of it passing into the inner solar system.     

Kinematics and parameters of the gas in the vicinity of TW Hya

The following conclusions about the kinematics and parameters of the gas in the vicinity of TW Hya have been drawn from an analysis of optical and ultraviolet line profiles and intensities. The accreting matter rises in the magnetosphere to a distance z>R_* above the disk plane and falls to the star near its equator almost perpendicular to its plane. The matter outflows from a disk region with an outer radius of ≤0.5 AU. The [OI], [SII], and H2 lines originate in the disk atmosphere outside the outflow region, where the turbulent gas velocity is close to the local speed of sound. In the formation region of the forbidden lines, T?8500 K and N_e?5×10⁶ cm^?3, and the hydrogen is almost neutral: x_e<0.03. The absorption features observed in the blue wings of some of the ultraviolet lines originate in the part of the wind that moves almost perpendicular to the disk plane, i.e., in the jet of TW Hya. The V _z gas velocity component in the jet decreases with increasing distance from the jet axis from 200 to 30 km s^?1. The matter outflowing from the inner disk boundary, moves perpendicular to the disk plane in the formation region of blue absorption line components, at a distance of ～0.5 AU from the axis of symmetry of the disk. This region of the wind is collimated into the jet at a distance of <3 AU from the disk plane. The gas temperature in the formation region of absorption components is ?2×10⁴ K, and the gas density is <3×10⁶ cm^?3. This region of the jet is on the order of several AU away from the disk plane, while free recombination in the jet begins even farther from the disk. The mass-loss rate for TW Hya is \(\dot M_w < 7 \times 10^{ - 10} M_ \odot yr^{ - 1}\), which is a factor of 3lower than the mean accretion rate. The relative abundance of silicon and aluminum in the jet gas is at least an order of magnitude lower than its standard value.     

The formation and origin of the IRAS zodiacal dust bands as a consequence of single collisions between asteroids

The zodiacal dust bands discovered by IRAS can be explained as products of single collisions between asteroids. Debris from such a collision is distributed about the plane of the ecliptic as particles experience differential precession of their ascending nodes due to dispersion of their semimajor axes. For each collision, two bands, one on each side of the ecliptic, are formed on time scales of 10⁵ to 10⁶ years. The band pairs observed by IRAS are most likely the result of collisions between asteroids ∼15 km in diameter that occured within the last several million years. Further analysis of the IRAS sky survey data and of any future, more sensitive surveys should reveal additional, fainter band pairs. Our model suggests that asteroid collisions are sufficient to account for the bulk of the observed zodiacal thermal emission.     

Vertical distribution of water vapor and mars model lower and middle atmosphere

Observations and model calculations of water vapor diffusion suggest that about half the amount of water vapor is distributed with constant mixing ratio in the Martian atmosphere, the other half is the excess water vapor in the lower troposphere. During 24 hr the total content of water vapor may vary by a factor of two. The eddy diffusion coefficient providing agreement between calculations and observations is K = (3–10) × 10⁶ cm² sec^?1 in the troposphere. An analytical expression is derived for condensate density in the stratosphere in terms of the temperature profile, the particle radius r, and K. The calculations agree with the Mars 5 measurements for r = 1.5 μm, condensate density 5 × 10^?12 g/cm³ in the layer maximum at 30 to 35 km, condensate column density 7 × 10^?6 cm^?2, K = (1?3) × 10⁶ cm² sec^?1, and the temperature profile T = 185 ? 0.05z ? 0.01z² at 20 to 40 km. Condensation conditions yield a temperature of 160°K at 60 km in the evening; the scale height for scattered radiation yields T = 110°k at 80 to 90 km. The Mars model atmosphere has been developed up to 125 km.     

On the process of accretion in the formation of the planets and comets

The physically reasonable assumption that the seed bodies which initiated the accretion of the individual asteroids, planets, and comets (subsequently these objects are collectively called planetoids) formed by stochastic processes requires a radius distribution function which is unique except for two scaling parameters: the total number of planetoids and their most probable radius. The former depends on the ease of formation of the seed bodies while the second is uniquely determined by the average pre-encounter velocity, V, of the accretable material relative to an individual planetoid. This theoretical radius function can be fit to the initial asteroid radius distribution which Anders (1965) derived from the present-day distribution by allowing for fragmentation collisions among the asteroids since their formation. Normalizing the theoretical function to this empirical distribution reveals that there were about 10² precollision asteroids and that V = (2?4) × 10^?2 km/sec which was presumably the turbulent velocity in the Solar Nebula. Knowing V we can determine the scale height of the dust in the Solar Nebula and consequently its space density. The density of accretable material determines the rate of accretion of the planetoids. From this we find, for example, that the Earth formed in about 8 × 10⁶ yr and it attained a maximum temperature through accretion of about 3 × 10³°K. From the total mass of the terrestrial planets and the theoretical radius function we find that about 2 × 10³ planetoids formed in the vicinity of the terrestrial planets. Except for the asteroids the smaller planetoids have since been accreted by the terrestrial planets. About 15% of the present mass of the terrestrial planets was accumulated by the secondary accretion of these smaller primary planetoids. There are far fewer primary planetoids than craters on the Moon or Mars. The craters were likely produced by the collisional breakup of a few primary planetoids with masses between one-tenth and one lunar mass. This deduction comes from comparing the collision cross sections of the planetoids in this mass range to that of the terrestrial planets. This comparison shows that two to three collisions leading to the breakup of four to six objects likely occurred among these objects before their accretion by the terrestrial planets. The number of these fragments is quite adequate to explain the lunar and Martin craters. Furthermore the mass spectrum of such fragments is a power-law distribution which results in a power-law distribution of crater radii of just the type observed on the Moon and Mars. Applying the same analysis to the planetoids which formed in the vicinity of the giant planets reveals that it is unlikely that any fragmentation collisions took place among them before they were accreted by these planets due to the integrated collision cross section of the giant planets being about three orders of magnitude greater than that of the terrestrial planets. We can thus anticipate a marked scarcity of impact craters on the satellites of these outer planets. This prediction can be tested by future space probes. Our knowledge of the radius function of the comets is consistent with their being primary planetoids. The primary difference between the radius function of the planetoids which formed in the inner part of the solar system and that of the comets results from the fact that the seed bodies which grew into the comets formed far more easily than those which grew into the asteroids and the terrestrial planets. Thus in the outer part of the Solar Nebula the principal solid material (water and ammonia snow) accreted into a huge (～10¹²⁺) number of relatively small objects (comets) while in the inner part of the nebula the solid material (hard-to-stick refractory substances) accumulated into only a few (～10³) large objects (asteroids and terrestrial planets). Uranus and Neptune presumably formed by the secondary accretion of the comets.     

There are ten,not eight planets

In 1946, E. Sevin postulated the global vibrations of the Sun with a period P ₀ = 1/9 day and a “wavelength” L ₀ = c × P ₀ = 19.24 AU and predicted the tenth planet at a mean distance of 4.0 × L ₀ ≈ 77.0 AU from the Sun (c is the speed of light). The global vibrations of the Sun, precisely with the period of 1/9 day, were actually detected in 1974. Recently, the largest Kuiper Bell object 2003 UB₃₁₃, or Eris, with an orbital semimajor axis ≈ 3.5 × L ₀ ≈ 67.5 AU was discovered. We adduce arguments for the status of Eris as our tenth planet: (i) the object is larger and farther from the Sun than Pluto and (ii) the semimajor axis of Eris agrees well with the sequence of planetary distances that follows from the resonance spectrum of the Solar system dimensions (with the scale L ₀ and for all 11 orbits, including those of Pluto, Eris, and the asteroid belt). We point to a mistake of the Prague (2006) IAU Assembly, which excluded Pluto from the family of planets by introducing a new, highly controversial class of objects—“dwarf planets.”     

Farmington Meteorite: A fragment of an Apollo asteriod?

We have attempted to reconstruct the orbit of the Farmington L5 chondrite which fell in Kansas in 1890. Because its radiation age is uniquely short (25 000 years), its orbit should still closely resemble that of its parent body. A search of 280 contemporary newspapers and other sources turned up more than 60 useable eyewitness reports from 32 localities, which led to the following estimate of the apparent radiant: height 60°, azimuth 20°, with an uncertainty of about 10°. Orbital elements were determined for this radiant for four plausible preatmospheric velocities: 13, 16, 19, and 22 km/sec. The results show quite definitely that Farmington had a small orbit of low inclination: semimajor axis 1–1.9 AU, perihelion ? 0.4 AU, aphelion ? 3.0 AU, inclination ? 16°. Because of the short radiation age, the parent body of Farmington must already have been in an Earth-crossing orbit when the meteorite was ejected from it by an impact. Of the 11 known Earth-crossing asteroids with encounter velocities below 22 km/sec, 1862 Apollo, Hermes, and 1865 Cerberus are passable matches, while 1620 Geographos and 1685 Toro are more marginal possibilities. Apparently Earth-crossing asteroids are the immediate parent bodies of at least some meteorites. Their ultimate source must be the ultimate source of most stony meteorites.