Searches for transplutonian planets using long-period comets

We discuss the dynamical connection of long-period and nearly parabolic comets with hypothetical transplutonian planets. The statistics includes 792 comets with periods P > 200 years. The orbital plane of the parent planet can be determined from the observed distribution of the perihelia and poles of cometary orbits. The radius of a planetary orbit can be calculated using the Radzievsky-Tisseran criterion. We calculated the minimum distance of each of the 792 orbits to 11 hypothetical planetary orbits. Testing for the kinematic connection of comets with transplutonian planets yielded a negative result. The presence of the nodes of cometary orbits in the transplutonian region is shown to be the result of a geometric effect. We found a high concentration of the nodes and perihelia of cometary orbits in the zone of the terrestrial planets.     

Galactic perturbations on nearly-parabolic cometary orbits

The effect of galactic perturbations on long-period comet orbits is examined via numerical and analytical means. Relations are found between a comet's initial perihelion position and the positions of succeeding perihelia. It was found that the galactic effects were strongest on the comets initially at galactic latitudes close to 40°. In such cases the galactic perturbations caused the orbit to become almost circular before becoming nearly parabolic again. This effect allows comets with semimajor axes of about 25 000 AU to make only a few passages through the inner solar system in a time interval of 10⁹yr. Thus the galactic field is an important factor in the evolution of long-period comet orbits. The observed distribution of perihelia of long-period comets indicates that galactic effects have been active.     

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).     

Evidence for an Extended Scattered Disk

By telescopic tracking, we have established that the transneptunian object (TNO) 2000 CR₁₀₅ has a semimajor axis of 220±1 AU and perihelion distance of 44.14±0.02 AU, beyond the domain which has heretofore been associated with the “scattered disk” of Kuiper Belt objects interacting via gravitational encounters with Neptune. We have also firmly established that the TNO 1995 TL₈ has a high perihelion (of 40.08±0.02 AU). These objects, and two other recent discoveries which appear to have perihelia outside 40 AU, have probably been placed on these orbits by a gravitational interaction which is not strong gravitational scattering off of any of the giant planets on their current orbits. Their existence may thus have profound cosmogonic implications for our understanding of the formation of the outer Solar System. We discuss some viable scenarios which could have produced these objects, including long-term diffusive chaos and scattering off of other massive bodies in the outer Solar System. This discovery implies that there must be a large population of TNOs in an “extended scattered disk” with perihelia above the previously suggested 38 AU boundary. The total population is difficult to estimate due to the ease with which such objects would have been lost. This illustrates the great value of frequent and well time-sampled recovery observations of trans-neptunian objects within their discovery opposition.     

On a nonlinear and lorentz-invariant version of Newtonian gravitation — II

This paper gives a full nonlinear version of Newtonian gravity in which the gravitational energy acts as a source of the gravitational field. The generalized field equation for the scalar gravitational potential is solved for a spherically symmetric localized distribution of matter. It is shown that the perihelia of orbits of test particles in such a field precess steadily. The effect is, however, too small to account for the observed shift in the perihelion of planet Mercury. Further, the bending of light in this theory is zero. It is suggested that these inadequacies of the quasi-Newtonian framework call for more sophisticated approaches to gravity.     

Planet crossing asteroids and parallel computing: Project spaceguard

The orbits of the asteroids crossing the orbit of the Earth and other planets are chaotic and cannot be computed in a deterministic way for a time span long enough to study the probability of collisions. It is possible to study the statistical behaviour of a large number of such orbits over a long span of time, provided enough computing resources and intelligent post processing software are available. The former, problem can be handled by exploiting the enormous power of parallel computing systems. The orbit of the asteroids can be studied as a restricted (N+M)-body problem which is suitable for the use of parallel processing, by using one processor to compute the orbits of the planets and the others to compute the orbits the asteroids. This scheme has been implemented on LCAP-2, an array of IBM and FPS processors with shared memory designed by E. Clementi (IBM). The parallelisation efficiency has been over 80%, and the overall speed over 90 MegaFLOPS; the orbits of all the asteroids with perihelia lower than the aphelion of Mars (410 objects) have been computed for 200,000, years (Project SPACEGUARD). The most difficult step of the project is the post processing of the very large amount of output data and to gather qualitative information on the behaviour of so many orbits without resorting to the traditional technique, i.e. human examination of output in graphical form. Within Project SPACEGUARD we have developed a qualitative classification of the orbits of the planet crossers. To develop an entirely automated classification of the qualitative orbital behaviour-including crossing behaviour, resonances (mean motion and secular), and protection mechanisms avoiding collisions-is a challenge to be met.     

A survey of meteor spectra and orbits: evidence for three populations of Na-free meteoroids

We present a survey of 97 spectra of mainly sporadic meteors in the magnitude range +3 to −1, corresponding to meteoroid sizes 1-10 mm. For the majority of the meteors, heliocentric orbits are known as well. We classified the spectra according to relative intensities of the lines of Mg, Na, and Fe. Theoretical intensities of these lines for a chondritic composition of the meteoroid and a wide range of excitation and ionization conditions were computed. We found that only a minority of the meteoroids show chondritic composition. Three distinct populations of Na-free meteoroids, each comprising ∼10% of sporadic meteoroids in the studied size range, were identified. The first population are meteoroids on asteroidal orbits containing only Fe lines in their spectra and possibly related to iron-nickel meteorites. The second population are meteoroids on orbits with small perihelia (q?0.2 AU), where Na was lost by thermal desorption. The third population of Na-free meteoroids resides on Halley type cometary orbits. This material was possibly formed by irradiation of cometary surfaces by cosmic rays in the Oort cloud. The composition of meteoroids on Halley type orbits is diverse, probably reflecting internal inhomogeneity of comets. On average, cometary dust has lower than chondritic Fe/Mg ratio. Surprisingly, iron meteoroids prevail among millimeter-sized meteoroids on typical Apollo-asteroid orbits. We have also found varying content of Na in the members of the Geminid meteoroid stream, suggesting that Geminid meteoroids were not released from their parent body at the same time.     

On the character of evolution of orbits in the vicinity of the 1 : 3 Kirkwood gap

The character of orbital evolution for bodies moving near the if 1 : 3 commensurability with Jupiter was studied by model calculations for the time interval of ～500 years. A comparison of oscillations of the orbital elements a, e, q and q′ is made for ensembles of bodies along three starting orbits in the vicinity of the sharp commensurability with Jupiter. These orbits are eccentric ones of low inclinations having perihelia near the Earth's orbit. Examples of a deceleration of the rate of orbital evolution near the sharp commensurability are revealed. The existence of a group of asteroids connected with the Kirkwood gap, i.e., being in a resonant motion with Jupiter, is suggested. A connection of asteroids 887 Alinda and 1915 Quetzalcoatl with this gap is confirmed.     

A Monte Carlo investigation of Jovian perturbations on short-period comet orbits

We present statistical distributions of Jovian perturbations on short-period comet orbits resulting from accurate numerical integrations. Our sample of 60, 000 cometary orbits with low inclinations and random orientations is characterized by perihelia between 0 and 7 AU and aphelia between 4 and 13 AU. The perturbations considered are those experienced because of Jupiter's gravitation per orbital revolution by the comets. Regularization and accurate step-length control in the numerical integration gives statistical results appreciably different from those computed by Rickman and Vaghi (1978). Their use of a crude method of integration led to erroneous results for close encounters. Strong asymmetries of the $\text{δ(}\text{1}\text{a}\text{)}$ distributions, in particular for the extreme tails, are observed for perihelion- or aphelion-tangent orbits. These orbits are also shown to experience the strongest energy perturbations on the average. Some results concerning the perturbations of Tisserand parameters are indicated. The perturbation distributions for the angular elements are described and discussed. The role of the minimum distance from Jupiter as an indicator of perturbations is investigated.     

A model of the galactic tidal interaction with the oort comet cloud

We consider a model of the in situ Oort cloud which is isotropic with a random distrihution of perihelia directions and angular momenta. The energy distribution adopted has a continuous range of values appropriate for long-period (>200 yr) comets. Only the tidal torque of the Galaxy is included as a perturbation of comet orbits and it is approximated to be that due to a quasi-steady state distribution of matter with disk-like symmetry. The time evolution of all orbital elements can be analytically obtained for this case. In particular, the change in the perihelion distance per orbit and its dependence on other orbital elements is readily found. We further make the assumption that a comet whose perihelion distance was beyond 15 AU during its last passage through the Solar System would have orbit parameters that are essentially unchanged by planetary perturbations. Conversely, if the prior passage was inside 15 AU we assume that planetary perturbations would have removed the comet from the in situ energy distribution accessible by the galactic tide. Comets which had their perihelia changed from beyond 15 AU to within 5 AU in a single orbit are taken to be observable. We are able to track the evolution of 10⁶ comets as they are made observable by the galactic tidal touque. Detailed results are obtained for the predicted distribution of new (0 < 1/ < 10^–4 AU^–1) comets. Further, correlations between orbital elements can be studied. We present predictions of observed distributions and compare them with the random in situ results as well as with the actual observed distributions of class I comets. The predictions are in reasonable agreement with actual observations and, in many cases, are significantly different from random when perihelia directions are separated into galactic northern and southern hemispheres. However the well-known asymmetry in the north-south populations of perihelia remains to be explained. Such an asymmetry is consistent with the dominance of tidal torques today if a major stochastic event produced it in the past since tidal torques are unable to cause the migration of perihelia across the latitude barriers ±26°.6 in the disk model.     

Orbital evolution of giant comet-like objects

We investigated by numerical integrations the long-term orbital evolution of four giant comets or comet-like objects. They are Chiron, P/Schwassmann-Wachmann 1 (SW1), Hidalgo, and 1992AD (5145), and their orbits were traced for 100–200 thousand years (kyr) toward both the past and the future. For each object, 13 orbits were calculated, one for the nominal orbital elements and other 12 with slightly modified elements based on the rms residual of the orbit determination and on the number of observations. As past studies indicate, their orbital evolution is found to be very chaotic, and thus can be described only in terms of probability. Plots of the semi-major axis (a) and perihelion distance (q) of the objects treated here seem to cross each other frequently, suggesting a possibility of their common evolutionary paths. About a half of all the calculated orbits showedq- ora-decreasing evolution. This indicates that, at least on the time scale in question, the giant comet-like objects are possibly on a dynamical track that can lead to capture from the outer solar system. We could hardly find the orbits with perihelia far outside the orbit of Saturn (q>15 AU). This is perhaps because the evolution of the orbits beyond Saturn is so slow that substantial orbital changes do not take place within 100–200 kyr.     

Vaporization of comet nuclei: Light curves and life times

We have examined the effects of vaporization from the nucleus of a comet and show that a latitude dependence of vaporization can, in some cases, explain asymmetries in cometary light curves. We also find that a non-uniform distribution of solar radiation over a comet can considerably shorten the vaporization lifetime compared to the results normally obtained by assuming that the nuclear surface is isothermal.Independent of any latitude effects, comets with CO₂-dominated nuclei and with perihelion distances less than 0.5 AU have vaporization lifetimes less than or comparable to their dynamical ejection times. This may explain the observed deficit of comets with small perihelion distances. Similarly comets with CO₂-dominated nuclei and perihelia near Jupiter's orbit have vaporization lifetimes that are shorter than the time for capture into short-period orbits. We suggest, therefore, that at least some new comets are composed in large part of CO₂, while only H₂O-dominated comets, with lower vaporization rates, can survive to be captured into short-period orbits.     

Collisional Rates within Newly Formed Asteroid Families

A statistical analysis of the mutual collisions among members of asteroid families during the very early times after family formation has been performed. The statistical properties of the collisions (probability, distribution of velocity, and so on) have been computed using an algorithm effective even in cases in which the longitude of the nodes and the longitudes of the perihelia of the orbits under consideration are not distributed uniformly. The results show the occurrence of a strong enhancement in the mutual collision rate among family members, immediately after family formation. Nevertheless, this episode lasts for a relatively short time, and it does not affect too severely the overall collisional evolution of the family. The early enhancement of mutual collisions, however, may influence the cratering record exhibited by the surfaces of family members, possibly laying the foundation for the early development of a surface regolith layer.     

Steady state populations of Apollo-Amor objects

The steady-state distribution of orbits of Apollo-Amor objects is calculated for a variety of possible sources. These include asteroids near the inner edge of the belt, cometary orbits similar to Encke, and hypothetical extinct cometary orbits with perihelia larger than that of Encke. In all but one case, the steady-state distributions are similar for all these sources, and predict Amor/Apollo ratios of 1.5 to 3. These ratios are lower than those predicted by work in which the effects of the ν₆ secular resonance were not considered. These results are in general agreement with observation, although the higher (～3) Amor/Apollo ratios found for many of the sources may turn out to be unacceptably high. The absolute number of Apollo-Amors observed is found to require an injection rate of ～15 objects/(10⁶ years). This rate is easily achieved if the present existence of Encke is assumed to be a reasonably probable event, and if Encke becomes a ～1-km-diameter Apollo object following exhaustion of its volatile material; best estimates of the injection rate from the asteroid belt [～1.5/(10⁶ years)] are too low. Hence a dominant cometary component is suggested. The predicted number of Apollo objects in small (q < 1.0 AU, a < 1.4 AU orbits is in agreement with observation. Predicted lunar and terrestrial cratering rates agree approximately with observation. An unexplained difference between the lunar and terrestrial results is probably caused by uncertainties in the scaling laws or crater counts used. This discrepancy precludes an exact test of these calculations using cratering data.     

Complex exposure histories for meteorites with “short” exposure ages

Abstract— We report measurements of ²⁶Al and ¹⁰Be activities in nine ordinary chondrites and of the light noble gas concentrations and ³⁶Cl and ⁴¹Ca activities in subsets of those meteorites. All but Murray have low ²¹Ne concentrations (<1.0 × 10^?8cm³STP/g) and have previously been used to estimate ²¹Ne production rates. Ladder Creek, Murchison, Sena, and Timochin have inventories of cosmogenic radionuclides that are compatible with a single stage of irradiation and give ²¹Ne production rates that are consistent with the standard L-chondrite value of 0.33 × 10^?8cm³STP/g/Ma. In contrast, Cullison, Guenie, Shaw, and Tsarev experienced complex irradiation histories. They and several other meteorites with low nominal exposure ages also have lower ³He/²¹Ne ratios than expected based on their ²²Ne/²¹Ne ratios. A general association between low ²¹Ne contents and ³He losses suggests that meteorites with short lifetimes often occupy orbits with small perihelia. However, meteorites with low ²¹Ne contents, one-stage exposure histories, and losses of cosmogenic ³He are rare. Possible explanations for the scarcity are (1) statistical, (2) that it is harder for more deeply buried protometeoroids to lose gas in a liberating collision, and (3) that it is harder to insert more deeply buried protometeoroids directly into orbits with small perihelia.     

The scattered disk population as a source of Oort cloud comets: evaluation of its current and past role in populating the Oort cloud

We have integrated the orbits of the 76 scattered disk objects (SDOs), discovered through the end of 2002, plus 399 clones for 5 Gyr to study their dynamical evolution and the probability of falling in one of the following end states: reaching Jupiter's influence zone, hyperbolic ejection, or transfer to the Oort cloud. We find that nearly 50% of the SDOs are transferred to the Oort cloud (i.e., they reach heliocentric distances greater than 20,000 AU in a barycentric elliptical orbit), from which about 60% have their perihelia beyond Neptune's orbit (31 AU<q<36 AU) at the moment of reaching the Oort cloud. This shows that Neptune acts as a dynamical barrier, scattering most of the bodies to near-parabolic orbits before they can approach or cross Neptune's orbit in non-resonant orbits (that may allow their transfer to the planetary region as Centaurs via close encounters with Neptune). Consequently, Neptune's dynamical barrier greatly favors insertion in the Oort cloud at the expense of the other end states mentioned above. We found that the current rate of SDOs with radii R>1 km incorporated into the Oort cloud is about 5 yr⁻¹, which might be a non-negligible fraction of comet losses from the Oort cloud (probably around or even above 10%). Therefore, we conclude that the Oort cloud may have experienced and may be even experiencing a significant renovation of its population, and that the trans-neptunian belt—via the scattered disk—may be the main feeding source.     

A former asteroidal planet as the origin of comets

The idea of a missing planet between Mars and Jupiter has been with us since the formulation of the Titius-Bode law. The discovery of the asteroid belt in that location led to speculation about a planetary breakup event. Both ideas remained conjectures until Ovenden's finding in 1972, from which it could be derived that the mass of the missing planet was about 90 Earth masses and that its breakup was astronomically recent. Apparently much of that mass was blown out of the solar system during the disruption of the planet. Because of the action of planetary perturbations, only two types of orbits of surviving fragments could remain at present-asteroid orbits and once-around very-long-period elliptical orbits. Objects in the latter type of orbit are known to exist-the very-long-period comets. A large number of these are on elliptical trajectories with periods of revolution of 5 million years; yet they are known to have made no more than one revolution in an orbit passing close to the Sun. By direct calculation it is possible to predict the distribution of the orbital elements of objects moving on long-period ellipses which might have originated in a breakup event in the asteroid belt 5 million years ago. The comet orbits have the predicted distribution in every case where a measure is possible. Some of the distribution anomalies, such as a bias in the directions of perihelion passage, are statistically strong and would be difficult to explain in any other uncontrived way. In addition, a relative deficiency of orbits with perihelia less than 1 AU indicates that the comets must have had small perihelion distances since their origin, rather than that they have been perturbed into small perihelion orbits from a distant “cloud” of comets by means of stellar encounters. The comet orbital data lead to the conclusion that all comets originated in a breakup event in the asteroid belt (5.5±0.6) × 10⁶ years ago. Asteroid and meteoritic evidence can now be interpreted in a way which not only is supportive but also provides fresh insights into understanding their physical, chemical, and dynamical properties. Particularily noteworthy are the young cosmic-ray exposure ages of meteorites, evidence of a previous high-temperature/pressure environment and of chemical differentiation of the parent body, and compositional similarities among comets, asteroids, and meteorites. Certain “explosion signatures” in asteroid orbital element distributions are likewise indicative. Tektites may also have originated in the same event; but if so, there are important implications regarding the absolute accuracy of certain geological dating methods. Little is known about possible planetary breakup mechanisms of the requisite type, though some speculations are offered. In any case, the asteroid belt is an existing fact; and the arguments presented here that a large planet did disintegrate 5 million years ago must be judged on their merits, even in the absence of a suitable theory of planetary explosions.     

The evidence of an early stellar encounter in Edgeworth-Kuiper belt

We investigate the influence of a stellar fly-by encounter on the Edgeworth-Kuiper belt objects through numerical orbital calculations, in order to explain both mass depletion and high orbital inclinations of the classical Edgeworth-Kuiper belt (CEKB) objects, which have semimajor axis of 42-48 AU and perihelia beyond 35 AU. The observationally inferred total mass of the CEKB is ∼1/10 Earth masses, which is only ∼0.02 of that extrapolated from the minimum-mass solar nebula model. The CEKB consists of bimodal population: “hot population” with inclinations i?0.2-0.6 radians and “cold population” with i?0.1. The observationally suggested difference in size and color of objects between the two populations may imply different origins of the two populations. We find that both the depletion of solid materials in the CEKB and the formation of the hot population are accounted for by a single close stellar encounter with pericenter distance of 80-100 AU and inclination relative to the initial protoplanetary disk ?50°-70°. Such a stellar encounter highly pumps up eccentricities of most objects in the CEKB and then their perihelia migrate within 35 AU. These objects would be removed by Neptune's perturbations after Neptune is formed at or migrates to the current position (30 AU). Less than 10% of the original objects remain in stable orbits with small eccentricities and perihelion distances larger than 35 AU, in the CEKB, which is consistent with the observation. We find that i of the remaining objects are as large as that of the observed hot population. The only problem is how to stop Neptune's migration at ∼30 AU, which is addressed in a separate paper. The depletion by the stellar encounter extends deeply into ∼30-35 AU, which provides the basis of the formation model for the cold population through Neptune's outward migration by Levison and Morbidelli (2003, Nature, 426, 419-421). The combination of our model with Levison and Morbidelli's model could consistently explain the mass depletion, truncation at 50 AU, bimodal distribution in i, and differences in size and color between the hot and the cold populations in the CEKB.     

On the actual existence of the periodic and long-period comet families of Uranus

Aphelion distances of the known periodic comets in the range 12–26 AU are analyzed. The aphelia of 12 of the 38 known comets are found to be concentrated at 19.23–20.91 AU, i.e., near the heliocentric distance of Uranus, which seems unlikely to be a coincidence. It is shown by testing that there is also a significant redundancy of distant nodes of the periodic comets’ orbits in the region of motion of Uranus. This is confirmed by the analysis of the MOIDs in the comet-Uranus system. The values of the Tisserand constant for some of the comets exhibit less dispersion relative to Uranus than to Saturn, Jupiter, and the Earth. We selected 20 long-period comets with distant nodes near the region of motion of Uranus. It is shown that, given a uniform spatial distribution, there must be 12 such nodes. Considering the distant nodes and the MOIDs, the planet is likely to have a dynamical connection with the selected group of comets. The distant nodes and perihelia of both periodic and long-period comets are found to be redundant in the directions 76° and 256°, which is qualitatively consistent with the hypothesis of eruptive origin of comets.     

The thermal and radiation exposure history of lunar meteorites

Abstract— We have measured the natural and induced thermoluminescence (TL) of seven lunar meteorites in order to examine their crystallization, irradiation, and recent thermal histories. Lunar meteorites have induced TL properties similar to Apollo samples of the same provenance (highland or mare), indicating similar crystallization and metamorphic histories. MacAlpine Hills 88104/5 has experienced the greatest degree of impact/regolith processing among the highland-dominated meteorites. The basaltic breccia QUE 94281 is dominated by mare component but may also contain a significant highland component. For the mare-dominated meteorites, EET 87521 may have a significant highland impact-melt component, while Asuka 881757 and Y-793169 have been heavily shocked. The thermal history of Y-793169 included slow cooling, either during impact processing or during its initial crystallization. Our natural TL data indicate that most lunar meteorites have apparently been irradiated in space a few thousand years, with most <15,000 a. Elephant Moraine 87521 has the lowest irradiation exposure time, being <1,000 a. Either the natural TL of ALHA81005, Asuka 881757 and Y-82192 was only partially reset by lunar ejection or these meteorites were in small perihelia orbits (≤0.7 AU).